Metaphysics.........................................................................................................................................................1

Aristotle...................................................................................................................................................1

ALL men by nature desire to know. An indication of this is the delight we take in our senses; for even apart

from their usefulness they are loved for themselves; and above all others the sense of sight. For not only with

a view to action, but even when we are not going to do anything, we prefer seeing (one might say) to

everything else. The reason is that this, most of all the senses, makes us know and brings to light many

By nature animals are born with the faculty of sensation, and from sensation memory is produced in some of

them, though not in others. And therefore the former are more intelligent and apt at learning than those which

cannot remember; those which are incapable of hearing sounds are intelligent though they cannot be taught,

e.g. the bee, and any other race of animals that may be like it; and those which besides memory have this

The animals other than man live by appearances and memories, and have but little of connected experience;

but the human race lives also by art and reasonings. Now from memory experience is produced in men; for

the several memories of the same thing produce finally the capacity for a single experience. And experience

seems pretty much like science and art, but really science and art come to men through experience; for

'experience made art', as Polus says, 'but inexperience luck.' Now art arises when from many notions gained

by experience one universal judgement about a class of objects is produced. For to have a judgement that

when Callias was ill of this disease this did him good, and similarly in the case of Socrates and in many

individual cases, is a matter of experience; but to judge that it has done good to all persons of a certain

constitution, marked off in one class, when they were ill of this disease, e.g. to phlegmatic or bilious people

With a view to action experience seems in no respect inferior to art, and men of experience succeed even

better than those who have theory without experience. (The reason is that experience is knowledge of

individuals, art of universals, and actions and productions are all concerned with the individual; for the

physician does not cure man, except in an incidental way, but Callias or Socrates or some other called by

some such individual name, who happens to be a man. If, then, a man has the theory without the experience,

and recognizes the universal but does not know the individual included in this, he will often fail to cure; for it

is the individual that is to be cured.) But yet we think that knowledge and understanding belong to art rather

than to experience, and we suppose artists to be wiser than men of experience (which implies that Wisdom

depends in all cases rather on knowledge); and this because the former know the cause, but the latter do not.

For men of experience know that the thing is so, but do not know why, while the others know the 'why' and

the cause. Hence we think also that the masterworkers in each craft are more honourable and know in a truer

sense and are wiser than the manual workers, because they know the causes of the things that are done (we

think the manual workers are like certain lifeless things which act indeed, but act without knowing what they

do, as fire burns,but while the lifeless things perform each of their functions by a natural tendency, the

labourers perform them through habit); thus we view them as being wiser not in virtue of being able to act,

but of having the theory for themselves and knowing the causes. And in general it is a sign of the man who

knows and of the man who does not know, that the former can teach, and therefore we think art more truly

knowledge than experience is; for artists can teach, and men of mere experience cannot.

Again, we do not regard any of the senses as Wisdom; yet surely these give the most authoritative knowledge

of particulars. But they do not tell us the 'why' of anythinge.g. why fire is hot; they only say that it is hot.

At first he who invented any art whatever that went beyond the common perceptions of man was naturally

admired by men, not only because there was something useful in the inventions, but because he was thought

wise and superior to the rest. But as more arts were invented, and some were directed to the necessities of

life, others to recreation, the inventors of the latter were naturally always regarded as wiser than the inventors

of the former, because their branches of knowledge did not aim at utility. Hence when all such inventions

were already established, the sciences which do not aim at giving pleasure or at the necessities of life were

discovered, and first in the places where men first began to have leisure. This is why the mathematical arts

were founded in Egypt; for there the priestly caste was allowed to be at leisure.

We have said in the Ethics what the difference is between art and science and the other kindred faculties; but

the point of our present discussion is this, that all men suppose what is called Wisdom to deal with the first

causes and the principles of things; so that, as has been said before, the man of experience is thought to be

wiser than the possessors of any senseperception whatever, the artist wiser than the men of experience, the

masterworker than the mechanic, and the theoretical kinds of knowledge to be more of the nature of Wisdom

than the productive. Clearly then Wisdom is knowledge about certain principles and causes.

Since we are seeking this knowledge, we must inquire of what kind are the causes and the principles, the

knowledge of which is Wisdom. If one were to take the notions we have about the wise man, this might

perhaps make the answer more evident. We suppose first, then, that the wise man knows all things, as far as

possible, although he has not knowledge of each of them in detail; secondly, that he who can learn things that

are difficult, and not easy for man to know, is wise (senseperception is common to all, and therefore easy

and no mark of Wisdom); again, that he who is more exact and more capable of teaching the causes is wiser,

in every branch of knowledge; and that of the sciences, also, that which is desirable on its own account and

for the sake of knowing it is more of the nature of Wisdom than that which is desirable on account of its

results, and the superior science is more of the nature of Wisdom than the ancillary; for the wise man must

not be ordered but must order, and he must not obey another, but the less wise must obey him.

Such and so many are the notions, then, which we have about Wisdom and the wise. Now of these

characteristics that of knowing all things must belong to him who has in the highest degree universal

knowledge; for he knows in a sense all the instances that fall under the universal. And these things, the most

universal, are on the whole the hardest for men to know; for they are farthest from the senses. And the most

exact of the sciences are those which deal most with first principles; for those which involve fewer principles

are more exact than those which involve additional principles, e.g. arithmetic than geometry. But the science

which investigates causes is also instructive, in a higher degree, for the people who instruct us are those who

tell the causes of each thing. And understanding and knowledge pursued for their own sake are found most in

the knowledge of that which is most knowable (for he who chooses to know for the sake of knowing will

choose most readily that which is most truly knowledge, and such is the knowledge of that which is most

knowable); and the first principles and the causes are most knowable; for by reason of these, and from these,

all other things come to be known, and not these by means of the things subordinate to them. And the science

which knows to what end each thing must be done is the most authoritative of the sciences, and more

authoritative than any ancillary science; and this end is the good of that thing, and in general the supreme

good in the whole of nature. Judged by all the tests we have mentioned, then, the name in question falls to the

same science; this must be a science that investigates the first principles and causes; for the good, i.e. the end,

That it is not a science of production is clear even from the history of the earliest philosophers. For it is owing

to their wonder that men both now begin and at first began to philosophize; they wondered originally at the

obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g. about

the phenomena of the moon and those of the sun and of the stars, and about the genesis of the universe. And a

man who is puzzled and wonders thinks himself ignorant (whence even the lover of myth is in a sense a lover

of Wisdom, for the myth is composed of wonders); therefore since they philosophized order to escape from

ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end. And this is

confirmed by the facts; for it was when almost all the necessities of life and the things that make for comfort

and recreation had been secured, that such knowledge began to be sought. Evidently then we do not seek it

for the sake of any other advantage; but as the man is free, we say, who exists for his own sake and not for

another's, so we pursue this as the only free science, for it alone exists for its own sake.

Hence also the possession of it might be justly regarded as beyond human power; for in many ways human

nature is in bondage, so that according to Simonides 'God alone can have this privilege', and it is unfitting

that man should not be content to seek the knowledge that is suited to him. If, then, there is something in

what the poets say, and jealousy is natural to the divine power, it would probably occur in this case above all,

and all who excelled in this knowledge would be unfortunate. But the divine power cannot be jealous (nay,

according to the proverb, 'bards tell a lie'), nor should any other science be thought more honourable than one

of this sort. For the most divine science is also most honourable; and this science alone must be, in two ways,

most divine. For the science which it would be most meet for God to have is a divine science, and so is any

science that deals with divine objects; and this science alone has both these qualities; for (1) God is thought

to be among the causes of all things and to be a first principle, and (2) such a science either God alone can

have, or God above all others. All the sciences, indeed, are more necessary than this, but none is better.

Yet the acquisition of it must in a sense end in something which is the opposite of our original inquiries. For

all men begin, as we said, by wondering that things are as they are, as they do about selfmoving

marionettes, or about the solstices or the incommensurability of the diagonal of a square with the side; for it

seems wonderful to all who have not yet seen the reason, that there is a thing which cannot be measured even

by the smallest unit. But we must end in the contrary and, according to the proverb, the better state, as is the

case in these instances too when men learn the cause; for there is nothing which would surprise a geometer so

We have stated, then, what is the nature of the science we are searching for, and what is the mark which our

Evidently we have to acquire knowledge of the original causes (for we say we know each thing only when we

think we recognize its first cause), and causes are spoken of in four senses. In one of these we mean the

substance, i.e. the essence (for the 'why' is reducible finally to the definition, and the ultimate 'why' is a cause

and principle); in another the matter or substratum, in a third the source of the change, and in a fourth the

cause opposed to this, the purpose and the good (for this is the end of all generation and change). We have

studied these causes sufficiently in our work on nature, but yet let us call to our aid those who have attacked

the investigation of being and philosophized about reality before us. For obviously they too speak of certain

principles and causes; to go over their views, then, will be of profit to the present inquiry, for we shall either

find another kind of cause, or be more convinced of the correctness of those which we now maintain.

Of the first philosophers, then, most thought the principles which were of the nature of matter were the only

principles of all things. That of which all things that are consist, the first from which they come to be, the last

into which they are resolved (the substance remaining, but changing in its modifications), this they say is the

element and this the principle of things, and therefore they think nothing is either generated or destroyed,

since this sort of entity is always conserved, as we say Socrates neither comes to be absolutely when he

comes to be beautiful or musical, nor ceases to be when loses these characteristics, because the substratum,

Socrates himself remains. just so they say nothing else comes to be or ceases to be; for there must be some

entityeither one or more than onefrom which all other things come to be, it being conserved.

Yet they do not all agree as to the number and the nature of these principles. Thales, the founder of this type

of philosophy, says the principle is water (for which reason he declared that the earth rests on water), getting

the notion perhaps from seeing that the nutriment of all things is moist, and that heat itself is generated from

the moist and kept alive by it (and that from which they come to be is a principle of all things). He got his

notion from this fact, and from the fact that the seeds of all things have a moist nature, and that water is the

Some think that even the ancients who lived long before the present generation, and first framed accounts of

the gods, had a similar view of nature; for they made Ocean and Tethys the parents of creation, and described

the oath of the gods as being by water, to which they give the name of Styx; for what is oldest is most

honourable, and the most honourable thing is that by which one swears. It may perhaps be uncertain whether

this opinion about nature is primitive and ancient, but Thales at any rate is said to have declared himself thus

about the first cause. Hippo no one would think fit to include among these thinkers, because of the paltriness

Anaximenes and Diogenes make air prior to water, and the most primary of the simple bodies, while

Hippasus of Metapontium and Heraclitus of Ephesus say this of fire, and Empedocles says it of the four

elements (adding a fourthearthto those which have been named); for these, he says, always remain and do

not come to be, except that they come to be more or fewer, being aggregated into one and segregated out of

Anaxagoras of Clazomenae, who, though older than Empedocles, was later in his philosophical activity, says

the principles are infinite in number; for he says almost all the things that are made of parts like themselves,

in the manner of water or fire, are generated and destroyed in this way, only by aggregation and segregation,

From these facts one might think that the only cause is the socalled material cause; but as men thus

advanced, the very facts opened the way for them and joined in forcing them to investigate the subject.

However true it may be that all generation and destruction proceed from some one or (for that matter) from

more elements, why does this happen and what is the cause? For at least the substratum itself does not make

itself change; e.g. neither the wood nor the bronze causes the change of either of them, nor does the wood

manufacture a bed and the bronze a statue, but something else is the cause of the change. And to seek this is

to seek the second cause, as we should say,that from which comes the beginning of the movement. Now

those who at the very beginning set themselves to this kind of inquiry, and said the substratum was one, were

not at all dissatisfied with themselves; but some at least of those who maintain it to be oneas though

defeated by this search for the second causesay the one and nature as a whole is unchangeable not only in

respect of generation and destruction (for this is a primitive belief, and all agreed in it), but also of all other

change; and this view is peculiar to them. Of those who said the universe was one, then none succeeded in

discovering a cause of this sort, except perhaps Parmenides, and he only inasmuch as he supposes that there

is not only one but also in some sense two causes. But for those who make more elements it is more possible

to state the second cause, e.g. for those who make hot and cold, or fire and earth, the elements; for they treat

fire as having a nature which fits it to move things, and water and earth and such things they treat in the

When these men and the principles of this kind had had their day, as the latter were found inadequate to

generate the nature of things men were again forced by the truth itself, as we said, to inquire into the next

kind of cause. For it is not likely either that fire or earth or any such element should be the reason why things

manifest goodness and, beauty both in their being and in their coming to be, or that those thinkers should

have supposed it was; nor again could it be right to entrust so great a matter to spontaneity and chance. When

one man said, then, that reason was presentas in animals, so throughout natureas the cause of order and of

all arrangement, he seemed like a sober man in contrast with the random talk of his predecessors. We know

that Anaxagoras certainly adopted these views, but Hermotimus of Clazomenae is credited with expressing

them earlier. Those who thought thus stated that there is a principle of things which is at the same time the

One might suspect that Hesiod was the first to look for such a thingor some one else who put love or desire

among existing things as a principle, as Parmenides, too, does; for he, in constructing the genesis of the

which implies that among existing things there must be from the first a cause which will move things and

bring them together. How these thinkers should be arranged with regard to priority of discovery let us be

allowed to decide later; but since the contraries of the various forms of good were also perceived to be

present in naturenot only order and the beautiful, but also disorder and the ugly, and bad things in greater

number than good, and ignoble things than beautifultherefore another thinker introduced friendship and

strife, each of the two the cause of one of these two sets of qualities. For if we were to follow out the view of

Empedocles, and interpret it according to its meaning and not to its lisping expression, we should find that

friendship is the cause of good things, and strife of bad. Therefore, if we said that Empedocles in a sense both

mentions, and is the first to mention, the bad and the good as principles, we should perhaps be right, since the

These thinkers, as we say, evidently grasped, and to this extent, two of the causes which we distinguished in

our work on naturethe matter and the source of the movementvaguely, however, and with no clearness, but

as untrained men behave in fights; for they go round their opponents and often strike fine blows, but they do

not fight on scientific principles, and so too these thinkers do not seem to know what they say; for it is

evident that, as a rule, they make no use of their causes except to a small extent. For Anaxagoras uses reason

as a deus ex machina for the making of the world, and when he is at a loss to tell from what cause something

necessarily is, then he drags reason in, but in all other cases ascribes events to anything rather than to reason.

And Empedocles, though he uses the causes to a greater extent than this, neither does so sufficiently nor

attains consistency in their use. At least, in many cases he makes love segregate things, and strife aggregate

them. For whenever the universe is dissolved into its elements by strife, fire is aggregated into one, and so is

each of the other elements; but whenever again under the influence of love they come together into one, the

Empedocles, then, in contrast with his precessors, was the first to introduce the dividing of this cause, not

positing one source of movement, but different and contrary sources. Again, he was the first to speak of four

material elements; yet he does not use four, but treats them as two only; he treats fire by itself, and its

oppositeearth, air, and wateras one kind of thing. We may learn this by study of his verses.

This philosopher then, as we say, has spoken of the principles in this way, and made them of this number.

Leucippus and his associate Democritus say that the full and the empty are the elements, calling the one being

and the other nonbeingthe full and solid being being, the empty nonbeing (whence they say being no

more is than nonbeing, because the solid no more is than the empty); and they make these the material

causes of things. And as those who make the underlying substance one generate all other things by its

modifications, supposing the rare and the dense to be the sources of the modifications, in the same way these

philosophers say the differences in the elements are the causes of all other qualities. These differences, they

say, are threeshape and order and position. For they say the real is differentiated only by 'rhythm and

'intercontact' and 'turning'; and of these rhythm is shape, intercontact is order, and turning is position; for A

differs from N in shape, AN from NA in order, M from W in position. The question of movementwhence or

Regarding the two causes, then, as we say, the inquiry seems to have been pushed thus far by the early

Contemporaneously with these philosophers and before them, the socalled Pythagoreans, who were the first

to take up mathematics, not only advanced this study, but also having been brought up in it they thought its

principles were the principles of all things. Since of these principles numbers are by nature the first, and in

numbers they seemed to see many resemblances to the things that exist and come into beingmore than in

fire and earth and water (such and such a modification of numbers being justice, another being soul and

reason, another being opportunityand similarly almost all other things being numerically expressible); since,

again, they saw that the modifications and the ratios of the musical scales were expressible in

numbers;since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers

seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements

of all things, and the whole heaven to be a musical scale and a number. And all the properties of numbers and

scales which they could show to agree with the attributes and parts and the whole arrangement of the

heavens, they collected and fitted into their scheme; and if there was a gap anywhere, they readily made

additions so as to make their whole theory coherent. E.g. as the number 10 is thought to be perfect and to

comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but

as the visible bodies are only nine, to meet this they invent a tenththe 'counterearth'. We have discussed

But the object of our review is that we may learn from these philosophers also what they suppose to be the

principles and how these fall under the causes we have named. Evidently, then, these thinkers also consider

that number is the principle both as matter for things and as forming both their modifications and their

permanent states, and hold that the elements of number are the even and the odd, and that of these the latter is

limited, and the former unlimited; and that the One proceeds from both of these (for it is both even and odd),

and number from the One; and that the whole heaven, as has been said, is numbers.

Other members of this same school say there are ten principles, which they arrange in two columns of

cognateslimit and unlimited, odd and even, one and plurality, right and left, male and female, resting and

moving, straight and curved, light and darkness, good and bad, square and oblong. In this way Alcmaeon of

Croton seems also to have conceived the matter, and either he got this view from them or they got it from

him; for he expressed himself similarly to them. For he says most human affairs go in pairs, meaning not

definite contrarieties such as the Pythagoreans speak of, but any chance contrarieties, e.g. white and black,

sweet and bitter, good and bad, great and small. He threw out indefinite suggestions about the other

contrarieties, but the Pythagoreans declared both how many and which their contraricties are.

From both these schools, then, we can learn this much, that the contraries are the principles of things; and

how many these principles are and which they are, we can learn from one of the two schools. But how these

principles can be brought together under the causes we have named has not been clearly and articulately

stated by them; they seem, however, to range the elements under the head of matter; for out of these as

From these facts we may sufficiently perceive the meaning of the ancients who said the elements of nature

were more than one; but there are some who spoke of the universe as if it were one entity, though they were

not all alike either in the excellence of their statement or in its conformity to the facts of nature. The

discussion of them is in no way appropriate to our present investigation of causes, for. they do not, like some

of the natural philosophers, assume being to be one and yet generate it out of the one as out of matter, but

they speak in another way; those others add change, since they generate the universe, but these thinkers say

the universe is unchangeable. Yet this much is germane to the present inquiry: Parmenides seems to fasten on

that which is one in definition, Melissus on that which is one in matter, for which reason the former says that

it is limited, the latter that it is unlimited; while Xenophanes, the first of these partisans of the One (for

Parmenides is said to have been his pupil), gave no clear statement, nor does he seem to have grasped the

nature of either of these causes, but with reference to the whole material universe he says the One is God.

Now these thinkers, as we said, must be neglected for the purposes of the present inquirytwo of them

entirely, as being a little too naive, viz. Xenophanes and Melissus; but Parmenides seems in places to speak

with more insight. For, claiming that, besides the existent, nothing nonexistent exists, he thinks that of

necessity one thing exists, viz. the existent and nothing else (on this we have spoken more clearly in our work

on nature), but being forced to follow the observed facts, and supposing the existence of that which is one in

definition, but more than one according to our sensations, he now posits two causes and two principles,

calling them hot and cold, i.e. fire and earth; and of these he ranges the hot with the existent, and the other

From what has been said, then, and from the wise men who have now sat in council with us, we have got thus

muchon the one hand from the earliest philosophers, who regard the first principle as corporeal (for water

and fire and such things are bodies), and of whom some suppose that there is one corporeal principle, others

that there are more than one, but both put these under the head of matter; and on the other hand from some

who posit both this cause and besides this the source of movement, which we have got from some as single

Down to the Italian school, then, and apart from it, philosophers have treated these subjects rather obscurely,

except that, as we said, they have in fact used two kinds of cause, and one of thesethe source of

movementsome treat as one and others as two. But the Pythagoreans have said in the same way that there

are two principles, but added this much, which is peculiar to them, that they thought that finitude and infinity

were not attributes of certain other things, e.g. of fire or earth or anything else of this kind, but that infinity

itself and unity itself were the substance of the things of which they are predicated. This is why number was

the substance of all things. On this subject, then, they expressed themselves thus; and regarding the question

of essence they began to make statements and definitions, but treated the matter too simply. For they both

defined superficially and thought that the first subject of which a given definition was predicable was the

substance of the thing defined, as if one supposed that 'double' and '2' were the same, because 2 is the first

thing of which 'double' is predicable. But surely to be double and to be 2 are not the same; if they are, one

thing will be manya consequence which they actually drew. From the earlier philosophers, then, and from

After the systems we have named came the philosophy of Plato, which in most respects followed these

thinkers, but had pecullarities that distinguished it from the philosophy of the Italians. For, having in his

youth first become familiar with Cratylus and with the Heraclitean doctrines (that all sensible things are ever

in a state of flux and there is no knowledge about them), these views he held even in later years. Socrates,

however, was busying himself about ethical matters and neglecting the world of nature as a whole but

seeking the universal in these ethical matters, and fixed thought for the first time on definitions; Plato

accepted his teaching, but held that the problem applied not to sensible things but to entities of another

kindfor this reason, that the common definition could not be a definition of any sensible thing, as they were

always changing. Things of this other sort, then, he called Ideas, and sensible things, he said, were all named

after these, and in virtue of a relation to these; for the many existed by participation in the Ideas that have the

same name as they. Only the name 'participation' was new; for the Pythagoreans say that things exist by

'imitation' of numbers, and Plato says they exist by participation, changing the name. But what the

participation or the imitation of the Forms could be they left an open question.

Further, besides sensible things and Forms he says there are the objects of mathematics, which occupy an

intermediate position, differing from sensible things in being eternal and unchangeable, from Forms in that

Since the Forms were the causes of all other things, he thought their elements were the elements of all things.

As matter, the great and the small were principles; as essential reality, the One; for from the great and the

But he agreed with the Pythagoreans in saying that the One is substance and not a predicate of something

else; and in saying that the Numbers are the causes of the reality of other things he agreed with them; but

positing a dyad and constructing the infinite out of great and small, instead of treating the infinite as one, is

peculiar to him; and so is his view that the Numbers exist apart from sensible things, while they say that the

things themselves are Numbers, and do not place the objects of mathematics between Forms and sensible

things. His divergence from the Pythagoreans in making the One and the Numbers separate from things, and

his introduction of the Forms, were due to his inquiries in the region of definitions (for the earlier thinkers

had no tincture of dialectic), and his making the other entity besides the One a dyad was due to the belief that

the numbers, except those which were prime, could be neatly produced out of the dyad as out of some plastic

material. Yet what happens is the contrary; the theory is not a reasonable one. For they make many things out

of the matter, and the form generates only once, but what we observe is that one table is made from one

matter, while the man who applies the form, though he is one, makes many tables. And the relation of the

male to the female is similar; for the latter is impregnated by one copulation, but the male impregnates many

Plato, then, declared himself thus on the points in question; it is evident from what has been said that he has

used only two causes, that of the essence and the material cause (for the Forms are the causes of the essence

of all other things, and the One is the cause of the essence of the Forms); and it is evident what the underlying

matter is, of which the Forms are predicated in the case of sensible things, and the One in the case of Forms,

viz. that this is a dyad, the great and the small. Further, he has assigned the cause of good and that of evil to

the elements, one to each of the two, as we say some of his predecessors sought to do, e.g. Empedocles and

Our review of those who have spoken about first principles and reality and of the way in which they have

spoken, has been concise and summary; but yet we have learnt this much from them, that of those who speak

about 'principle' and 'cause' no one has mentioned any principle except those which have been distinguished

in our work on nature, but all evidently have some inkling of them, though only vaguely. For some speak of

the first principle as matter, whether they suppose one or more first principles, and whether they suppose this

to be a body or to be incorporeal; e.g. Plato spoke of the great and the small, the Italians of the infinite,

Empedocles of fire, earth, water, and air, Anaxagoras of the infinity of things composed of similar parts.

These, then, have all had a notion of this kind of cause, and so have all who speak of air or fire or water, or

something denser than fire and rarer than air; for some have said the prime element is of this kind.

These thinkers grasped this cause only; but certain others have mentioned the source of movement, e.g. those

The essence, i.e. the substantial reality, no one has expressed distinctly. It is hinted at chiefly by those who

believe in the Forms; for they do not suppose either that the Forms are the matter of sensible things, and the

One the matter of the Forms, or that they are the source of movement (for they say these are causes rather of

immobility and of being at rest), but they furnish the Forms as the essence of every other thing, and the One

That for whose sake actions and changes and movements take place, they assert to be a cause in a way, but

not in this way, i.e. not in the way in which it is its nature to be a cause. For those who speak of reason or

friendship class these causes as goods; they do not speak, however, as if anything that exists either existed or

came into being for the sake of these, but as if movements started from these. In the same way those who say

the One or the existent is the good, say that it is the cause of substance, but not that substance either is or

comes to be for the sake of this. Therefore it turns out that in a sense they both say and do not say the good is

All these thinkers then, as they cannot pitch on another cause, seem to testify that we have determined rightly

both how many and of what sort the causes are. Besides this it is plain that when the causes are being looked

for, either all four must be sought thus or they must be sought in one of these four ways. Let us next discuss

the possible difficulties with regard to the way in which each of these thinkers has spoken, and with regard to

Those, then, who say the universe is one and posit one kind of thing as matter, and as corporeal matter which

has spatial magnitude, evidently go astray in many ways. For they posit the elements of bodies only, not of

incorporeal things, though there are also incorporeal things. And in trying to state the causes of generation

and destruction, and in giving a physical account of all things, they do away with the cause of movement.

Further, they err in not positing the substance, i.e. the essence, as the cause of anything, and besides this in

lightly calling any of the simple bodies except earth the first principle, without inquiring how they are

produced out of one anothersI mean fire, water, earth, and air. For some things are produced out of each

other by combination, others by separation, and this makes the greatest difference to their priority and

posteriority. For (1) in a way the property of being most elementary of all would seem to belong to the first

thing from which they are produced by combination, and this property would belong to the most finegrained

and subtle of bodies. For this reason those who make fire the principle would be most in agreement with this

argument. But each of the other thinkers agrees that the element of corporeal things is of this sort. At least

none of those who named one element claimed that earth was the element, evidently because of the

coarseness of its grain. (Of the other three elements each has found some judge on its side; for some maintain

that fire, others that water, others that air is the element. Yet why, after all, do they not name earth also, as

most men do? For people say all things are earth Hesiod says earth was produced first of corporeal things; so

primitive and popular has the opinion been.) According to this argument, then, no one would be right who

either says the first principle is any of the elements other than fire, or supposes it to be denser than air but

rarer than water. But (2) if that which is later in generation is prior in nature, and that which is concocted and

compounded is later in generation, the contrary of what we have been saying must be true,water must be

So much, then, for those who posit one cause such as we mentioned; but the same is true if one supposes

more of these, as Empedocles says matter of things is four bodies. For he too is confronted by consequences

some of which are the same as have been mentioned, while others are peculiar to him. For we see these

bodies produced from one another, which implies that the same body does not always remain fire or earth (we

have spoken about this in our works on nature); and regarding the cause of movement and the question

whether we must posit one or two, he must be thought to have spoken neither correctly nor altogether

plausibly. And in general, change of quality is necessarily done away with for those who speak thus, for on

their view cold will not come from hot nor hot from cold. For if it did there would be something that accepted

the contraries themselves, and there would be some one entity that became fire and water, which Empedocles

As regards Anaxagoras, if one were to suppose that he said there were two elements, the supposition would

accord thoroughly with an argument which Anaxagoras himself did not state articulately, but which he must

have accepted if any one had led him on to it. True, to say that in the beginning all things were mixed is

absurd both on other grounds and because it follows that they must have existed before in an unmixed form,

and because nature does not allow any chance thing to be mixed with any chance thing, and also because on

this view modifications and accidents could be separated from substances (for the same things which are

mixed can be separated); yet if one were to follow him up, piecing together what he means, he would perhaps

be seen to be somewhat modern in his views. For when nothing was separated out, evidently nothing could be

truly asserted of the substance that then existed. I mean, e.g. that it was neither white nor black, nor grey nor

any other colour, but of necessity colourless; for if it had been coloured, it would have had one of these

colours. And similarly, by this same argument, it was flavourless, nor had it any similar attribute; for it could

not be either of any quality or of any size, nor could it be any definite kind of thing. For if it were, one of the

particular forms would have belonged to it, and this is impossible, since all were mixed together; for the

particular form would necessarily have been already separated out, but he all were mixed except reason, and

this alone was unmixed and pure. From this it follows, then, that he must say the principles are the One (for

this is simple and unmixed) and the Other, which is of such a nature as we suppose the indefinite to be before

it is defined and partakes of some form. Therefore, while expressing himself neither rightly nor clearly, he

means something like what the later thinkers say and what is now more clearly seen to be the case.

But these thinkers are, after all, at home only in arguments about generation and destruction and movement;

for it is practically only of this sort of substance that they seek the principles and the causes. But those who

extend their vision to all things that exist, and of existing things suppose some to be perceptible and others

not perceptible, evidently study both classes, which is all the more reason why one should devote some time

to seeing what is good in their views and what bad from the standpoint of the inquiry we have now before us.

The 'Pythagoreans' treat of principles and elements stranger than those of the physical philosophers (the

reason is that they got the principles from nonsensible things, for the objects of mathematics, except those

of astronomy, are of the class of things without movement); yet their discussions and investigations are all

about nature; for they generate the heavens, and with regard to their parts and attributes and functions they

observe the phenomena, and use up the principles and the causes in explaining these, which implies that they

agree with the others, the physical philosophers, that the real is just all that which is perceptible and contained

by the socalled 'heavens'. But the causes and the principles which they mention are, as we said, sufficient to

act as steps even up to the higher realms of reality, and are more suited to these than to theories about nature.

They do not tell us at all, however, how there can be movement if limit and unlimited and odd and even are

the only things assumed, or how without movement and change there can be generation and destruction, or

Further, if one either granted them that spatial magnitude consists of these elements, or this were proved, still

how would some bodies be light and others have weight? To judge from what they assume and maintain they

are speaking no more of mathematical bodies than of perceptible; hence they have said nothing whatever

about fire or earth or the other bodies of this sort, I suppose because they have nothing to say which applies

Further, how are we to combine the beliefs that the attributes of number, and number itself, are causes of

what exists and happens in the heavens both from the beginning and now, and that there is no other number

than this number out of which the world is composed? When in one particular region they place opinion and

opportunity, and, a little above or below, injustice and decision or mixture, and allege, as proof, that each of

these is a number, and that there happens to be already in this place a plurality of the extended bodies

composed of numbers, because these attributes of number attach to the various places,this being so, is this

number, which we must suppose each of these abstractions to be, the same number which is exhibited in the

material universe, or is it another than this? Plato says it is different; yet even he thinks that both these bodies

and their causes are numbers, but that the intelligible numbers are causes, while the others are sensible.

Let us leave the Pythagoreans for the present; for it is enough to have touched on them as much as we have

done. But as for those who posit the Ideas as causes, firstly, in seeking to grasp the causes of the things

around us, they introduced others equal in number to these, as if a man who wanted to count things thought

he would not be able to do it while they were few, but tried to count them when he had added to their number.

For the Forms are practically equal toor not fewer thanthe things, in trying to explain which these thinkers

proceeded from them to the Forms. For to each thing there answers an entity which has the same name and

exists apart from the substances, and so also in the case of all other groups there is a one over many, whether

Further, of the ways in which we prove that the Forms exist, none is convincing; for from some no inference

necessarily follows, and from some arise Forms even of things of which we think there are no Forms. For

according to the arguments from the existence of the sciences there will be Forms of all things of which there

are sciences and according to the 'one over many' argument there will be Forms even of negations, and

according to the argument that there is an object for thought even when the thing has perished, there will be

Forms of perishable things; for we have an image of these. Further, of the more accurate arguments, some

lead to Ideas of relations, of which we say there is no independent class, and others introduce the 'third man'.

And in general the arguments for the Forms destroy the things for whose existence we are more zealous than

for the existence of the Ideas; for it follows that not the dyad but number is first, i.e. that the relative is prior

to the absolute,besides all the other points on which certain people by following out the opinions held about

Further, according to the assumption on which our belief in the Ideas rests, there will be Forms not only of

substances but also of many other things (for the concept is single not only in the case of substances but also

in the other cases, and there are sciences not only of substance but also of other things, and a thousand other

such difficulties confront them). But according to the necessities of the case and the opinions held about the

Forms, if Forms can be shared in there must be Ideas of substances only. For they are not shared in

incidentally, but a thing must share in its Form as in something not predicated of a subject (by 'being shared

in incidentally' I mean that e.g. if a thing shares in 'double itself', it shares also in 'eternal', but incidentally;

for 'eternal' happens to be predicable of the 'double'). Therefore the Forms will be substance; but the same

terms indicate substance in this and in the ideal world (or what will be the meaning of saying that there is

something apart from the particularsthe one over many?). And if the Ideas and the particulars that share in

them have the same form, there will be something common to these; for why should '2' be one and the same

in the perishable 2's or in those which are many but eternal, and not the same in the '2' itself' as in the

particular 2? But if they have not the same form, they must have only the name in common, and it is as if one

were to call both Callias and a wooden image a 'man', without observing any community between them.

Above all one might discuss the question what on earth the Forms contribute to sensible things, either to

those that are eternal or to those that come into being and cease to be. For they cause neither movement nor

any change in them. But again they help in no wise either towards the knowledge of the other things (for they

are not even the substance of these, else they would have been in them), or towards their being, if they are not

in the particulars which share in them; though if they were, they might be thought to be causes, as white

causes whiteness in a white object by entering into its composition. But this argument, which first

Anaxagoras and later Eudoxus and certain others used, is very easily upset; for it is not difficult to collect

But, further, all other things cannot come from the Forms in any of the usual senses of 'from'. And to say that

they are patterns and the other things share in them is to use empty words and poetical metaphors. For what is

it that works, looking to the Ideas? And anything can either be, or become, like another without being copied

from it, so that whether Socrates or not a man Socrates like might come to be; and evidently this might be so

even if Socrates were eternal. And there will be several patterns of the same thing, and therefore several

Forms; e.g. 'animal' and 'twofooted' and also 'man himself' will be Forms of man. Again, the Forms are

patterns not only sensible things, but of Forms themselves also; i.e. the genus, as genus of various species,

Again, it would seem impossible that the substance and that of which it is the substance should exist apart;

how, therefore, could the Ideas, being the substances of things, exist apart? In the Phaedo' the case is stated in

this waythat the Forms are causes both of being and of becoming; yet when the Forms exist, still the things

that share in them do not come into being, unless there is something to originate movement; and many other

things come into being (e.g. a house or a ring) of which we say there are no Forms. Clearly, therefore, even

the other things can both be and come into being owing to such causes as produce the things just mentioned.

Again, if the Forms are numbers, how can they be causes? Is it because existing things are other numbers,

e.g. one number is man, another is Socrates, another Callias? Why then are the one set of numbers causes of

the other set? It will not make any difference even if the former are eternal and the latter are not. But if it is

because things in this sensible world (e.g. harmony) are ratios of numbers, evidently the things between

which they are ratios are some one class of things. If, then, thisthe matteris some definite thing,

evidently the numbers themselves too will be ratios of something to something else. E.g. if Callias is a

numerical ratio between fire and earth and water and air, his Idea also will be a number of certain other

underlying things; and man himself, whether it is a number in a sense or not, will still be a numerical ratio of

certain things and not a number proper, nor will it be a of number merely because it is a numerical ratio.

Again, from many numbers one number is produced, but how can one Form come from many Forms? And if

the number comes not from the many numbers themselves but from the units in them, e.g. in 10,000, how is it

with the units? If they are specifically alike, numerous absurdities will follow, and also if they are not alike

(neither the units in one number being themselves like one another nor those in other numbers being all like

to all); for in what will they differ, as they are without quality? This is not a plausible view, nor is it

Further, they must set up a second kind of number (with which arithmetic deals), and all the objects which are

called 'intermediate' by some thinkers; and how do these exist or from what principles do they proceed? Or

why must they be intermediate between the things in this sensible world and the thingsthemselves?

Again, besides what has been said, if the units are diverse the Platonists should have spoken like those who

say there are four, or two, elements; for each of these thinkers gives the name of element not to that which is

common, e.g. to body, but to fire and earth, whether there is something common to them, viz. body, or not.

But in fact the Platonists speak as if the One were homogeneous like fire or water; and if this is so, the

numbers will not be substances. Evidently, if there is a One itself and this is a first principle, 'one' is being

When we wish to reduce substances to their principles, we state that lines come from the short and long (i.e.

from a kind of small and great), and the plane from the broad and narrow, and body from the deep and

shallow. Yet how then can either the plane contain a line, or the solid a line or a plane? For the broad and

narrow is a different class from the deep and shallow. Therefore, just as number is not present in these,

because the many and few are different from these, evidently no other of the higher classes will be present in

the lower. But again the broad is not a genus which includes the deep, for then the solid would have been a

species of plane. Further, from what principle will the presence of the points in the line be derived? Plato

even used to object to this class of things as being a geometrical fiction. He gave the name of principle of the

lineand this he often positedto the indivisible lines. Yet these must have a limit; therefore the argument

from which the existence of the line follows proves also the existence of the point.

In general, though philosophy seeks the cause of perceptible things, we have given this up (for we say

nothing of the cause from which change takes its start), but while we fancy we are stating the substance of

perceptible things, we assert the existence of a second class of substances, while our account of the way in

which they are the substances of perceptible things is empty talk; for 'sharing', as we said before, means

Nor have the Forms any connexion with what we see to be the cause in the case of the arts, that for whose

sake both all mind and the whole of nature are operative,with this cause which we assert to be one of the

first principles; but mathematics has come to be identical with philosophy for modern thinkers, though they

say that it should be studied for the sake of other things. Further, one might suppose that the substance which

according to them underlies as matter is too mathematical, and is a predicate and differentia of the substance,

ie. of the matter, rather than matter itself; i.e. the great and the small are like the rare and the dense which the

physical philosophers speak of, calling these the primary differentiae of the substratum; for these are a kind

of excess and defect. And regarding movement, if the great and the small are to he movement, evidently the

Forms will be moved; but if they are not to be movement, whence did movement come? The whole study of

And what is thought to be easyto show that all things are oneis not done; for what is proved by the method

of setting out instances is not that all things are one but that there is a One itself,if we grant all the

assumptions. And not even this follows, if we do not grant that the universal is a genus; and this in some

Nor can it be explained either how the lines and planes and solids that come after the numbers exist or can

exist, or what significance they have; for these can neither be Forms (for they are not numbers), nor the

intermediates (for those are the objects of mathematics), nor the perishable things. This is evidently a distinct

In general, if we search for the elements of existing things without distinguishing the many senses in which

things are said to exist, we cannot find them, especially if the search for the elements of which things are

made is conducted in this manner. For it is surely impossible to discover what 'acting' or 'being acted on', or

'the straight', is made of, but if elements can be discovered at all, it is only the elements of substances;

therefore either to seek the elements of all existing things or to think one has them is incorrect.

And how could we learn the elements of all things? Evidently we cannot start by knowing anything before.

For as he who is learning geometry, though he may know other things before, knows none of the things with

which the science deals and about which he is to learn, so is it in all other cases. Therefore if there is a

science of all things, such as some assert to exist, he who is learning this will know nothing before. Yet all

learning is by means of premisses which are (either all or some of them) known before,whether the learning

be by demonstration or by definitions; for the elements of the definition must be known before and be

familiar; and learning by induction proceeds similarly. But again, if the science were actually innate, it were

Again, how is one to come to know what all things are made of, and how is this to be made evident? This

also affords a difficulty; for there might be a conflict of opinion, as there is about certain syllables; some say

za is made out of s and d and a, while others say it is a distinct sound and none of those that are familiar.

Further, how could we know the objects of sense without having the sense in question? Yet we ought to, if

the elements of which all things consist, as complex sounds consist of the clements proper to sound, are the

It is evident, then, even from what we have said before, that all men seem to seek the causes named in the

Physics, and that we cannot name any beyond these; but they seek these vaguely; and though in a sense they

have all been described before, in a sense they have not been described at all. For the earliest philosophy is,

on all subjects, like one who lisps, since it is young and in its beginnings. For even Empedocles says bone

exists by virtue of the ratio in it. Now this is the essence and the substance of the thing. But it is similarly

necessary that flesh and each of the other tissues should be the ratio of its elements, or that not one of them

should; for it is on account of this that both flesh and bone and everything else will exist, and not on account

of the matter, which he names,fire and earth and water and air. But while he would necessarily have agreed

On these questions our views have been expressed before; but let us return to enumerate the difficulties that

might be raised on these same points; for perhaps we may get from them some help towards our later

THE investigation of the truth is in one way hard, in another easy. An indication of this is found in the fact

that no one is able to attain the truth adequately, while, on the other hand, we do not collectively fail, but

every one says something true about the nature of things, and while individually we contribute little or

nothing to the truth, by the union of all a considerable amount is amassed. Therefore, since the truth seems to

be like the proverbial door, which no one can fail to hit, in this respect it must be easy, but the fact that we

can have a whole truth and not the particular part we aim at shows the difficulty of it.

Perhaps, too, as difficulties are of two kinds, the cause of the present difficulty is not in the facts but in us.

For as the eyes of bats are to the blaze of day, so is the reason in our soul to the things which are by nature

It is just that we should be grateful, not only to those with whose views we may agree, but also to those who

have expressed more superficial views; for these also contributed something, by developing before us the

powers of thought. It is true that if there had been no Timotheus we should have been without much of our

lyric poetry; but if there had been no Phrynis there would have been no Timotheus. The same holds good of

those who have expressed views about the truth; for from some thinkers we have inherited certain opinions,

It is right also that philosophy should be called knowledge of the truth. For the end of theoretical knowledge

is truth, while that of practical knowledge is action (for even if they consider how things are, practical men do

not study the eternal, but what is relative and in the present). Now we do not know a truth without its cause;

and a thing has a quality in a higher degree than other things if in virtue of it the similar quality belongs to the

other things as well (e.g. fire is the hottest of things; for it is the cause of the heat of all other things); so that

that causes derivative truths to be true is most true. Hence the principles of eternal things must be always

most true (for they are not merely sometimes true, nor is there any cause of their being, but they themselves

are the cause of the being of other things), so that as each thing is in respect of being, so is it in respect of

But evidently there is a first principle, and the causes of things are neither an infinite series nor infinitely

various in kind. For neither can one thing proceed from another, as from matter, ad infinitum (e.g. flesh from

earth, earth from air, air from fire, and so on without stopping), nor can the sources of movement form an

endless series (man for instance being acted on by air, air by the sun, the sun by Strife, and so on without

limit). Similarly the final causes cannot go on ad infinitum,walking being for the sake of health, this for the

sake of happiness, happiness for the sake of something else, and so one thing always for the sake of another.

And the case of the essence is similar. For in the case of intermediates, which have a last term and a term

prior to them, the prior must be the cause of the later terms. For if we had to say which of the three is the

cause, we should say the first; surely not the last, for the final term is the cause of none; nor even the

intermediate, for it is the cause only of one. (It makes no difference whether there is one intermediate or

more, nor whether they are infinite or finite in number.) But of series which are infinite in this way, and of

the infinite in general, all the parts down to that now present are alike intermediates; so that if there is no first

Nor can there be an infinite process downwards, with a beginning in the upward direction, so that water

should proceed from fire, earth from water, and so always some other kind should be produced. For one thing

comes from another in two waysnot in the sense in which 'from' means 'after' (as we say 'from the Isthmian

games come the Olympian'), but either (i) as the man comes from the boy, by the boy's changing, or (ii) as air

comes from water. By 'as the man comes from the boy' we mean 'as that which has come to be from that

which is coming to be' or 'as that which is finished from that which is being achieved' (for as becoming is

between being and not being, so that which is becoming is always between that which is and that which is

not; for the learner is a man of science in the making, and this is what is meant when we say that from a

learner a man of science is being made); on the other hand, coming from another thing as water comes from

air implies the destruction of the other thing. This is why changes of the former kind are not reversible, and

the boy does not come from the man (for it is not that which comes to be something that comes to be as a

result of coming to be, but that which exists after the coming to be; for it is thus that the day, too, comes from

the morningin the sense that it comes after the morning; which is the reason why the morning cannot come

from the day); but changes of the other kind are reversible. But in both cases it is impossible that the number

of terms should be infinite. For terms of the former kind, being intermediates, must have an end, and terms of

the latter kind change back into one another, for the destruction of either is the generation of the other.

At the same time it is impossible that the first cause, being eternal, should be destroyed; for since the process

of becoming is not infinite in the upward direction, that which is the first thing by whose destruction

Further, the final cause is an end, and that sort of end which is not for the sake of something else, but for

whose sake everything else is; so that if there is to be a last term of this sort, the process will not be infinite;

but if there is no such term, there will be no final cause, but those who maintain the infinite series eliminate

the Good without knowing it (yet no one would try to do anything if he were not going to come to a limit);

nor would there be reason in the world; the reasonable man, at least, always acts for a purpose, and this is a

But the essence, also, cannot be reduced to another definition which is fuller in expression. For the original

definition is always more of a definition, and not the later one; and in a series in which the first term has not

the required character, the next has not it either. Further, those who speak thus destroy science; for it is not

possible to have this till one comes to the unanalysable terms. And knowledge becomes impossible; for how

can one apprehend things that are infinite in this way? For this is not like the case of the line, to whose

divisibility there is no stop, but which we cannot think if we do not make a stop (for which reason one who is

tracing the infinitely divisible line cannot be counting the possibilities of section), but the whole line also

must be apprehended by something in us that does not move from part to part.Again, nothing infinite can

But if the kinds of causes had been infinite in number, then also knowledge would have been impossible; for

we think we know, only when we have ascertained the causes, that but that which is infinite by addition

The effect which lectures produce on a hearer depends on his habits; for we demand the language we are

accustomed to, and that which is different from this seems not in keeping but somewhat unintelligible and

foreign because of its unwontedness. For it is the customary that is intelligible. The force of habit is shown by

the laws, in which the legendary and childish elements prevail over our knowledge about them, owing to

habit. Thus some people do not listen to a speaker unless he speaks mathematically, others unless he gives

instances, while others expect him to cite a poet as witness. And some want to have everything done

accurately, while others are annoyed by accuracy, either because they cannot follow the connexion of thought

or because they regard it as pettifoggery. For accuracy has something of this character, so that as in trade so

in argument some people think it mean. Hence one must be already trained to know how to take each sort of

argument, since it is absurd to seek at the same time knowledge and the way of attaining knowledge; and it is

The minute accuracy of mathematics is not to be demanded in all cases, but only in the case of things which

have no matter. Hence method is not that of natural science; for presumably the whole of nature has matter.

Hence we must inquire first what nature is: for thus we shall also see what natural science treats of (and

whether it belongs to one science or to more to investigate the causes and the principles of things).

WE must, with a view to the science which we are seeking, first recount the subjects that should be first

discussed. These include both the other opinions that some have held on the first principles, and any point

besides these that happens to have been overlooked. For those who wish to get clear of difficulties it is

advantageous to discuss the difficulties well; for the subsequent free play of thought implies the solution of

the previous difficulties, and it is not possible to untie a knot of which one does not know. But the difficulty

of our thinking points to a 'knot' in the object; for in so far as our thought is in difficulties, it is in like case

with those who are bound; for in either case it is impossible to go forward. Hence one should have surveyed

all the difficulties beforehand, both for the purposes we have stated and because people who inquire without

first stating the difficulties are like those who do not know where they have to go; besides, a man does not

otherwise know even whether he has at any given time found what he is looking for or not; for the end is not

clear to such a man, while to him who has first discussed the difficulties it is clear. Further, he who has heard

all the contending arguments, as if they were the parties to a case, must be in a better position for judging.

The first problem concerns the subject which we discussed in our prefatory remarks. It is this(1) whether the

investigation of the causes belongs to one or to more sciences, and (2) whether such a science should survey

only the first principles of substance, or also the principles on which all men base their proofs, e.g. whether it

is possible at the same time to assert and deny one and the same thing or not, and all other such questions;

and (3) if the science in question deals with substance, whether one science deals with all substances, or more

than one, and if more, whether all are akin, or some of them must be called forms of Wisdom and the others

something else. And (4) this itself is also one of the things that must be discussedwhether sensible

substances alone should be said to exist or others also besides them, and whether these others are of one kind

or there are several classes of substances, as is supposed by those who believe both in Forms and in

mathematical objects intermediate between these and sensible things. Into these questions, then, as we say,

we must inquire, and also (5) whether our investigation is concerned only with substances or also with the

essential attributes of substances. Further, with regard to the same and other and like and unlike and

contrariety, and with regard to prior and posterior and all other such terms about which the dialecticians try to

inquire, starting their investigation from probable premises only,whose business is it to inquire into all

these? Further, we must discuss the essential attributes of these themselves; and we must ask not only what

each of these is, but also whether one thing always has one contrary. Again (6), are the principles and

elements of things the genera, or the parts present in each thing, into which it is divided; and (7) if they are

the genera, are they the genera that are predicated proximately of the individuals, or the highest genera, e.g. is

animal or man the first principle and the more independent of the individual instance? And (8) we must

inquire and discuss especially whether there is, besides the matter, any thing that is a cause in itself or not,

and whether this can exist apart or not, and whether it is one or more in number, and whether there is

something apart from the concrete thing (by the concrete thing I mean the matter with something already

predicated of it), or there is nothing apart, or there is something in some cases though not in others, and what

sort of cases these are. Again (9) we ask whether the principles are limited in number or in kind, both those in

the definitions and those in the substratum; and (10) whether the principles of perishable and of imperishable

things are the same or different; and whether they are all imperishable or those of perishable things are

perishable. Further (11) there is the question which is hardest of all and most perplexing, whether unity and

being, as the Pythagoreans and Plato said, are not attributes of something else but the substance of existing

things, or this is not the case, but the substratum is something else,as Empedocles says, love; as some one

else says, fire; while another says water or air. Again (12) we ask whether the principles are universal or like

individual things, and (13) whether they exist potentially or actually, and further, whether they are potential

or actual in any other sense than in reference to movement; for these questions also would present much

difficulty. Further (14), are numbers and lines and figures and points a kind of substance or not, and if they

are substances are they separate from sensible things or present in them? With regard to all these matters not

only is it hard to get possession of the truth, but it is not easy even to think out the difficulties well.

(1) First then with regard to what we mentioned first, does it belong to one or to more sciences to investigate

all the kinds of causes? How could it belong to one science to recognize the principles if these are not

Further, there are many things to which not all the principles pertain. For how can a principle of change or the

nature of the good exist for unchangeable things, since everything that in itself and by its own nature is good

is an end, and a cause in the sense that for its sake the other things both come to be and are, and since an end

or purpose is the end of some action, and all actions imply change? So in the case of unchangeable things this

principle could not exist, nor could there be a good itself. This is why in mathematics nothing is proved by

means of this kind of cause, nor is there any demonstration of this kind'because it is better, or worse'; indeed

no one even mentions anything of the kind. And so for this reason some of the Sophists, e.g. Aristippus, used

to ridicule mathematics; for in the arts (he maintained), even in the industrial arts, e.g. in carpentry and

cobbling, the reason always given is 'because it is better, or worse,' but the mathematical sciences take no

But if there are several sciences of the causes, and a different science for each different principle, which of

these sciences should be said to be that which we seek, or which of the people who possess them has the most

scientific knowledge of the object in question? The same thing may have all the kinds of causes, e.g. the

moving cause of a house is the art or the builder, the final cause is the function it fulfils, the matter is earth

and stones, and the form is the definition. To judge from our previous discussion of the question which of the

sciences should be called Wisdom, there is reason for applying the name to each of them. For inasmuch as it

is most architectonic and authoritative and the other sciences, like slavewomen, may not even contradict it,

the science of the end and of the good is of the nature of Wisdom (for the other things are for the sake of the

end). But inasmuch as it was described' as dealing with the first causes and that which is in the highest sense

object of knowledge, the science of substance must be of the nature of Wisdom. For since men may know the

same thing in many ways, we say that he who recognizes what a thing is by its being so and so knows more

fully than he who recognizes it by its not being so and so, and in the former class itself one knows more fully

than another, and he knows most fully who knows what a thing is, not he who knows its quantity or quality or

what it can by nature do or have done to it. And further in all cases also we think that the knowledge of each

even of the things of which demonstration is possible is present only when we know what the thing is, e.g.

what squaring a rectangle is, viz. that it is the finding of a mean; and similarly in all other cases. And we

know about becomings and actions and about every change when we know the source of the movement; and

this is other than and opposed to the end. Therefore it would seem to belong to different sciences to

But (2), taking the startingpoints of demonstration as well as the causes, it is a disputable question whether

they are the object of one science or of more (by the startingpoints of demonstration I mean the common

beliefs, on which all men base their proofs); e.g. that everything must be either affirmed or denied, and that a

thing cannot at the same time be and not be, and all other such premisses:the question is whether the same

science deals with them as with substance, or a different science, and if it is not one science, which of the two

must be identified with that which we now seek.It is not reasonable that these topics should be the object of

one science; for why should it be peculiarly appropriate to geometry or to any other science to understand

these matters? If then it belongs to every science alike, and cannot belong to all, it is not peculiar to the

science which investigates substances, any more than to any other science, to know about these topics.And,

at the same time, in what way can there be a science of the first principles? For we are aware even now what

each of them in fact is (at least even other sciences use them as familiar); but if there is a demonstrative

science which deals with them, there will have to be an underlying kind, and some of them must be

demonstrable attributes and others must be axioms (for it is impossible that there should be demonstration

about all of them); for the demonstration must start from certain premisses and be about a certain subject and

prove certain attributes. Therefore it follows that all attributes that are proved must belong to a single class;

But if the science of substance and the science which deals with the axioms are different, which of them is by

nature more authoritative and prior? The axioms are most universal and are principles of all things. And if it

is not the business of the philosopher, to whom else will it belong to inquire what is true and what is untrue

(3) In general, do all substances fall under one science or under more than one? If the latter, to what sort of

substance is the present science to be assigned?On the other hand, it is not reasonable that one science

should deal with all. For then there would be one demonstrative science dealing with all attributes. For ever

demonstrative science investigates with regard to some subject its essential attributes, starting from the

common beliefs. Therefore to investigate the essential attributes of one class of things, starting from one set

of beliefs, is the business of one science. For the subject belongs to one science, and the premisses belong to

one, whether to the same or to another; so that the attributes do so too, whether they are investigated by these

(5) Further, does our investigation deal with substances alone or also with their attributes? I mean for

instance, if the solid is a substance and so are lines and planes, is it the business of the same science to know

these and to know the attributes of each of these classes (the attributes about which the mathematical sciences

offer proofs), or of a different science? If of the same, the science of substance also must be a demonstrative

science, but it is thought that there is no demonstration of the essence of things. And if of another, what will

be the science that investigates the attributes of substance? This is a very difficult question.

(4) Further, must we say that sensible substances alone exist, or that there are others besides these? And are

substances of one kind or are there in fact several kinds of substances, as those say who assert the existence

both of the Forms and of the intermediates, with which they say the mathematical sciences deal?The sense

in which we say the Forms are both causes and selfdependent substances has been explained in our first

remarks about them; while the theory presents difficulties in many ways, the most paradoxical thing of all is

the statement that there are certain things besides those in the material universe, and that these are the same as

sensible things except that they are eternal while the latter are perishable. For they say there is a manhimself

and a horseitself and healthitself, with no further qualification,a procedure like that of the people who

said there are gods, but in human form. For they were positing nothing but eternal men, nor are the Platonists

Further, if we are to posit besides the Forms and the sensibles the intermediates between them, we shall have

many difficulties. For clearly on the same principle there will be lines besides the linesthemselves and the

sensible lines, and so with each of the other classes of things; so that since astronomy is one of these

mathematical sciences there will also be a heaven besides the sensible heaven, and a sun and a moon (and so

with the other heavenly bodies) besides the sensible. Yet how are we to believe in these things? It is not

reasonable even to suppose such a body immovable, but to suppose it moving is quite impossible.And

similarly with the things of which optics and mathematical harmonics treat; for these also cannot exist apart

from the sensible things, for the same reasons. For if there are sensible things and sensations intermediate

between Form and individual, evidently there will also be animals intermediate between animalsthemselves

and the perishable animals.We might also raise the question, with reference to which kind of existing things

we must look for these sciences of intermediates. If geometry is to differ from mensuration only in this, that

the latter deals with things that we perceive, and the former with things that are not perceptible, evidently

there will also be a science other than medicine, intermediate between medicalscienceitself and this

individual medical science, and so with each of the other sciences. Yet how is this possible? There would

have to be also healthy things besides the perceptible healthy things and the healthyitself.And at the same

time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it

But on the other hand astronomy cannot be dealing with perceptible magnitudes nor with this heaven above

us. For neither are perceptible lines such lines as the geometer speaks of (for no perceptible thing is straight

or round in the way in which he defines 'straight' and 'round'; for a hoop touches a straight edge not at a point,

but as Protagoras used to say it did, in his refutation of the geometers), nor are the movements and spiral

orbits in the heavens like those of which astronomy treats, nor have geometrical points the same nature as the

actual stars.Now there are some who say that these socalled intermediates between the Forms and the

perceptible things exist, not apart from the perceptible things, however, but in these; the impossible results of

this view would take too long to enumerate, but it is enough to consider even such points as the following:It

is not reasonable that this should be so only in the case of these intermediates, but clearly the Forms also

might be in the perceptible things; for both statements are parts of the same theory. Further, it follows from

this theory that there are two solids in the same place, and that the intermediates are not immovable, since

they are in the moving perceptible things. And in general to what purpose would one suppose them to exist

indeed, but to exist in perceptible things? For the same paradoxical results will follow which we have already

mentioned; there will be a heaven besides the heaven, only it will be not apart but in the same place; which is

(6) Apart from the great difficulty of stating the case truly with regard to these matters, it is very hard to say,

with regard to the first principles, whether it is the genera that should be taken as elements and principles, or

rather the primary constituents of a thing; e.g. it is the primary parts of which articulate sounds consist that

are thought to be elements and principles of articulate sound, not the common genusarticulate sound; and

we give the name of 'elements' to those geometrical propositions, the proofs of which are implied in the

proofs of the others, either of all or of most. Further, both those who say there are several elements of

corporeal things and those who say there is one, say the parts of which bodies are compounded and consist

are principles; e.g. Empedocles says fire and water and the rest are the constituent elements of things, but

does not describe these as genera of existing things. Besides this, if we want to examine the nature of

anything else, we examine the parts of which, e.g. a bed consists and how they are put together, and then we

To judge from these arguments, then, the principles of things would not be the genera; but if we know each

thing by its definition, and the genera are the principles or startingpoints of definitions, the genera must also

be the principles of definable things. And if to get the knowledge of the species according to which things are

named is to get the knowledge of things, the genera are at least startingpoints of the species. And some also

of those who say unity or being, or the great and the small, are elements of things, seem to treat them as

But, again, it is not possible to describe the principles in both ways. For the formula of the essence is one; but

definition by genera will be different from that which states the constituent parts of a thing.

(7) Besides this, even if the genera are in the highest degree principles, should one regard the first of the

genera as principles, or those which are predicated directly of the individuals? This also admits of dispute.

For if the universals are always more of the nature of principles, evidently the uppermost of the genera are the

principles; for these are predicated of all things. There will, then, be as many principles of things as there are

primary genera, so that both being and unity will be principles and substances; for these are most of all

predicated of all existing things. But it is not possible that either unity or being should be a single genus of

things; for the differentiae of any genus must each of them both have being and be one, but it is not possible

for the genus taken apart from its species (any more than for the species of the genus) to be predicated of its

proper differentiae; so that if unity or being is a genus, no differentia will either have being or be one. But if

unity and being are not genera, neither will they be principles, if the genera are the principles. Again, the

intermediate kinds, in whose nature the differentiae are included, will on this theory be genera, down to the

indivisible species; but as it is, some are thought to be genera and others are not thought to be so. Besides

this, the differentiae are principles even more than the genera; and if these also are principles, there comes to

be practically an infinite number of principles, especially if we suppose the highest genus to be a

principle.But again, if unity is more of the nature of a principle, and the indivisible is one, and everything

indivisible is so either in quantity or in species, and that which is so in species is the prior, and genera are

divisible into species for man is not the genus of individual men), that which is predicated directly of the

individuals will have more unity.Further, in the case of things in which the distinction of prior and posterior

is present, that which is predicable of these things cannot be something apart from them (e.g. if two is the first

of numbers, there will not be a Number apart from the kinds of numbers; and similarly there will not be a

Figure apart from the kinds of figures; and if the genera of these things do not exist apart from the species,

the genera of other things will scarcely do so; for genera of these things are thought to exist if any do). But

among the individuals one is not prior and another posterior. Further, where one thing is better and another

worse, the better is always prior; so that of these also no genus can exist. From these considerations, then, the

species predicated of individuals seem to be principles rather than the genera. But again, it is not easy to say

in what sense these are to be taken as principles. For the principle or cause must exist alongside of the things

of which it is the principle, and must be capable of existing in separation from them; but for what reason

should we suppose any such thing to exist alongside of the individual, except that it is predicated universally

and of all? But if this is the reason, the things that are more universal must be supposed to be more of the

(8) There is a difficulty connected with these, the hardest of all and the most necessary to examine, and of

this the discussion now awaits us. If, on the one hand, there is nothing apart from individual things, and the

individuals are infinite in number, how then is it possible to get knowledge of the infinite individuals? For all

things that we come to know, we come to know in so far as they have some unity and identity, and in so far

But if this is necessary, and there must be something apart from the individuals, it will be necessary that the

genera exist apart from the individuals, either the lowest or the highest genera; but we found by discussion

Further, if we admit in the fullest sense that something exists apart from the concrete thing, whenever

something is predicated of the matter, must there, if there is something apart, be something apart from each

set of individuals, or from some and not from others, or from none? (A) If there is nothing apart from

individuals, there will be no object of thought, but all things will be objects of sense, and there will not be

knowledge of anything, unless we say that sensation is knowledge. Further, nothing will be eternal or

unmovable; for all perceptible things perish and are in movement. But if there is nothing eternal, neither can

there be a process of coming to be; for there must be something that comes to be, i.e. from which something

comes to be, and the ultimate term in this series cannot have come to be, since the series has a limit and since

nothing can come to be out of that which is not. Further, if generation and movement exist there must also be

a limit; for no movement is infinite, but every movement has an end, and that which is incapable of

completing its coming to be cannot be in process of coming to be; and that which has completed its coming to

be must he as soon as it has come to be. Further, since the matter exists, because it is ungenerated, it is a

fortiori reasonable that the substance or essence, that which the matter is at any time coming to be, should

exist; for if neither essence nor matter is to be, nothing will be at all, and since this is impossible there must

But again (B) if we are to suppose this, it is hard to say in which cases we are to suppose it and in which not.

For evidently it is not possible to suppose it in all cases; we could not suppose that there is a house besides

the particular houses.Besides this, will the substance of all the individuals, e.g. of all men, be one? This is

paradoxical, for all the things whose substance is one are one. But are the substances many and different?

This also is unreasonable.At the same time, how does the matter become each of the individuals, and how is

(9) Again, one might ask the following question also about the first principles. If they are one in kind only,

nothing will be numerically one, not even unityitself and beingitself; and how will knowing exist, if there

But if there is a common element which is numerically one, and each of the principles is one, and the

principles are not as in the case of perceptible things different for different things (e.g. since this particular

syllable is the same in kind whenever it occurs, the elements it are also the same in kind; only in kind, for

these also, like the syllable, are numerically different in different contexts),if it is not like this but the

principles of things are numerically one, there will be nothing else besides the elements (for there is no

difference of meaning between 'numerically one' and 'individual'; for this is just what we mean by the

individualthe numerically one, and by the universal we mean that which is predicable of the individuals).

Therefore it will be just as if the elements of articulate sound were limited in number; all the language in the

world would be confined to the ABC, since there could not be two or more letters of the same kind.

(10) One difficulty which is as great as any has been neglected both by modern philosophers and by their

predecessorswhether the principles of perishable and those of imperishable things are the same or different.

If they are the same, how are some things perishable and others imperishable, and for what reason? The

school of Hesiod and all the theologians thought only of what was plausible to themselves, and had no regard

to us. For, asserting the first principles to be gods and born of gods, they say that the beings which did not

taste of nectar and ambrosia became mortal; and clearly they are using words which are familiar to

themselves, yet what they have said about the very application of these causes is above our comprehension.

For if the gods taste of nectar and ambrosia for their pleasure, these are in no wise the causes of their

existence; and if they taste them to maintain their existence, how can gods who need food be eternal?But

into the subtleties of the mythologists it is not worth our while to inquire seriously; those, however, who use

the language of proof we must crossexamine and ask why, after all, things which consist of the same

elements are, some of them, eternal in nature, while others perish. Since these philosophers mention no cause,

and it is unreasonable that things should be as they say, evidently the principles or causes of things cannot be

the same. Even the man whom one might suppose to speak most consistentlyEmpedocles, even he has made

the same mistake; for he maintains that strife is a principle that causes destruction, but even strife would seem

no less to produce everything, except the One; for all things excepting God proceed from strife. At least he

The implication is evident even apart from these words; for if strife had not been present in things, all things

would have been one, according to him; for when they have come together, 'then strife stood outermost.'

Hence it also follows on his theory that God most blessed is less wise than all others; for he does not know all

the elements; for he has in him no strife, and knowledge is of the like by the like. 'For by earth,' he says,

Butand this is the point we started from this at least is evident, that on his theory it follows that strife is as

much the cause of existence as of destruction. And similarly love is not specially the cause of existence; for

in collecting things into the One it destroys all other things. And at the same time Empedocles mentions no

This implies that change was necessary; but he shows no cause of the necessity. But yet so far at least he

alone speaks consistently; for he does not make some things perishable and others imperishable, but makes

all perishable except the elements. The difficulty we are speaking of now is, why some things are perishable

Let this suffice as proof of the fact that the principles cannot be the same. But if there are different principles,

one difficulty is whether these also will be imperishable or perishable. For if they are perishable, evidently

these also must consist of certain elements (for all things that perish, perish by being resolved into the

elements of which they consist); so that it follows that prior to the principles there are other principles. But

this is impossible, whether the process has a limit or proceeds to infinity. Further, how will perishable things

exist, if their principles are to be annulled? But if the principles are imperishable, why will things composed

of some imperishable principles be perishable, while those composed of the others are imperishable? This is

not probable, but is either impossible or needs much proof. Further, no one has even tried to maintain

different principles; they maintain the same principles for all things. But they swallow the difficulty we stated

(11) The inquiry that is both the hardest of all and the most necessary for knowledge of the truth is whether

being and unity are the substances of things, and whether each of them, without being anything else, is being

or unity respectively, or we must inquire what being and unity are, with the implication that they have some

other underlying nature. For some people think they are of the former, others think they are of the latter

character. Plato and the Pythagoreans thought being and unity were nothing else, but this was their nature,

their essence being just unity and being. But the natural philosophers take a different line; e.g.

Empedoclesas though reducing to something more intelligiblesays what unity is; for he would seem to say

it is love: at least, this is for all things the cause of their being one. Others say this unity and being, of which

things consist and have been made, is fire, and others say it is air. A similar view is expressed by those who

make the elements more than one; for these also must say that unity and being are precisely all the things

(A) If we do not suppose unity and being to be substances, it follows that none of the other universals is a

substance; for these are most universal of all, and if there is no unity itself or beingitself, there will scarcely

be in any other case anything apart from what are called the individuals. Further, if unity is not a substance,

evidently number also will not exist as an entity separate from the individual things; for number is units, and

But (B) if there is a unityitself and a being itself, unity and being must be their substance; for it is not

something else that is predicated universally of the things that are and are one, but just unity and being. But if

there is to be a beingitself and a unityitself, there is much difficulty in seeing how there will be anything

else besides these,I mean, how things will be more than one in number. For what is different from being

does not exist, so that it necessarily follows, according to the argument of Parmenides, that all things that are

There are objections to both views. For whether unity is not a substance or there is a unityitself, number

cannot be a substance. We have already said why this result follows if unity is not a substance; and if it is, the

same difficulty arises as arose with regard to being. For whence is there to be another one besides

unityitself? It must be notone; but all things are either one or many, and of the many each is one.

Further, if unityitself is indivisible, according to Zeno's postulate it will be nothing. For that which neither

when added makes a thing greater nor when subtracted makes it less, he asserts to have no being, evidently

assuming that whatever has being is a spatial magnitude. And if it is a magnitude, it is corporeal; for the

corporeal has being in every dimension, while the other objects of mathematics, e.g. a plane or a line, added

in one way will increase what they are added to, but in another way will not do so, and a point or a unit does

so in no way. But, since his theory is of a low order, and an indivisible thing can exist in such a way as to

have a defence even against him (for the indivisible when added will make the number, though not the size,

greater),yet how can a magnitude proceed from one such indivisible or from many? It is like saying that the

But even if ore supposes the case to be such that, as some say, number proceeds from unityitself and

something else which is not one, none the less we must inquire why and how the product will be sometimes a

number and sometimes a magnitude, if the notone was inequality and was the same principle in either case.

For it is not evident how magnitudes could proceed either from the one and this principle, or from some

(14) A question connected with these is whether numbers and bodies and planes and points are substances of

a kind, or not. If they are not, it baffles us to say what being is and what the substances of things are. For

modifications and movements and relations and dispositions and ratios do not seem to indicate the substance

of anything; for all are predicated of a subject, and none is a 'this'. And as to the things which might seem

most of all to indicate substance, water and earth and fire and air, of which composite bodies consist, heat and

cold and the like are modifications of these, not substances, and the body which is thus modified alone

persists as something real and as a substance. But, on the other hand, the body is surely less of a substance

than the surface, and the surface than the line, and the line than the unit and the point. For the body is

bounded by these; and they are thought to be capable of existing without body, but body incapable of existing

without these. This is why, while most of the philosophers and the earlier among them thought that substance

and being were identical with body, and that all other things were modifications of this, so that the first

principles of the bodies were the first principles of being, the more recent and those who were held to be

wiser thought numbers were the first principles. As we said, then, if these are not substance, there is no

substance and no being at all; for the accidents of these it cannot be right to call beings.

But if this is admitted, that lines and points are substance more than bodies, but we do not see to what sort of

bodies these could belong (for they cannot be in perceptible bodies), there can be no substance.Further,

these are all evidently divisions of body,one in breadth, another in depth, another in length. Besides this, no

sort of shape is present in the solid more than any other; so that if the Hermes is not in the stone, neither is the

half of the cube in the cube as something determinate; therefore the surface is not in it either; for if any sort of

surface were in it, the surface which marks off the half of the cube would be in it too. And the same account

applies to the line and to the point and the unit. Therefore, if on the one hand body is in the highest degree

substance, and on the other hand these things are so more than body, but these are not even instances of

substance, it baffles us to say what being is and what the substance of things is.For besides what has been

said, the questions of generation and instruction confront us with further paradoxes. For if substance, not

having existed before, now exists, or having existed before, afterwards does not exist, this change is thought

to be accompanied by a process of becoming or perishing; but points and lines and surfaces cannot be in

process either of becoming or of perishing, when they at one time exist and at another do not. For when

bodies come into contact or are divided, their boundaries simultaneously become one in the one case when

they touch, and two in the otherwhen they are divided; so that when they have been put together one

boundary does not exist but has perished, and when they have been divided the boundaries exist which before

did not exist (for it cannot be said that the point, which is indivisible, was divided into two). And if the

boundaries come into being and cease to be, from what do they come into being? A similar account may also

be given of the 'now' in time; for this also cannot be in process of coming into being or of ceasing to be, but

yet seems to be always different, which shows that it is not a substance. And evidently the same is true of

points and lines and planes; for the same argument applies, since they are all alike either limits or divisions.

In general one might raise the question why after all, besides perceptible things and the intermediates, we

have to look for another class of things, i.e. the Forms which we posit. If it is for this reason, because the

objects of mathematics, while they differ from the things in this world in some other respect, differ not at all

in that there are many of the same kind, so that their first principles cannot be limited in number (just as the

elements of all the language in this sensible world are not limited in number, but in kind, unless one takes the

elements of this individual syllable or of this individual articulate soundwhose elements will be limited even

in number; so is it also in the case of the intermediates; for there also the members of the same kind are

infinite in number), so that if there are notbesides perceptible and mathematical objectsothers such as some

maintain the Forms to be, there will be no substance which is one in number, but only in kind, nor will the

first principles of things be determinate in number, but only in kind:if then this must be so, the Forms also

must therefore be held to exist. Even if those who support this view do not express it articulately, still this is

what they mean, and they must be maintaining the Forms just because each of the Forms is a substance and

But if we are to suppose both that the Forms exist and that the principles are one in number, not in kind, we

(13) Closely connected with this is the question whether the elements exist potentially or in some other

manner. If in some other way, there will be something else prior to the first principles; for the potency is prior

to the actual cause, and it is not necessary for everything potential to be actual.But if the elements exist

potentially, it is possible that everything that is should not be. For even that which is not yet is capable of

being; for that which is not comes to be, but nothing that is incapable of being comes to be.

(12) We must not only raise these questions about the first principles, but also ask whether they are universal

or what we call individuals. If they are universal, they will not be substances; for everything that is common

indicates not a 'this' but a 'such', but substance is a 'this'. And if we are to be allowed to lay it down that a

common predicate is a 'this' and a single thing, Socrates will be several animalshimself and 'man' and

If, then, the principles are universals, these universal. Therefore if there is to be results follow; if they are not

universals but of knowledge of the principles there must be the nature of individuals, they will not be other

principles prior to them, namely those knowable; for the knowledge of anything is that are universally

THERE is a science which investigates being as being and the attributes which belong to this in virtue of its

own nature. Now this is not the same as any of the socalled special sciences; for none of these others treats

universally of being as being. They cut off a part of being and investigate the attribute of this part; this is

what the mathematical sciences for instance do. Now since we are seeking the first principles and the highest

causes, clearly there must be some thing to which these belong in virtue of its own nature. If then those who

sought the elements of existing things were seeking these same principles, it is necessary that the elements

must be elements of being not by accident but just because it is being. Therefore it is of being as being that

There are many senses in which a thing may be said to 'be', but all that 'is' is related to one central point, one

definite kind of thing, and is not said to 'be' by a mere ambiguity. Everything which is healthy is related to

health, one thing in the sense that it preserves health, another in the sense that it produces it, another in the

sense that it is a symptom of health, another because it is capable of it. And that which is medical is relative

to the medical art, one thing being called medical because it possesses it, another because it is naturally

adapted to it, another because it is a function of the medical art. And we shall find other words used similarly

to these. So, too, there are many senses in which a thing is said to be, but all refer to one startingpoint; some

things are said to be because they are substances, others because they are affections of substance, others

because they are a process towards substance, or destructions or privations or qualities of substance, or

productive or generative of substance, or of things which are relative to substance, or negations of one of

these thing of substance itself. It is for this reason that we say even of nonbeing that it is nonbeing. As, then,

there is one science which deals with all healthy things, the same applies in the other cases also. For not only

in the case of things which have one common notion does the investigation belong to one science, but also in

the case of things which are related to one common nature; for even these in a sense have one common

notion. It is clear then that it is the work of one science also to study the things that are, qua being.But

everywhere science deals chiefly with that which is primary, and on which the other things depend, and in

virtue of which they get their names. If, then, this is substance, it will be of substances that the philosopher

Now for each one class of things, as there is one perception, so there is one science, as for instance grammar,

being one science, investigates all articulate sounds. Hence to investigate all the species of being qua being is

the work of a science which is generically one, and to investigate the several species is the work of the

If, now, being and unity are the same and are one thing in the sense that they are implied in one another as

principle and cause are, not in the sense that they are explained by the same definition (though it makes no

difference even if we suppose them to be like thatin fact this would even strengthen our case); for 'one man'

and 'man' are the same thing, and so are 'existent man' and 'man', and the doubling of the words in 'one man

and one existent man' does not express anything different (it is clear that the two things are not separated

either in coming to be or in ceasing to be); and similarly 'one existent man' adds nothing to 'existent man', and

that it is obvious that the addition in these cases means the same thing, and unity is nothing apart from being;

and if, further, the substance of each thing is one in no merely accidental way, and similarly is from its very

nature something that is:all this being so, there must be exactly as many species of being as of unity. And to

investigate the essence of these is the work of a science which is generically oneI mean, for instance, the

discussion of the same and the similar and the other concepts of this sort; and nearly all contraries may be

referred to this origin; let us take them as having been investigated in the 'Selection of Contraries'.

And there are as many parts of philosophy as there are kinds of substance, so that there must necessarily be

among them a first philosophy and one which follows this. For being falls immediately into genera; for which

reason the sciences too will correspond to these genera. For the philosopher is like the mathematician, as that

word is used; for mathematics also has parts, and there is a first and a second science and other successive

Now since it is the work of one science to investigate opposites, and plurality is opposed to unityand it

belongs to one science to investigate the negation and the privation because in both cases we are really

investigating the one thing of which the negation or the privation is a negation or privation (for we either say

simply that that thing is not present, or that it is not present in some particular class; in the latter case

difference is present over and above what is implied in negation; for negation means just the absence of the

thing in question, while in privation there is also employed an underlying nature of which the privation is

asserted):in view of all these facts, the contraries of the concepts we named above, the other and the

dissimilar and the unequal, and everything else which is derived either from these or from plurality and unity,

must fall within the province of the science above named. And contrariety is one of these concepts; for

contrariety is a kind of difference, and difference is a kind of otherness. Therefore, since there are many

senses in which a thing is said to be one, these terms also will have many senses, but yet it belongs to one

science to know them all; for a term belongs to different sciences not if it has different senses, but if it has not

one meaning and its definitions cannot be referred to one central meaning. And since all things are referred to

that which is primary, as for instance all things which are called one are referred to the primary one, we must

say that this holds good also of the same and the other and of contraries in general; so that after distinguishing

the various senses of each, we must then explain by reference to what is primary in the case of each of the

predicates in question, saying how they are related to it; for some will be called what they are called because

It is evident, then, that it belongs to one science to be able to give an account of these concepts as well as of

substance (this was one of the questions in our book of problems), and that it is the function of the

philosopher to be able to investigate all things. For if it is not the function of the philosopher, who is it who

will inquire whether Socrates and Socrates seated are the same thing, or whether one thing has one contrary,

or what contrariety is, or how many meanings it has? And similarly with all other such questions. Since, then,

these are essential modifications of unity qua unity and of being qua being, not qua numbers or lines or fire, it

is clear that it belongs to this science to investigate both the essence of these concepts and their properties.

And those who study these properties err not by leaving the sphere of philosophy, but by forgetting that

substance, of which they have no correct idea, is prior to these other things. For number qua number has

peculiar attributes, such as oddness and evenness, commensurability and equality, excess and defect, and

these belong to numbers either in themselves or in relation to one another. And similarly the solid and the

motionless and that which is in motion and the weightless and that which has weight have other peculiar

properties. So too there are certain properties peculiar to being as such, and it is about these that the

philosopher has to investigate the truth.An indication of this may be mentioned: dialecticians and sophists

assume the same guise as the philosopher, for sophistic is Wisdom which exists only in semblance, and

dialecticians embrace all things in their dialectic, and being is common to all things; but evidently their

dialectic embraces these subjects because these are proper to philosophy.For sophistic and dialectic turn on

the same class of things as philosophy, but this differs from dialectic in the nature of the faculty required and

from sophistic in respect of the purpose of the philosophic life. Dialectic is merely critical where philosophy

Again, in the list of contraries one of the two columns is privative, and all contraries are reducible to being

and nonbeing, and to unity and plurality, as for instance rest belongs to unity and movement to plurality.

And nearly all thinkers agree that being and substance are composed of contraries; at least all name contraries

as their first principlessome name odd and even, some hot and cold, some limit and the unlimited, some

love and strife. And all the others as well are evidently reducible to unity and plurality (this reduction we

must take for granted), and the principles stated by other thinkers fall entirely under these as their genera. It is

obvious then from these considerations too that it belongs to one science to examine being qua being. For all

things are either contraries or composed of contraries, and unity and plurality are the startingpoints of all

contraries. And these belong to one science, whether they have or have not one single meaning. Probably the

truth is that they have not; yet even if 'one' has several meanings, the other meanings will be related to the

primary meaning (and similarly in the case of the contraries), even if being or unity is not a universal and the

same in every instance or is not separable from the particular instances (as in fact it probably is not; the unity

is in some cases that of common reference, in some cases that of serial succession). And for this reason it

does not belong to the geometer to inquire what is contrariety or completeness or unity or being or the same

or the other, but only to presuppose these concepts and reason from this startingpoint.Obviously then it is

the work of one science to examine being qua being, and the attributes which belong to it qua being, and the

same science will examine not only substances but also their attributes, both those above named and the

concepts 'prior' and 'posterior', 'genus' and 'species', 'whole' and 'part', and the others of this sort.

We must state whether it belongs to one or to different sciences to inquire into the truths which are in

mathematics called axioms, and into substance. Evidently, the inquiry into these also belongs to one science,

and that the science of the philosopher; for these truths hold good for everything that is, and not for some

special genus apart from others. And all men use them, because they are true of being qua being and each

genus has being. But men use them just so far as to satisfy their purposes; that is, as far as the genus to which

their demonstrations refer extends. Therefore since these truths clearly hold good for all things qua being (for

this is what is common to them), to him who studies being qua being belongs the inquiry into these as well.

And for this reason no one who is conducting a special inquiry tries to say anything about their truth or

falsity,neither the geometer nor the arithmetician. Some natural philosophers indeed have done so, and their

procedure was intelligible enough; for they thought that they alone were inquiring about the whole of nature

and about being. But since there is one kind of thinker who is above even the natural philosopher (for nature

is only one particular genus of being), the discussion of these truths also will belong to him whose inquiry is

universal and deals with primary substance. Physics also is a kind of Wisdom, but it is not the first kind.And

the attempts of some of those who discuss the terms on which truth should be accepted, are due to a want of

training in logic; for they should know these things already when they come to a special study, and not be

Evidently then it belongs to the philosopher, i.e. to him who is studying the nature of all substance, to inquire

also into the principles of syllogism. But he who knows best about each genus must be able to state the most

certain principles of his subject, so that he whose subject is existing things qua existing must be able to state

the most certain principles of all things. This is the philosopher, and the most certain principle of all is that

regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men

may be mistaken about things which they do not know), and nonhypothetical. For a principle which every

one must have who understands anything that is, is not a hypothesis; and that which every one must know

who knows anything, he must already have when he comes to a special study. Evidently then such a principle

is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at

the same time belong and not belong to the same subject and in the same respect; we must presuppose, to

guard against dialectical objections, any further qualifications which might be added. This, then, is the most

certain of all principles, since it answers to the definition given above. For it is impossible for any one to

believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not

necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same

subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts

another is contrary to it, obviously it is impossible for the same man at the same time to believe the same

thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the

same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate

There are some who, as we said, both themselves assert that it is possible for the same thing to be and not to

be, and say that people can judge this to be the case. And among others many writers about nature use this

language. But we have now posited that it is impossible for anything at the same time to be and not to be, and

by this means have shown that this is the most indisputable of all principles.Some indeed demand that even

this shall be demonstrated, but this they do through want of education, for not to know of what things one

should demand demonstration, and of what one should not, argues want of education. For it is impossible that

there should be demonstration of absolutely everything (there would be an infinite regress, so that there

would still be no demonstration); but if there are things of which one should not demand demonstration, these

persons could not say what principle they maintain to be more selfevident than the present one.

We can, however, demonstrate negatively even that this view is impossible, if our opponent will only say

something; and if he says nothing, it is absurd to seek to give an account of our views to one who cannot give

an account of anything, in so far as he cannot do so. For such a man, as such, is from the start no better than a

vegetable. Now negative demonstration I distinguish from demonstration proper, because in a demonstration

one might be thought to be begging the question, but if another person is responsible for the assumption we

shall have negative proof, not demonstration. The startingpoint for all such arguments is not the demand that

our opponent shall say that something either is or is not (for this one might perhaps take to be a begging of

the question), but that he shall say something which is significant both for himself and for another; for this is

necessary, if he really is to say anything. For, if he means nothing, such a man will not be capable of

reasoning, either with himself or with another. But if any one grants this, demonstration will be possible; for

we shall already have something definite. The person responsible for the proof, however, is not he who

demonstrates but he who listens; for while disowning reason he listens to reason. And again he who admits

this has admitted that something is true apart from demonstration (so that not everything will be 'so and not

First then this at least is obviously true, that the word 'be' or 'not be' has a definite meaning, so that not

everything will be 'so and not so'. Again, if 'man' has one meaning, let this be 'twofooted animal'; by having

one meaning I understand this:if 'man' means 'X', then if A is a man 'X' will be what 'being a man' means for

him. (It makes no difference even if one were to say a word has several meanings, if only they are limited in

number; for to each definition there might be assigned a different word. For instance, we might say that 'man'

has not one meaning but several, one of which would have one definition, viz. 'twofooted animal', while

there might be also several other definitions if only they were limited in number; for a peculiar name might

be assigned to each of the definitions. If, however, they were not limited but one were to say that the word

has an infinite number of meanings, obviously reasoning would be impossible; for not to have one meaning is

to have no meaning, and if words have no meaning our reasoning with one another, and indeed with

ourselves, has been annihilated; for it is impossible to think of anything if we do not think of one thing; but if

Let it be assumed then, as was said at the beginning, that the name has a meaning and has one meaning; it is

impossible, then, that 'being a man' should mean precisely 'not being a man', if 'man' not only signifies

something about one subject but also has one significance (for we do not identify 'having one significance'

with 'signifying something about one subject', since on that assumption even 'musical' and 'white' and 'man'

would have had one significance, so that all things would have been one; for they would all have had the

And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one

whom we call 'man', others were to call 'notman'; but the point in question is not this, whether the same

thing can at the same time be and not be a man in name, but whether it can in fact. Now if 'man' and

'notman' mean nothing different, obviously 'not being a man' will mean nothing different from 'being a man';

so that 'being a man' will be 'not being a man'; for they will be one. For being one means thisbeing related as

'raiment' and 'dress' are, if their definition is one. And if 'being a man' and 'being a notman' are to be one,

they must mean one thing. But it was shown earlier' that they mean different things.Therefore, if it is true to

say of anything that it is a man, it must be a twofooted animal (for this was what 'man' meant); and if this is

necessary, it is impossible that the same thing should not at that time be a twofooted animal; for this is what

'being necessary' meansthat it is impossible for the thing not to be. It is, then, impossible that it should be at

The same account holds good with regard to 'not being a man', for 'being a man' and 'being a notman' mean

different things, since even 'being white' and 'being a man' are different; for the former terms are much more

different so that they must a fortiori mean different things. And if any one says that 'white' means one and the

same thing as 'man', again we shall say the same as what was said before, that it would follow that all things

are one, and not only opposites. But if this is impossible, then what we have maintained will follow, if our

And if, when one asks the question simply, he adds the contradictories, he is not answering the question. For

there is nothing to prevent the same thing from being both a man and white and countless other things: but

still, if one asks whether it is or is not true to say that this is a man, our opponent must give an answer which

means one thing, and not add that 'it is also white and large'. For, besides other reasons, it is impossible to

enumerate its accidental attributes, which are infinite in number; let him, then, enumerate either all or none.

Similarly, therefore, even if the same thing is a thousand times a man and a notman, he must not, in

answering the question whether this is a man, add that it is also at the same time a notman, unless he is

bound to add also all the other accidents, all that the subject is or is not; and if he does this, he is not

And in general those who say this do away with substance and essence. For they must say that all attributes

are accidents, and that there is no such thing as 'being essentially a man' or 'an animal'. For if there is to be

any such thing as 'being essentially a man' this will not be 'being a notman' or 'not being a man' (yet these

are negations of it); for there was one thing which it meant, and this was the substance of something. And

denoting the substance of a thing means that the essence of the thing is nothing else. But if its being

essentially a man is to be the same as either being essentially a notman or essentially not being a man, then

its essence will be something else. Therefore our opponents must say that there cannot be such a definition of

anything, but that all attributes are accidental; for this is the distinction between substance and

accident'white' is accidental to man, because though he is white, whiteness is not his essence. But if all

statements are accidental, there will be nothing primary about which they are made, if the accidental always

implies predication about a subject. The predication, then, must go on ad infinitum. But this is impossible; for

not even more than two terms can be combined in accidental predication. For (1) an accident is not an

accident of an accident, unless it be because both are accidents of the same subject. I mean, for instance, that

the white is musical and the latter is white, only because both are accidental to man. But (2) Socrates is

musical, not in this sense, that both terms are accidental to something else. Since then some predicates are

accidental in this and some in that sense, (a) those which are accidental in the latter sense, in which white is

accidental to Socrates, cannot form an infinite series in the upward direction; e.g. Socrates the white has not

yet another accident; for no unity can be got out of such a sum. Nor again (b) will 'white' have another term

accidental to it, e.g. 'musical'. For this is no more accidental to that than that is to this; and at the same time

we have drawn the distinction, that while some predicates are accidental in this sense, others are so in the

sense in which 'musical' is accidental to Socrates; and the accident is an accident of an accident not in cases

of the latter kind, but only in cases of the other kind, so that not all terms will be accidental. There must, then,

even so be something which denotes substance. And if this is so, it has been shown that contradictories

Again, if all contradictory statements are true of the same subject at the same time, evidently all things will be

one. For the same thing will be a trireme, a wall, and a man, if of everything it is possible either to affirm or

to deny anything (and this premiss must be accepted by those who share the views of Protagoras). For if any

one thinks that the man is not a trireme, evidently he is not a trireme; so that he also is a trireme, if, as they

say, contradictory statements are both true. And we thus get the doctrine of Anaxagoras, that all things are

mixed together; so that nothing really exists. They seem, then, to be speaking of the indeterminate, and, while

fancying themselves to be speaking of being, they are speaking about nonbeing; for it is that which exists

potentially and not in complete reality that is indeterminate. But they must predicate of every subject the

affirmation or the negation of every attribute. For it is absurd if of each subject its own negation is to be

predicable, while the negation of something else which cannot be predicated of it is not to be predicable of it;

for instance, if it is true to say of a man that he is not a man, evidently it is also true to say that he is either a

trireme or not a trireme. If, then, the affirmative can be predicated, the negative must be predicable too; and if

the affirmative is not predicable, the negative, at least, will be more predicable than the negative of the

subject itself. If, then, even the latter negative is predicable, the negative of 'trireme' will be also predicable;

Those, then, who maintain this view are driven to this conclusion, and to the further conclusion that it is not

necessary either to assert or to deny. For if it is true that a thing is a man and a notman, evidently also it will

be neither a man nor a notman. For to the two assertions there answer two negations, and if the former is

treated as a single proposition compounded out of two, the latter also is a single proposition opposite to the

Again, either the theory is true in all cases, and a thing is both white and notwhite, and existent and

nonexistent, and all other assertions and negations are similarly compatible or the theory is true of some

statements and not of others. And if not of all, the exceptions will be contradictories of which admittedly only

one is true; but if of all, again either the negation will be true wherever the assertion is, and the assertion true

wherever the negation is, or the negation will be true where the assertion is, but the assertion not always true

where the negation is. And (a) in the latter case there will be something which fixedly is not, and this will be

an indisputable belief; and if nonbeing is something indisputable and knowable, the opposite assertion will

be more knowable. But (b) if it is equally possible also to assert all that it is possible to deny, one must either

be saying what is true when one separates the predicates (and says, for instance, that a thing is white, and

again that it is notwhite), or not. And if (i) it is not true to apply the predicates separately, our opponent is

not saying what he professes to say, and also nothing at all exists; but how could nonexistent things speak or

walk, as he does? Also all things would on this view be one, as has been already said, and man and God and

trireme and their contradictories will be the same. For if contradictories can be predicated alike of each

subject, one thing will in no wise differ from another; for if it differ, this difference will be something true

and peculiar to it. And (ii) if one may with truth apply the predicates separately, the abovementioned result

follows none the less, and, further, it follows that all would then be right and all would be in error, and our

opponent himself confesses himself to be in error.And at the same time our discussion with him is evidently

about nothing at all; for he says nothing. For he says neither 'yes' nor 'no', but 'yes and no'; and again he

denies both of these and says 'neither yes nor no'; for otherwise there would already be something definite.

Again if when the assertion is true, the negation is false, and when this is true, the affirmation is false, it will

not be possible to assert and deny the same thing truly at the same time. But perhaps they might say this was

Again, is he in error who judges either that the thing is so or that it is not so, and is he right who judges both?

If he is right, what can they mean by saying that the nature of existing things is of this kind? And if he is not

right, but more right than he who judges in the other way, being will already be of a definite nature, and this

will be true, and not at the same time also not true. But if all are alike both wrong and right, one who is in this

condition will not be able either to speak or to say anything intelligible; for he says at the same time both 'yes'

and 'no.' And if he makes no judgement but 'thinks' and 'does not think', indifferently, what difference will

there be between him and a vegetable?Thus, then, it is in the highest degree evident that neither any one of

those who maintain this view nor any one else is really in this position. For why does a man walk to Megara

and not stay at home, when he thinks he ought to be walking there? Why does he not walk early some

morning into a well or over a precipice, if one happens to be in his way? Why do we observe him guarding

against this, evidently because he does not think that falling in is alike good and not good? Evidently, then, he

judges one thing to be better and another worse. And if this is so, he must also judge one thing to be a man

and another to be notaman, one thing to be sweet and another to be notsweet. For he does not aim at and

judge all things alike, when, thinking it desirable to drink water or to see a man, he proceeds to aim at these

things; yet he ought, if the same thing were alike a man and notaman. But, as was said, there is no one who

does not obviously avoid some things and not others. Therefore, as it seems, all men make unqualified

judgements, if not about all things, still about what is better and worse. And if this is not knowledge but

opinion, they should be all the more anxious about the truth, as a sick man should be more anxious about his

health than one who is healthy; for he who has opinions is, in comparison with the man who knows, not in a

Again, however much all things may be 'so and not so', still there is a more and a less in the nature of things;

for we should not say that two and three are equally even, nor is he who thinks four things are five equally

wrong with him who thinks they are a thousand. If then they are not equally wrong, obviously one is less

wrong and therefore more right. If then that which has more of any quality is nearer the norm, there must be

some truth to which the more true is nearer. And even if there is not, still there is already something better

founded and liker the truth, and we shall have got rid of the unqualified doctrine which would prevent us

From the same opinion proceeds the doctrine of Protagoras, and both doctrines must be alike true or alike

untrue. For on the one hand, if all opinions and appearances are true, all statements must be at the same time

true and false. For many men hold beliefs in which they conflict with one another, and think those mistaken

who have not the same opinions as themselves; so that the same thing must both be and not be. And on the

other hand, if this is so, all opinions must be true; for those who are mistaken and those who are right are

opposed to one another in their opinions; if, then, reality is such as the view in question supposes, all will be

Evidently, then, both doctrines proceed from the same way of thinking. But the same method of discussion

must not be used with all opponents; for some need persuasion, and others compulsion. Those who have been

driven to this position by difficulties in their thinking can easily be cured of their ignorance; for it is not their

expressed argument but their thought that one has to meet. But those who argue for the sake of argument can

Those who really feel the difficulties have been led to this opinion by observation of the sensible world. (1)

They think that contradictories or contraries are true at the same time, because they see contraries coming

into existence out of the same thing. If, then, that which is not cannot come to be, the thing must have existed

before as both contraries alike, as Anaxagoras says all is mixed in all, and Democritus too; for he says the

void and the full exist alike in every part, and yet one of these is being, and the other nonbeing. To those,

then, whose belief rests on these grounds, we shall say that in a sense they speak rightly and in a sense they

err. For 'that which is' has two meanings, so that in some sense a thing can come to be out of that which is

not, while in some sense it cannot, and the same thing can at the same time be in being and not in beingbut

not in the same respect. For the same thing can be potentially at the same time two contraries, but it cannot

actually. And again we shall ask them to believe that among existing things there is also another kind of

substance to which neither movement nor destruction nor generation at all belongs.

And (2) similarly some have inferred from observation of the sensible world the truth of appearances. For

they think that the truth should not be determined by the large or small number of those who hold a belief,

and that the same thing is thought sweet by some when they taste it, and bitter by others, so that if all were ill

or all were mad, and only two or three were well or sane, these would be thought ill and mad, and not the

And again, they say that many of the other animals receive impressions contrary to ours; and that even to the

senses of each individual, things do not always seem the same. Which, then, of these impressions are true and

which are false is not obvious; for the one set is no more true than the other, but both are alike. And this is

why Democritus, at any rate, says that either there is no truth or to us at least it is not evident.

And in general it is because these thinkers suppose knowledge to be sensation, and this to be a physical

alteration, that they say that what appears to our senses must be true; for it is for these reasons that both

Empedocles and Democritus and, one may almost say, all the others have fallen victims to opinions of this

sort. For Empedocles says that when men change their condition they change their knowledge;

A saying of Anaxagoras to some of his friends is also related,that things would be for them such as they

supposed them to be. And they say that Homer also evidently had this opinion, because he made Hector,

when he was unconscious from the blow, lie 'thinking other thoughts',which implies that even those who are

bereft of thought have thoughts, though not the same thoughts. Evidently, then, if both are forms of

knowledge, the real things also are at the same time 'both so and not so'. And it is in this direction that the

consequences are most difficult. For if those who have seen most of such truth as is possible for us (and these

are those who seek and love it most)if these have such opinions and express these views about the truth, is it

not natural that beginners in philosophy should lose heart? For to seek the truth would be to follow flying

But the reason why these thinkers held this opinion is that while they were inquiring into the truth of that

which is, they thought, 'that which is' was identical with the sensible world; in this, however, there is largely

present the nature of the indeterminateof that which exists in the peculiar sense which we have explained;

and therefore, while they speak plausibly, they do not say what is true (for it is fitting to put the matter so

rather than as Epicharmus put it against Xenophanes). And again, because they saw that all this world of

nature is in movement and that about that which changes no true statement can be made, they said that of

course, regarding that which everywhere in every respect is changing, nothing could truly be affirmed. It was

this belief that blossomed into the most extreme of the views above mentioned, that of the professed

Heracliteans, such as was held by Cratylus, who finally did not think it right to say anything but only moved

his finger, and criticized Heraclitus for saying that it is impossible to step twice into the same river; for he

But we shall say in answer to this argument also that while there is some justification for their thinking that

the changing, when it is changing, does not exist, yet it is after all disputable; for that which is losing a

quality has something of that which is being lost, and of that which is coming to be, something must already

be. And in general if a thing is perishing, will be present something that exists; and if a thing is coming to be,

there must be something from which it comes to be and something by which it is generated, and this process

cannot go on ad infinitum.But, leaving these arguments, let us insist on this, that it is not the same thing to

change in quantity and in quality. Grant that in quantity a thing is not constant; still it is in respect of its form

that we know each thing.And again, it would be fair to criticize those who hold this view for asserting about

the whole material universe what they saw only in a minority even of sensible things. For only that region of

the sensible world which immediately surrounds us is always in process of destruction and generation; but

this isso to speaknot even a fraction of the whole, so that it would have been juster to acquit this part of the

world because of the other part, than to condemn the other because of this.And again, obviously we shall

make to them also the same reply that we made long ago; we must show them and persuade them that there is

something whose nature is changeless. Indeed, those who say that things at the same time are and are not,

should in consequence say that all things are at rest rather than that they are in movement; for there is nothing

into which they can change, since all attributes belong already to all subjects.

Regarding the nature of truth, we must maintain that not everything which appears is true; firstly, because

even if sensationat least of the object peculiar to the sense in questionis not false, still appearance is not the

same as sensation.Again, it is fair to express surprise at our opponents' raising the question whether

magnitudes are as great, and colours are of such a nature, as they appear to people at a distance, or as they

appear to those close at hand, and whether they are such as they appear to the healthy or to the sick, and

whether those things are heavy which appear so to the weak or those which appear so to the strong, and those

things true which appear to the slee ing or to the waking. For obviously they do not think these to be open

questions; no one, at least, if when he is in Libya he has fancied one night that he is in Athens, starts for the

concert hall.And again with regard to the future, as Plato says, surely the opinion of the physician and that

of the ignorant man are not equally weighty, for instance, on the question whether a man will get well or

not.And again, among sensations themselves the sensation of a foreign object and that of the appropriate

object, or that of a kindred object and that of the object of the sense in question, are not equally authoritative,

but in the case of colour sight, not taste, has the authority, and in the case of flavour taste, not sight; each of

which senses never says at the same time of the same object that it simultaneously is 'so and not so'.But not

even at different times does one sense disagree about the quality, but only about that to which the quality

belongs. I mean, for instance, that the same wine might seem, if either it or one's body changed, at one time

sweet and at another time not sweet; but at least the sweet, such as it is when it exists, has never yet changed,

but one is always right about it, and that which is to be sweet is of necessity of such and such a nature. Yet all

these views destroy this necessity, leaving nothing to be of necessity, as they leave no essence of anything;

for the necessary cannot be in this way and also in that, so that if anything is of necessity, it will not be 'both

And, in general, if only the sensible exists, there would be nothing if animate things were not; for there would

be no faculty of sense. Now the view that neither the sensible qualities nor the sensations would exist is

doubtless true (for they are affections of the perceiver), but that the substrata which cause the sensation

should not exist even apart from sensation is impossible. For sensation is surely not the sensation of itself, but

there is something beyond the sensation, which must be prior to the sensation; for that which moves is prior

in nature to that which is moved, and if they are correlative terms, this is no less the case.

There are, both among those who have these convictions and among those who merely profess these views,

some who raise a difficulty by asking, who is to be the judge of the healthy man, and in general who is likely

to judge rightly on each class of questions. But such inquiries are like puzzling over the question whether we

are now asleep or awake. And all such questions have the same meaning. These people demand that a reason

shall be given for everything; for they seek a startingpoint, and they seek to get this by demonstration, while

it is obvious from their actions that they have no conviction. But their mistake is what we have stated it to be;

they seek a reason for things for which no reason can be given; for the startingpoint of demonstration is not

These, then, might be easily persuaded of this truth, for it is not difficult to grasp; but those who seek merely

compulsion in argument seek what is impossible; for they demand to be allowed to contradict themselvesa

claim which contradicts itself from the very first.But if not all things are relative, but some are selfexistent,

not everything that appears will be true; for that which appears is apparent to some one; so that he who says

all things that appear are true, makes all things relative. And, therefore, those who ask for an irresistible

argument, and at the same time demand to be called to account for their views, must guard themselves by

saying that the truth is not that what appears exists, but that what appears exists for him to whom it appears,

and when, and to the sense to which, and under the conditions under which it appears. And if they give an

account of their view, but do not give it in this way, they will soon find themselves contradicting themselves.

For it is possible that the same thing may appear to be honey to the sight, but not to the taste, and that, since

we have two eyes, things may not appear the same to each, if their sight is unlike. For to those who for the

reasons named some time ago say that what appears is true, and therefore that all things are alike false and

true, for things do not appear either the same to all men or always the same to the same man, but often have

contrary appearances at the same time (for touch says there are two objects when we cross our fingers, while

sight says there is one)to these we shall say 'yes, but not to the same sense and in the same part of it and

under the same conditions and at the same time', so that what appears will be with these qualifications true.

But perhaps for this reason those who argue thus not because they feel a difficulty but for the sake of

argument, should say that this is not true, but true for this man. And as has been said before, they must make

everything relativerelative to opinion and perception, so that nothing either has come to be or will be

without some one's first thinking so. But if things have come to be or will be, evidently not all things will be

relative to opinion.Again, if a thing is one, it is in relation to one thing or to a definite number of things; and

if the same thing is both half and equal, it is not to the double that the equal is correlative. If, then, in relation

to that which thinks, man and that which is thought are the same, man will not be that which thinks, but only

that which is thought. And if each thing is to be relative to that which thinks, that which thinks will be

Let this, then, suffice to show (1) that the most indisputable of all beliefs is that contradictory statements are

not at the same time true, and (2) what consequences follow from the assertion that they are, and (3) why

people do assert this. Now since it is impossible that contradictories should be at the same time true of the

same thing, obviously contraries also cannot belong at the same time to the same thing. For of contraries, one

is a privation no less than it is a contraryand a privation of the essential nature; and privation is the denial of

a predicate to a determinate genus. If, then, it is impossible to affirm and deny truly at the same time, it is also

impossible that contraries should belong to a subject at the same time, unless both belong to it in particular

But on the other hand there cannot be an intermediate between contradictories, but of one subject we must

either affirm or deny any one predicate. This is clear, in the first place, if we define what the true and the false

are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of

what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what

is true or what is false; but neither what is nor what is not is said to be or not to be.Again, the intermediate

between the contradictories will be so either in the way in which grey is between black and white, or as that

which is neither man nor horse is between man and horse. (a) If it were of the latter kind, it could not change

into the extremes (for change is from notgood to good, or from good to notgood), but as a matter of fact

when there is an intermediate it is always observed to change into the extremes. For there is no change except

to opposites and to their intermediates. (b) But if it is really intermediate, in this way too there would have to

be a change to white, which was not from notwhite; but as it is, this is never seen.Again, every object of

understanding or reason the understanding either affirms or deniesthis is obvious from the

definitionwhenever it says what is true or false. When it connects in one way by assertion or negation, it

says what is true, and when it does so in another way, what is false.Again, there must be an intermediate

between all contradictories, if one is not arguing merely for the sake of argument; so that it will be possible

for a man to say what is neither true nor untrue, and there will be a middle between that which is and that

which is not, so that there will also be a kind of change intermediate between generation and

destruction.Again, in all classes in which the negation of an attribute involves the assertion of its contrary,

even in these there will be an intermediate; for instance, in the sphere of numbers there will be number which

is neither odd nor notodd. But this is impossible, as is obvious from the definition.Again, the process will

go on ad infinitum, and the number of realities will be not only half as great again, but even greater. For again

it will be possible to deny this intermediate with reference both to its assertion and to its negation, and this

new term will be some definite thing; for its essence is something different.Again, when a man, on being

asked whether a thing is white, says 'no', he has denied nothing except that it is; and its not being is a

Some people have acquired this opinion as other paradoxical opinions have been acquired; when men cannot

refute eristical arguments, they give in to the argument and agree that the conclusion is true. This, then, is

why some express this view; others do so because they demand a reason for everything. And the

startingpoint in dealing with all such people is definition. Now the definition rests on the necessity of their

meaning something; for the form of words of which the word is a sign will be its definition.While the

doctrine of Heraclitus, that all things are and are not, seems to make everything true, that of Anaxagoras, that

there is an intermediate between the terms of a contradiction, seems to make everything false; for when

things are mixed, the mixture is neither good nor notgood, so that one cannot say anything that is true.

In view of these distinctions it is obvious that the onesided theories which some people express about all

things cannot be validon the one hand the theory that nothing is true (for, say they, there is nothing to

prevent every statement from being like the statement 'the diagonal of a square is commensurate with the

side'), on the other hand the theory that everything is true. These views are practically the same as that of

Heraclitus; for he who says that all things are true and all are false also makes each of these statements

separately, so that since they are impossible, the double statement must be impossible too.Again, there are

obviously contradictories which cannot be at the same time truenor on the other hand can all statements be

false; yet this would seem more possible in the light of what has been said.But against all such views we

must postulate, as we said above,' not that something is or is not, but that something has a meaning, so that

we must argue from a definition, viz. by assuming what falsity or truth means. If that which it is true to affirm

is nothing other than that which it is false to deny, it is impossible that all statements should be false; for one

side of the contradiction must be true. Again, if it is necessary with regard to everything either to assert or to

deny it, it is impossible that both should be false; for it is one side of the contradiction that is false.Therefore

all such views are also exposed to the often expressed objection, that they destroy themselves. For he who

says that everything is true makes even the statement contrary to his own true, and therefore his own not true

(for the contrary statement denies that it is true), while he who says everything is false makes himself also

false.And if the former person excepts the contrary statement, saying it alone is not true, while the latter

excepts his own as being not false, none the less they are driven to postulate the truth or falsity of an infinite

number of statements; for that which says the true statement is true is true, and this process will go on to

Evidently, again, those who say all things are at rest are not right, nor are those who say all things are in

movement. For if all things are at rest, the same statements will always be true and the same always

false,but this obviously changes; for he who makes a statement, himself at one time was not and again will

not be. And if all things are in motion, nothing will be true; everything therefore will be false. But it has been

shown that this is impossible. Again, it must be that which is that changes; for change is from something to

something. But again it is not the case that all things are at rest or in motion sometimes, and nothing for ever;

for there is something which always moves the things that are in motion, and the first mover is itself

'BEGINNING' means (1) that part of a thing from which one would start first, e.g a line or a road has a

beginning in either of the contrary directions. (2) That from which each thing would best be originated, e.g.

even in learning we must sometimes begin not from the first point and the beginning of the subject, but from

the point from which we should learn most easily. (4) That from which, as an immanent part, a thing first

comes to be, e,g, as the keel of a ship and the foundation of a house, while in animals some suppose the heart,

others the brain, others some other part, to be of this nature. (4) That from which, not as an immanent part, a

thing first comes to be, and from which the movement or the change naturally first begins, as a child comes

from its father and its mother, and a fight from abusive language. (5) That at whose will that which is moved

is moved and that which changes changes, e.g. the magistracies in cities, and oligarchies and monarchies and

tyrannies, are called arhchai, and so are the arts, and of these especially the architectonic arts. (6) That from

which a thing can first be known,this also is called the beginning of the thing, e.g. the hypotheses are the

beginnings of demonstrations. (Causes are spoken of in an equal number of senses; for all causes are

beginnings.) It is common, then, to all beginnings to be the first point from which a thing either is or comes to

be or is known; but of these some are immanent in the thing and others are outside. Hence the nature of a

thing is a beginning, and so is the element of a thing, and thought and will, and essence, and the final

causefor the good and the beautiful are the beginning both of the knowledge and of the movement of many

'Cause' means (1) that from which, as immanent material, a thing comes into being, e.g. the bronze is the

cause of the statue and the silver of the saucer, and so are the classes which include these. (2) The form or

pattern, i.e. the definition of the essence, and the classes which include this (e.g. the ratio 2:1 and number in

general are causes of the octave), and the parts included in the definition. (3) That from which the change or

the resting from change first begins; e.g. the adviser is a cause of the action, and the father a cause of the

child, and in general the maker a cause of the thing made and the changeproducing of the changing. (4) The

end, i.e. that for the sake of which a thing is; e.g. health is the cause of walking. For 'Why does one walk?' we

say; 'that one may be healthy'; and in speaking thus we think we have given the cause. The same is true of all

the means that intervene before the end, when something else has put the process in motion, as e.g. thinning

or purging or drugs or instruments intervene before health is reached; for all these are for the sake of the end,

though they differ from one another in that some are instruments and others are actions.

These, then, are practically all the senses in which causes are spoken of, and as they are spoken of in several

senses it follows both that there are several causes of the same thing, and in no accidental sense (e.g. both the

art of sculpture and the bronze are causes of the statue not in respect of anything else but qua statue; not,

however, in the same way, but the one as matter and the other as source of the movement), and that things

can be causes of one another (e.g. exercise of good condition, and the latter of exercise; not, however, in the

same way, but the one as end and the other as source of movement).Again, the same thing is the cause of

contraries; for that which when present causes a particular thing, we sometimes charge, when absent, with the

contrary, e.g. we impute the shipwreck to the absence of the steersman, whose presence was the cause of

safety; and boththe presence and the privationare causes as sources of movement.

All the causes now mentioned fall under four senses which are the most obvious. For the letters are the cause

of syllables, and the material is the cause of manufactured things, and fire and earth and all such things are

the causes of bodies, and the parts are causes of the whole, and the hypotheses are causes of the conclusion,

in the sense that they are that out of which these respectively are made; but of these some are cause as the

substratum (e.g. the parts), others as the essence (the whole, the synthesis, and the form). The semen, the

physician, the adviser, and in general the agent, are all sources of change or of rest. The remainder are causes

as the end and the good of the other things; for that for the sake of which other things are tends to be the best

and the end of the other things; let us take it as making no difference whether we call it good or apparent

These, then, are the causes, and this is the number of their kinds, but the varieties of causes are many in

number, though when summarized these also are comparatively few. Causes are spoken of in many senses,

and even of those which are of the same kind some are causes in a prior and others in a posterior sense, e.g.

both 'the physician' and 'the professional man' are causes of health, and both 'the ratio 2:1' and 'number' are

causes of the octave, and the classes that include any particular cause are always causes of the particular

effect. Again, there are accidental causes and the classes which include these; e.g. while in one sense 'the

sculptor' causes the statue, in another sense 'Polyclitus' causes it, because the sculptor happens to be

Polyclitus; and the classes that include the accidental cause are also causes, e.g. 'man'or in general

'animal'is the cause of the statue, because Polyclitus is a man, and man is an animal. Of accidental causes

also some are more remote or nearer than others, as, for instance, if 'the white' and 'the musical' were called

causes of the statue, and not only 'Polyclitus' or 'man'. But besides all these varieties of causes, whether

proper or accidental, some are called causes as being able to act, others as acting; e.g. the cause of the house's

being built is a builder, or a builder who is building.The same variety of language will be found with regard

to the effects of causes; e.g. a thing may be called the cause of this statue or of a statue or in general of an

image, and of this bronze or of bronze or of matter in general; and similarly in the case of accidental effects.

Again, both accidental and proper causes may be spoken of in combination; e.g. we may say not 'Polyclitus'

nor 'the sculptor' but 'Polyclitus the sculptor'. Yet all these are but six in number, while each is spoken of in

two ways; for (A) they are causes either as the individual, or as the genus, or as the accidental, or as the genus

that includes the accidental, and these either as combined, or as taken simply; and (B) all may be taken as

acting or as having a capacity. But they differ inasmuch as the acting causes, i.e. the individuals, exist, or do

not exist, simultaneously with the things of which they are causes, e.g. this particular man who is healing,

with this particular man who is recovering health, and this particular builder with this particular thing that is

being built; but the potential causes are not always in this case; for the house does not perish at the same time

'Element' means (1) the primary component immanent in a thing, and indivisible in kind into other kinds; e.g.

the elements of speech are the parts of which speech consists and into which it is ultimately divided, while

they are no longer divided into other forms of speech different in kind from them. If they are divided, their

parts are of the same kind, as a part of water is water (while a part of the syllable is not a syllable). Similarly

those who speak of the elements of bodies mean the things into which bodies are ultimately divided, while

they are no longer divided into other things differing in kind; and whether the things of this sort are one or

more, they call these elements. The socalled elements of geometrical proofs, and in general the elements of

demonstrations, have a similar character; for the primary demonstrations, each of which is implied in many

demonstrations, are called elements of demonstrations; and the primary syllogisms, which have three terms

(2) People also transfer the word 'element' from this meaning and apply it to that which, being one and small,

is useful for many purposes; for which reason what is small and simple and indivisible is called an element.

Hence come the facts that the most universal things are elements (because each of them being one and simple

is present in a plurality of things, either in all or in as many as possible), and that unity and the point are

thought by some to be first principles. Now, since the socalled genera are universal and indivisible (for there

is no definition of them), some say the genera are elements, and more so than the differentia, because the

genus is more universal; for where the differentia is present, the genus accompanies it, but where the genus is

present, the differentia is not always so. It is common to all the meanings that the element of each thing is the

'Nature' means (1) the genesis of growing thingsthe meaning which would be suggested if one were to

pronounce the 'u' in phusis long. (2) That immanent part of a growing thing, from which its growth first

proceeds. (3) The source from which the primary movement in each natural object is present in it in virtue of

its own essence. Those things are said to grow which derive increase from something else by contact and

either by organic unity, or by organic adhesion as in the case of embryos. Organic unity differs from contact;

for in the latter case there need not be anything besides the contact, but in organic unities there is something

identical in both parts, which makes them grow together instead of merely touching, and be one in respect of

continuity and quantity, though not of quality.(4) 'Nature' means the primary material of which any natural

object consists or out of which it is made, which is relatively unshaped and cannot be changed from its own

potency, as e.g. bronze is said to be the nature of a statue and of bronze utensils, and wood the nature of

wooden things; and so in all other cases; for when a product is made out of these materials, the first matter is

preserved throughout. For it is in this way that people call the elements of natural objects also their nature,

some naming fire, others earth, others air, others water, others something else of the sort, and some naming

more than one of these, and others all of them.(5) 'Nature' means the essence of natural objects, as with

those who say the nature is the primary mode of composition, or as Empedocles says:

Hence as regards the things that are or come to be by nature, though that from which they naturally come to

be or are is already present, we say they have not their nature yet, unless they have their form or shape. That

which comprises both of these exists by nature, e.g. the animals and their parts; and not only is the first

matter nature (and this in two senses, either the first, counting from the thing, or the first in general; e.g. in

the case of works in bronze, bronze is first with reference to them, but in general perhaps water is first, if all

things that can be melted are water), but also the form or essence, which is the end of the process of

becoming.(6) By an extension of meaning from this sense of 'nature' every essence in general has come to

From what has been said, then, it is plain that nature in the primary and strict sense is the essence of things

which have in themselves, as such, a source of movement; for the matter is called the nature because it is

qualified to receive this, and processes of becoming and growing are called nature because they are

movements proceeding from this. And nature in this sense is the source of the movement of natural objects,

We call 'necessary' (1) (a) that without which, as a condition, a thing cannot live; e.g. breathing and food are

necessary for an animal; for it is incapable of existing without these; (b) the conditions without which good

cannot be or come to be, or without which we cannot get rid or be freed of evil; e.g. drinking the medicine is

necessary in order that we may be cured of disease, and a man's sailing to Aegina is necessary in order that he

may get his money.(2) The compulsory and compulsion, i.e. that which impedes and tends to hinder,

contrary to impulse and purpose. For the compulsory is called necessary (whence the necessary is painful, as

Evenus says: 'For every necessary thing is ever irksome'), and compulsion is a form of necessity, as

Sophocles says: 'But force necessitates me to this act'. And necessity is held to be something that cannot be

persuadedand rightly, for it is contrary to the movement which accords with purpose and with

reasoning.(3) We say that that which cannot be otherwise is necessarily as it is. And from this sense of

'necessary' all the others are somehow derived; for a thing is said to do or suffer what is necessary in the

sense of compulsory, only when it cannot act according to its impulse because of the compelling

forceswhich implies that necessity is that because of which a thing cannot be otherwise; and similarly as

regards the conditions of life and of good; for when in the one case good, in the other life and being, are not

possible without certain conditions, these are necessary, and this kind of cause is a sort of necessity. Again,

demonstration is a necessary thing because the conclusion cannot be otherwise, if there has been

demonstration in the unqualified sense; and the causes of this necessity are the first premisses, i.e. the fact

Now some things owe their necessity to something other than themselves; others do not, but are themselves

the source of necessity in other things. Therefore the necessary in the primary and strict sense is the simple;

for this does not admit of more states than one, so that it cannot even be in one state and also in another; for if

it did it would already be in more than one. If, then, there are any things that are eternal and unmovable,

'One' means (1) that which is one by accident, (2) that which is one by its own nature. (1) Instances of the

accidentally one are 'Coriscus and what is musical', and 'musical Coriscus' (for it is the same thing to say

'Coriscus and what is musical', and 'musical Coriscus'), and 'what is musical and what is just', and 'musical

Coriscus and just Coriscus'. For all of these are called one by virtue of an accident, 'what is just and what is

musical' because they are accidents of one substance, 'what is musical and Coriscus' because the one is an

accident of the other; and similarly in a sense 'musical Coriscus' is one with 'Coriscus' because one of the

parts of the phrase is an accident of the other, i.e. 'musical' is an accident of Coriscus; and 'musical Coriscus'

is one with 'just Coriscus' because one part of each is an accident of one and the same subject. The case is

similar if the accident is predicated of a genus or of any universal name, e.g. if one says that man is the same

as 'musical man'; for this is either because 'musical' is an accident of man, which is one substance, or because

both are accidents of some individual, e.g. Coriscus. Both, however, do not belong to him in the same way,

but one presumably as genus and included in his substance, the other as a state or affection of the substance.

The things, then, that are called one in virtue of an accident, are called so in this way. (2) Of things that are

called one in virtue of their own nature some (a) are so called because they are continuous, e.g. a bundle is

made one by a band, and pieces of wood are made one by glue; and a line, even if it is bent, is called one if it

is continuous, as each part of the body is, e.g. the leg or the arm. Of these themselves, the continuous by

nature are more one than the continuous by art. A thing is called continuous which has by its own nature one

movement and cannot have any other; and the movement is one when it is indivisible, and it is indivisible in

respect of time. Those things are continuous by their own nature which are one not merely by contact; for if

you put pieces of wood touching one another, you will not say these are one piece of wood or one body or

one continuum of any other sort. Things, then, that are continuous in any way called one, even if they admit

of being bent, and still more those which cannot be bent; e.g. the shin or the thigh is more one than the leg,

because the movement of the leg need not be one. And the straight line is more one than the bent; but that

which is bent and has an angle we call both one and not one, because its movement may be either

simultaneous or not simultaneous; but that of the straight line is always simultaneous, and no part of it which

(b)(i) Things are called one in another sense because their substratum does not differ in kind; it does not

differ in the case of things whose kind is indivisible to sense. The substratum meant is either the nearest to, or

the farthest from, the final state. For, one the one hand, wine is said to be one and water is said to be one, qua

indivisible in kind; and, on the other hand, all juices, e.g. oil and wine, are said to be one, and so are all things

that can be melted, because the ultimate substratum of all is the same; for all of these are water or air.

(ii) Those things also are called one whose genus is one though distinguished by opposite differentiaethese

too are all called one because the genus which underlies the differentiae is one (e.g. horse, man, and dog form

a unity, because all are animals), and indeed in a way similar to that in which the matter is one. These are

sometimes called one in this way, but sometimes it is the higher genus that is said to be the same (if they are

infimae species of their genus)the genus above the proximate genera; e.g. the isosceles and the equilateral

are one and the same figure because both are triangles; but they are not the same triangles.

definition which shows us the other (though in itself every definition is divisible). Thus even that which has

increased or is diminishing is one, because its definition is one, as, in the case of plane figures, is the

definition of their form. In general those things the thought of whose essence is indivisible, and cannot

separate them either in time or in place or in definition, are most of all one, and of these especially those

which are substances. For in general those things that do not admit of division are called one in so far as they

do not admit of it; e.g. if two things are indistinguishable qua man, they are one kind of man; if qua animal,

one kind of animal; if qua magnitude, one kind of magnitude.Now most things are called one because they

either do or have or suffer or are related to something else that is one, but the things that are primarily called

one are those whose substance is one,and one either in continuity or in form or in definition; for we count as

more than one either things that are not continuous, or those whose form is not one, or those whose definition

While in a sense we call anything one if it is a quantity and continuous, in a sense we do not unless it is a

whole, i.e. unless it has unity of form; e.g. if we saw the parts of a shoe put together anyhow we should not

call them one all the same (unless because of their continuity); we do this only if they are put together so as to

be a shoe and to have already a certain single form. This is why the circle is of all lines most truly one,

(3) The essence of what is one is to be some kind of beginning of number; for the first measure is the

beginning, since that by which we first know each class is the first measure of the class; the one, then, is the

beginning of the knowable regarding each class. But the one is not the same in all classes. For here it is a

quartertone, and there it is the vowel or the consonant; and there is another unit of weight and another of

movement. But everywhere the one is indivisible either in quantity or in kind. Now that which is indivisible

in quantity is called a unit if it is not divisible in any dimension and is without position, a point if it is not

divisible in any dimension and has position, a line if it is divisible in one dimension, a plane if in two, a body

if divisible in quantity in alli.e. in threedimensions. And, reversing the order, that which is divisible in

two dimensions is a plane, that which is divisible in one a line, that which is in no way divisible in quantity is

a point or a unit,that which has not position a unit, that which has position a point.

Again, some things are one in number, others in species, others in genus, others by analogy; in number those

whose matter is one, in species those whose definition is one, in genus those to which the same figure of

predication applies, by analogy those which are related as a third thing is to a fourth. The latter kinds of unity

are always found when the former are; e.g. things that are one in number are also one in species, while things

that are one in species are not all one in number; but things that are one in species are all one in genus, while

things that are so in genus are not all one in species but are all one by analogy; while things that are one by

Evidently 'many' will have meanings opposite to those of 'one'; some things are many because they are not

continuous, others because their mattereither the proximate matter or the ultimateis divisible in kind,

(1) In an accidental sense, e.g. we say 'the righteous doer is musical', and 'the man is musical', and 'the

musician is a man', just as we say 'the musician builds', because the builder happens to be musical or the

musician to be a builder; for here 'one thing is another' means 'one is an accident of another'. So in the cases

we have mentioned; for when we say 'the man is musical' and 'the musician is a man', or 'he who is pale is

musical' or 'the musician is pale', the last two mean that both attributes are accidents of the same thing; the

first that the attribute is an accident of that which is, while 'the musical is a man' means that 'musical' is an

accident of a man. (In this sense, too, the notpale is said to be, because that of which it is an accident is.)

Thus when one thing is said in an accidental sense to be another, this is either because both belong to the

same thing, and this is, or because that to which the attribute belongs is, or because the subject which has as

(2) The kinds of essential being are precisely those that are indicated by the figures of predication; for the

senses of 'being' are just as many as these figures. Since, then, some predicates indicate what the subject is,

others its quality, others quantity, others relation, others activity or passivity, others its 'where', others its

'when', 'being' has a meaning answering to each of these. For there is no difference between 'the man is

recovering' and 'the man recovers', nor between 'the man is walking or cutting' and 'the man walks' or 'cuts';

(3) Again, 'being' and 'is' mean that a statement is true, 'not being' that it is not true but falsesand this alike in

the case of affirmation and of negation; e.g. 'Socrates is musical' means that this is true, or 'Socrates is

notpale' means that this is true; but 'the diagonal of the square is not commensurate with the side' means that

(4) Again, 'being' and 'that which is' mean that some of the things we have mentioned 'are' potentially, others

in complete reality. For we say both of that which sees potentially and of that which sees actually, that it is

'seeing', and both of that which can actualize its knowledge and of that which is actualizing it, that it knows,

and both of that to which rest is already present and of that which can rest, that it rests. And similarly in the

case of substances; we say the Hermes is in the stone, and the half of the line is in the line, and we say of that

which is not yet ripe that it is corn. When a thing is potential and when it is not yet potential must be

We call 'substance' (1) the simple bodies, i.e. earth and fire and water and everything of the sort, and in

general bodies and the things composed of them, both animals and divine beings, and the parts of these. All

these are called substance because they are not predicated of a subject but everything else is predicated of

them.(2) That which, being present in such things as are not predicated of a subject, is the cause of their

being, as the soul is of the being of an animal.(3) The parts which are present in such things, limiting them

and marking them as individuals, and by whose destruction the whole is destroyed, as the body is by the

destruction of the plane, as some say, and the plane by the destruction of the line; and in general number is

thought by some to be of this nature; for if it is destroyed, they say, nothing exists, and it limits all things.(4)

The essence, the formula of which is a definition, is also called the substance of each thing.

It follows, then, that 'substance' has two senses, (A) ultimate substratum, which is no longer predicated of

anything else, and (B) that which, being a 'this', is also separable and of this nature is the shape or form of

'The same' means (1) that which is the same in an accidental sense, e.g. 'the pale' and 'the musical' are the

same because they are accidents of the same thing, and 'a man' and 'musical' because the one is an accident of

the other; and 'the musical' is 'a man' because it is an accident of the man. (The complex entity is the same as

either of the simple ones and each of these is the same as it; for both 'the man' and 'the musical' are said to be

the same as 'the musical man', and this the same as they.) This is why all of these statements are made not

universally; for it is not true to say that every man is the same as 'the musical' (for universal attributes belong

to things in virtue of their own nature, but accidents do not belong to them in virtue of their own nature); but

of the individuals the statements are made without qualification. For 'Socrates' and 'musical Socrates' are

thought to be the same; but 'Socrates' is not predicable of more than one subject, and therefore we do not say

Some things are said to be the same in this sense, others (2) are the same by their own nature, in as many

senses as that which is one by its own nature is so; for both the things whose matter is one either in kind or in

number, and those whose essence is one, are said to be the same. Clearly, therefore, sameness is a unity of the

being either of more than one thing or of one thing when it is treated as more than one, ie. when we say a

Things are called 'other' if either their kinds or their matters or the definitions of their essence are more than

'Different' is applied (1) to those things which though other are the same in some respect, only not in number

but either in species or in genus or by analogy; (2) to those whose genus is other, and to contraries, and to an

Those things are called 'like' which have the same attributes in every respect, and those which have more

attributes the same than different, and those whose quality is one; and that which shares with another thing

the greater number or the more important of the attributes (each of them one of two contraries) in respect of

which things are capable of altering, is like that other thing. The senses of 'unlike' are opposite to those of

The term 'opposite' is applied to contradictories, and to contraries, and to relative terms, and to privation and

possession, and to the extremes from which and into which generation and dissolution take place; and the

attributes that cannot be present at the same time in that which is receptive of both, are said to be

opposed,either themselves of their constituents. Grey and white colour do not belong at the same time to the

The term 'contrary' is applied (1) to those attributes differing in genus which cannot belong at the same time

to the same subject, (2) to the most different of the things in the same genus, (3) to the most different of the

attributes in the same recipient subject, (4) to the most different of the things that fall under the same faculty,

(5) to the things whose difference is greatest either absolutely or in genus or in species. The other things that

are called contrary are so called, some because they possess contraries of the above kind, some because they

are receptive of such, some because they are productive of or susceptible to such, or are producing or

suffering them, or are losses or acquisitions, or possessions or privations, of such. Since 'one' and 'being' have

many senses, the other terms which are derived from these, and therefore 'same', 'other', and 'contrary', must

The term 'other in species' is applied to things which being of the same genus are not subordinate the one to

the other, or which being in the same genus have a difference, or which have a contrariety in their substance;

and contraries are other than one another in species (either all contraries or those which are so called in the

primary sense), and so are those things whose definitions differ in the infima species of the genus (e.g. man

and horse are indivisible in genus, but their definitions are different), and those which being in the same

substance have a difference. 'The same in species' has the various meanings opposite to these.

The words 'prior' and 'posterior' are applied (1) to some things (on the assumption that there is a first, i.e. a

beginning, in each class) because they are nearer some beginning determined either absolutely and by nature,

or by reference to something or in some place or by certain people; e.g. things are prior in place because they

are nearer either to some place determined by nature (e.g. the middle or the last place), or to some chance

object; and that which is farther is posterior.Other things are prior in time; some by being farther from the

present, i.e. in the case of past events (for the Trojan war is prior to the Persian, because it is farther from the

present), others by being nearer the present, i.e. in the case of future events (for the Nemean games are prior

to the Pythian, if we treat the present as beginning and first point, because they are nearer the present).Other

things are prior in movement; for that which is nearer the first mover is prior (e.g. the boy is prior to the

man); and the prime mover also is a beginning absolutely.Others are prior in power; for that which exceeds

in power, i.e. the more powerful, is prior; and such is that according to whose will the otheri.e. the

posteriormust follow, so that if the prior does not set it in motion the other does not move, and if it sets it in

motion it does move; and here will is a beginning.Others are prior in arrangement; these are the things that

are placed at intervals in reference to some one definite thing according to some rule, e.g. in the chorus the

second man is prior to the third, and in the lyre the second lowest string is prior to the lowest; for in the one

These, then, are called prior in this sense, but (2) in another sense that which is prior for knowledge is treated

as also absolutely prior; of these, the things that are prior in definition do not coincide with those that are

prior in relation to perception. For in definition universals are prior, in relation to perception individuals. And

in definition also the accident is prior to the whole, e.g. 'musical' to 'musical man', for the definition cannot

exist as a whole without the part; yet musicalness cannot exist unless there is some one who is musical.

(3) The attributes of prior things are called prior, e.g. straightness is prior to smoothness; for one is an

Some things then are called prior and posterior in this sense, others (4) in respect of nature and substance, i.e.

those which can be without other things, while the others cannot be without them,a distinction which Plato

used. (If we consider the various senses of 'being', firstly the subject is prior, so that substance is prior;

secondly, according as potency or complete reality is taken into account, different things are prior, for some

things are prior in respect of potency, others in respect of complete reality, e.g. in potency the half line is

prior to the whole line, and the part to the whole, and the matter to the concrete substance, but in complete

reality these are posterior; for it is only when the whole has been dissolved that they will exist in complete

reality.) In a sense, therefore, all things that are called prior and posterior are so called with reference to this

fourth sense; for some things can exist without others in respect of generation, e.g. the whole without the

parts, and others in respect of dissolution, e.g. the part without the whole. And the same is true in all other

'Potency' means (1) a source of movement or change, which is in another thing than the thing moved or in the

same thing qua other; e.g. the art of building is a potency which is not in the thing built, while the art of

healing, which is a potency, may be in the man healed, but not in him qua healed. 'Potency' then means the

source, in general, of change or movement in another thing or in the same thing qua other, and also (2) the

source of a thing's being moved by another thing or by itself qua other. For in virtue of that principle, in

virtue of which a patient suffers anything, we call it 'capable' of suffering; and this we do sometimes if it

suffers anything at all, sometimes not in respect of everything it suffers, but only if it suffers a change for the

better(3) The capacity of performing this well or according to intention; for sometimes we say of those

who merely can walk or speak but not well or not as they intend, that they cannot speak or walk. So too (4) in

the case of passivity(5) The states in virtue of which things are absolutely impassive or unchangeable, or

not easily changed for the worse, are called potencies; for things are broken and crushed and bent and in

general destroyed not by having a potency but by not having one and by lacking something, and things are

impassive with respect to such processes if they are scarcely and slightly affected by them, because of a

'Potency' having this variety of meanings, so too the 'potent' or 'capable' in one sense will mean that which

can begin a movement (or a change in general, for even that which can bring things to rest is a 'potent' thing)

in another thing or in itself qua other; and in one sense that over which something else has such a potency;

and in one sense that which has a potency of changing into something, whether for the worse or for the better

(for even that which perishes is thought to be 'capable' of perishing, for it would not have perished if it had

not been capable of it; but, as a matter of fact, it has a certain disposition and cause and principle which fits it

to suffer this; sometimes it is thought to be of this sort because it has something, sometimes because it is

deprived of something; but if privation is in a sense 'having' or 'habit', everything will be capable by having

something, so that things are capable both by having a positive habit and principle, and by having the

privation of this, if it is possible to have a privation; and if privation is not in a sense 'habit', 'capable' is used

in two distinct senses); and a thing is capable in another sense because neither any other thing, nor itself qua

other, has a potency or principle which can destroy it. Again, all of these are capable either merely because

the thing might chance to happen or not to happen, or because it might do so well. This sort of potency is

found even in lifeless things, e.g. in instruments; for we say one lyre can speak, and another cannot speak at

Incapacity is privation of capacityi.e. of such a principle as has been described either in general or in the

case of something that would naturally have the capacity, or even at the time when it would naturally already

have it; for the senses in which we should call a boy and a man and a eunuch 'incapable of begetting' are

distinct.Again, to either kind of capacity there is an opposite incapacityboth to that which only can produce

Some things, then, are called adunata in virtue of this kind of incapacity, while others are so in another sense;

i.e. both dunaton and adunaton are used as follows. The impossible is that of which the contrary is of

necessity true, e.g. that the diagonal of a square is commensurate with the side is impossible, because such a

statement is a falsity of which the contrary is not only true but also necessary; that it is commensurate, then,

is not only false but also of necessity false. The contrary of this, the possible, is found when it is not

necessary that the contrary is false, e.g. that a man should be seated is possible; for that he is not seated is not

of necessity false. The possible, then, in one sense, as has been said, means that which is not of necessity

false; in one, that which is true; in one, that which may be true.A 'potency' or 'power' in geometry is so

called by a change of meaning.These senses of 'capable' or 'possible' involve no reference to potency. But

the senses which involve a reference to potency all refer to the primary kind of potency; and this is a source

of change in another thing or in the same thing qua other. For other things are called 'capable', some because

something else has such a potency over them, some because it has not, some because it has it in a particular

way. The same is true of the things that are incapable. Therefore the proper definition of the primary kind of

potency will be 'a source of change in another thing or in the same thing qua other'.

'Quantum' means that which is divisible into two or more constituent parts of which each is by nature a 'one'

and a 'this'. A quantum is a plurality if it is numerable, a magnitude if it is a measurable. 'Plurality' means that

which is divisible potentially into noncontinuous parts, 'magnitude' that which is divisible into continuous

parts; of magnitude, that which is continuous in one dimension is length; in two breadth, in three depth. Of

these, limited plurality is number, limited length is a line, breadth a surface, depth a solid.

Again, some things are called quanta in virtue of their own nature, others incidentally; e.g. the line is a

quantum by its own nature, the musical is one incidentally. Of the things that are quanta by their own nature

some are so as substances, e.g. the line is a quantum (for 'a certain kind of quantum' is present in the

definition which states what it is), and others are modifications and states of this kind of substance, e.g. much

and little, long and short, broad and narrow, deep and shallow, heavy and light, and all other such attributes.

And also great and small, and greater and smaller, both in themselves and when taken relatively to each other,

are by their own nature attributes of what is quantitative; but these names are transferred to other things also.

Of things that are quanta incidentally, some are so called in the sense in which it was said that the musical

and the white were quanta, viz. because that to which musicalness and whiteness belong is a quantum, and

some are quanta in the way in which movement and time are so; for these also are called quanta of a sort and

continuous because the things of which these are attributes are divisible. I mean not that which is moved, but

the space through which it is moved; for because that is a quantum movement also is a quantum, and because

'Quality' means (1) the differentia of the essence, e.g. man is an animal of a certain quality because he is

twofooted, and the horse is so because it is fourfooted; and a circle is a figure of particular quality because

it is without angles,which shows that the essential differentia is a quality.This, then, is one meaning of

qualitythe differentia of the essence, but (2) there is another sense in which it applies to the unmovable

objects of mathematics, the sense in which the numbers have a certain quality, e.g. the composite numbers

which are not in one dimension only, but of which the plane and the solid are copies (these are those which

have two or three factors); and in general that which exists in the essence of numbers besides quantity is

quality; for the essence of each is what it is once, e.g. that of is not what it is twice or thrice, but what it is

(3) All the modifications of substances that move (e.g. heat and cold, whiteness and blackness, heaviness and

lightness, and the others of the sort) in virtue of which, when they change, bodies are said to alter. (4) Quality

Quality, then, seems to have practically two meanings, and one of these is the more proper. The primary

quality is the differentia of the essence, and of this the quality in numbers is a part; for it is a differentia of

essences, but either not of things that move or not of them qua moving. Secondly, there are the modifications

of things that move, qua moving, and the differentiae of movements. Virtue and vice fall among these

modifications; for they indicate differentiae of the movement or activity, according to which the things in

motion act or are acted on well or badly; for that which can be moved or act in one way is good, and that

which can do so in anotherthe contraryway is vicious. Good and evil indicate quality especially in living

Things are 'relative' (1) as double to half, and treble to a third, and in general that which contains something

else many times to that which is contained many times in something else, and that which exceeds to that

which is exceeded; (2) as that which can heat to that which can be heated, and that which can cut to that

which can be cut, and in general the active to the passive; (3) as the measurable to the measure, and the

(1) Relative terms of the first kind are numerically related either indefinitely or definitely, to numbers

themselves or to 1. E.g. the double is in a definite numerical relation to 1, and that which is 'many times as

great' is in a numerical, but not a definite, relation to 1, i.e. not in this or in that numerical relation to it; the

relation of that which is half as big again as something else to that something is a definite numerical relation

to a number; that which is n+I/n times something else is in an indefinite relation to that something, as that

which is 'many times as great' is in an indefinite relation to 1; the relation of that which exceeds to that which

is exceeded is numerically quite indefinite; for number is always commensurate, and 'number' is not

predicated of that which is not commensurate, but that which exceeds is, in relation to that which is exceeded,

so much and something more; and this something is indefinite; for it can, indifferently, be either equal or not

equal to that which is exceeded.All these relations, then, are numerically expressed and are determinations

of number, and so in another way are the equal and the like and the same. For all refer to unity. Those things

are the same whose substance is one; those are like whose quality is one; those are equal whose quantity is

one; and 1 is the beginning and measure of number, so that all these relations imply number, though not in

(2) Things that are active or passive imply an active or a passive potency and the actualizations of the

potencies; e.g. that which is capable of heating is related to that which is capable of being heated, because it

can heat it, and, again, that which heats is related to that which is heated and that which cuts to that which is

cut, in the sense that they actually do these things. But numerical relations are not actualized except in the

sense which has been elsewhere stated; actualizations in the sense of movement they have not. Of relations

which imply potency some further imply particular periods of time, e.g. that which has made is relative to

that which has been made, and that which will make to that which will be made. For it is in this way that a

father is called the father of his son; for the one has acted and the other has been acted on in a certain way.

Further, some relative terms imply privation of potency, i.e. 'incapable' and terms of this sort, e.g. 'invisible'.

Relative terms which imply number or potency, therefore, are all relative because their very essence includes

in its nature a reference to something else, not because something else involves a reference to it; but (3) that

which is measurable or knowable or thinkable is called relative because something else involves a reference

to it. For 'that which is thinkable' implies that the thought of it is possible, but the thought is not relative to

'that of which it is the thought'; for we should then have said the same thing twice. Similarly sight is the sight

of something, not 'of that of which it is the sight' (though of course it is true to say this); in fact it is relative to

colour or to something else of the sort. But according to the other way of speaking the same thing would be

Things that are by their own nature called relative are called so sometimes in these senses, sometimes if the

classes that include them are of this sort; e.g. medicine is a relative term because its genus, science, is thought

to be a relative term. Further, there are the properties in virtue of which the things that have them are called

relative, e.g. equality is relative because the equal is, and likeness because the like is. Other things are relative

by accident; e.g. a man is relative because he happens to be double of something and double is a relative

term; or the white is relative, if the same thing happens to be double and white.

What is called 'complete' is (1) that outside which it is not possible to find any, even one, of its parts; e.g. the

complete time of each thing is that outside which it is not possible to find any time which is a part proper to

it.(2) That which in respect of excellence and goodness cannot be excelled in its kind; e.g. we have a

complete doctor or a complete fluteplayer, when they lack nothing in respect of the form of their proper

excellence. And thus, transferring the word to bad things, we speak of a complete scandalmonger and a

complete thief; indeed we even call them good, i.e. a good thief and a good scandalmonger. And excellence

is a completion; for each thing is complete and every substance is complete, when in respect of the form of its

proper excellence it lacks no part of its natural magnitude.(3) The things which have attained their end, this

being good, are called complete; for things are complete in virtue of having attained their end. Therefore,

since the end is something ultimate, we transfer the word to bad things and say a thing has been completely

spoilt, and completely destroyed, when it in no wise falls short of destruction and badness, but is at its last

point. This is why death, too, is by a figure of speech called the end, because both are last things. But the

ultimate purpose is also an end.Things, then, that are called complete in virtue of their own nature are so

called in all these senses, some because in respect of goodness they lack nothing and cannot be excelled and

no part proper to them can be found outside them, others in general because they cannot be exceeded in their

several classes and no part proper to them is outside them; the others presuppose these first two kinds, and are

called complete because they either make or have something of the sort or are adapted to it or in some way or

other involve a reference to the things that are called complete in the primary sense.

'Limit' means (1) the last point of each thing, i.e. the first point beyond which it is not possible to find any

part, and the first point within which every part is; (2) the form, whatever it may be, of a spatial magnitude or

of a thing that has magnitude; (3) the end of each thing (and of this nature is that towards which the

movement and the action are, not that from which they arethough sometimes it is both, that from which and

that to which the movement is, i.e. the final cause); (4) the substance of each thing, and the essence of each;

for this is the limit of knowledge; and if of knowledge, of the object also. Evidently, therefore, 'limit' has as

many senses as 'beginning', and yet more; for the beginning is a limit, but not every limit is a beginning.

'That in virtue of which' has several meanings:(1) the form or substance of each thing, e.g. that in virtue of

which a man is good is the good itself, (2) the proximate subject in which it is the nature of an attribute to be

found, e.g. colour in a surface. 'That in virtue of which', then, in the primary sense is the form, and in a

secondary sense the matter of each thing and the proximate substratum of each.In general 'that in virtue of

which' will found in the same number of senses as 'cause'; for we say indifferently (3) in virtue of what has he

come?' or 'for what end has he come?'; and (4) in virtue of what has he inferred wrongly, or inferred?' or

'what is the cause of the inference, or of the wrong inference?'Further (5) Kath' d is used in reference to

position, e.g. 'at which he stands' or 'along which he walks; for all such phrases indicate place and position.

Therefore 'in virtue of itself' must likewise have several meanings. The following belong to a thing in virtue

of itself:(1) the essence of each thing, e.g. Callias is in virtue of himself Callias and what it was to be

Callias;(2) whatever is present in the 'what', e.g. Callias is in virtue of himself an animal. For 'animal' is

present in his definition; Callias is a particular animal.(3) Whatever attribute a thing receives in itself

directly or in one of its parts; e.g. a surface is white in virtue of itself, and a man is alive in virtue of himself;

for the soul, in which life directly resides, is a part of the man.(4) That which has no cause other than itself;

man has more than one causeanimal, twofootedbut yet man is man in virtue of himself.(5) Whatever

attributes belong to a thing alone, and in so far as they belong to it merely by virtue of itself considered apart

'Disposition' means the arrangement of that which has parts, in respect either of place or of potency or of

kind; for there must be a certain position, as even the word 'disposition' shows.

'Having' means (1) a kind of activity of the haver and of what he hassomething like an action or movement.

For when one thing makes and one is made, between them there is a making; so too between him who has a

garment and the garment which he has there is a having. This sort of having, then, evidently we cannot have;

for the process will go on to infinity, if it is to be possible to have the having of what we have.(2) 'Having'

or 'habit' means a disposition according to which that which is disposed is either well or ill disposed, and

either in itself or with reference to something else; e.g. health is a 'habit'; for it is such a disposition.(3) We

speak of a 'habit' if there is a portion of such a disposition; and so even the excellence of the parts is a 'habit'

'Affection' means (1) a quality in respect of which a thing can be altered, e.g. white and black, sweet and

bitter, heaviness and lightness, and all others of the kind.(2) The actualization of thesethe already

accomplished alterations.(3) Especially, injurious alterations and movements, and, above all painful

injuries.(4) Misfortunes and painful experiences when on a large scale are called affections.

We speak of 'privation' (1) if something has not one of the attributes which a thing might naturally have, even

if this thing itself would not naturally have it; e.g. a plant is said to be 'deprived' of eyes.(2) If, though either

the thing itself or its genus would naturally have an attribute, it has it not; e.g. a blind man and a mole are in

different senses 'deprived' of sight; the latter in contrast with its genus, the former in contrast with his own

normal nature.(3) If, though it would naturally have the attribute, and when it would naturally have it, it has

it not; for blindness is a privation, but one is not 'blind' at any and every age, but only if one has not sight at

the age at which one would naturally have it. Similarly a thing is called blind if it has not sight in the medium

in which, and in respect of the organ in respect of which, and with reference to the object with reference to

which, and in the circumstances in which, it would naturally have it.(4) The violent taking away of anything

Indeed there are just as many kinds of privations as there are of words with negative prefixes; for a thing is

called unequal because it has not equality though it would naturally have it, and invisible either because it has

no colour at all or because it has a poor colour, and apodous either because it has no feet at all or because it

has imperfect feet. Again, a privative term may be used because the thing has little of the attribute (and this

means having it in a sense imperfectly), e.g. 'kernelless'; or because it has it not easily or not well (e.g. we

call a thing uncuttable not only if it cannot be cut but also if it cannot be cut easily or well); or because it has

not the attribute at all; for it is not the oneeyed man but he who is sightless in both eyes that is called blind.

This is why not every man is 'good' or 'bad', 'just' or 'unjust', but there is also an intermediate state.

To 'have' or 'hold' means many things:(1) to treat a thing according to one's own nature or according to one's

own impulse; so that fever is said to have a man, and tyrants to have their cities, and people to have the

clothes they wear.(2) That in which a thing is present as in something receptive of it is said to have the

thing; e.g. the bronze has the form of the statue, and the body has the disease.(3) As that which contains

holds the things contained; for a thing is said to be held by that in which it is as in a container; e.g. we say

that the vessel holds the liquid and the city holds men and the ship sailors; and so too that the whole holds the

parts.(4) That which hinders a thing from moving or acting according to its own impulse is said to hold it, as

pillars hold the incumbent weights, and as the poets make Atlas hold the heavens, implying that otherwise

they would collapse on the earth, as some of the natural philosophers also say. In this way also that which

holds things together is said to hold the things it holds together, since they would otherwise separate, each

'Being in something' has similar and corresponding meanings to 'holding' or 'having'.

'To come from something' means (1) to come from something as from matter, and this in two senses, either in

respect of the highest genus or in respect of the lowest species; e.g. in a sense all things that can be melted

come from water, but in a sense the statue comes from bronze.(2) As from the first moving principle; e.g.

'what did the fight come from?' From abusive language, because this was the origin of the fight.(3) From the

compound of matter and shape, as the parts come from the whole, and the verse from the Iliad, and the stones

from the house; (in every such case the whole is a compound of matter and shape,) for the shape is the end,

and only that which attains an end is complete.(4) As the form from its part, e.g. man from 'twofooted'and

syllable from 'letter'; for this is a different sense from that in which the statue comes from bronze; for the

composite substance comes from the sensible matter, but the form also comes from the matter of the

form.Some things, then, are said to come from something else in these senses; but (5) others are so

described if one of these senses is applicable to a part of that other thing; e.g. the child comes from its father

and mother, and plants come from the earth, because they come from a part of those things.(6) It means

coming after a thing in time, e.g. night comes from day and storm from fine weather, because the one comes

after the other. Of these things some are so described because they admit of change into one another, as in the

cases now mentioned; some merely because they are successive in time, e.g. the voyage took place 'from' the

equinox, because it took place after the equinox, and the festival of the Thargelia comes 'from' the Dionysia,

'Part' means (1) (a) that into which a quantum can in any way be divided; for that which is taken from a

quantum qua quantum is always called a part of it, e.g. two is called in a sense a part of three. It means (b), of

the parts in the first sense, only those which measure the whole; this is why two, though in one sense it is, in

another is not, called a part of three.(2) The elements into which a kind might be divided apart from the

quantity are also called parts of it; for which reason we say the species are parts of the genus.(3) The

elements into which a whole is divided, or of which it consiststhe 'whole' meaning either the form or that

which has the form; e.g. of the bronze sphere or of the bronze cube both the bronzei.e. the matter in which

the form isand the characteristic angle are parts.(4) The elements in the definition which explains a thing

are also parts of the whole; this is why the genus is called a part of the species, though in another sense the

'A whole' means (1) that from which is absent none of the parts of which it is said to be naturally a whole, and

(2) that which so contains the things it contains that they form a unity; and this in two senseseither as being

each severally one single thing, or as making up the unity between them. For (a) that which is true of a whole

class and is said to hold good as a whole (which implies that it is a kind whole) is true of a whole in the sense

that it contains many things by being predicated of each, and by all of them, e.g. man, horse, god, being

severally one single thing, because all are living things. But (b) the continuous and limited is a whole, when it

is a unity consisting of several parts, especially if they are present only potentially, but, failing this, even if

they are present actually. Of these things themselves, those which are so by nature are wholes in a higher

degree than those which are so by art, as we said in the case of unity also, wholeness being in fact a sort of

Again (3) of quanta that have a beginning and a middle and an end, those to which the position does not make

a difference are called totals, and those to which it does, wholes. Those which admit of both descriptions are

both wholes and totals. These are the things whose nature remains the same after transposition, but whose

form does not, e.g. wax or a coat; they are called both wholes and totals; for they have both characteristics.

Water and all liquids and number are called totals, but 'the whole number' or 'the whole water' one does not

speak of, except by an extension of meaning. To things, to which qua one the term 'total' is applied, the term

'all' is applied when they are treated as separate; 'this total number,' 'all these units.'

It is not any chance quantitative thing that can be said to be 'mutilated'; it must be a whole as well as

divisible. For not only is two not 'mutilated' if one of the two ones is taken away (for the part removed by

mutilation is never equal to the remainder), but in general no number is thus mutilated; for it is also necessary

that the essence remain; if a cup is mutilated, it must still be a cup; but the number is no longer the same.

Further, even if things consist of unlike parts, not even these things can all be said to be mutilated, for in a

sense a number has unlike parts (e.g. two and three) as well as like; but in general of the things to which their

position makes no difference, e.g. water or fire, none can be mutilated; to be mutilated, things must be such

as in virtue of their essence have a certain position. Again, they must be continuous; for a musical scale

consists of unlike parts and has position, but cannot become mutilated. Besides, not even the things that are

wholes are mutilated by the privation of any part. For the parts removed must be neither those which

determine the essence nor any chance parts, irrespective of their position; e.g. a cup is not mutilated if it is

bored through, but only if the handle or a projecting part is removed, and a man is mutilated not if the flesh or

the spleen is removed, but if an extremity is, and that not every extremity but one which when completely

The term 'race' or 'genus' is used (1) if generation of things which have the same form is continuous, e.g.

'while the race of men lasts' means 'while the generation of them goes on continuously'.(2) It is used with

reference to that which first brought things into existence; for it is thus that some are called Hellenes by race

and others Ionians, because the former proceed from Hellen and the latter from Ion as their first begetter. And

the word is used in reference to the begetter more than to the matter, though people also get a racename

from the female, e.g. 'the descendants of Pyrrha'.(3) There is genus in the sense in which 'plane' is the genus

of plane figures and solid' of solids; for each of the figures is in the one case a plane of such and such a kind,

and in the other a solid of such and such a kind; and this is what underlies the differentiae. Again (4) in

definitions the first constituent element, which is included in the 'what', is the genus, whose differentiae the

qualities are said to be 'Genus' then is used in all these ways, (1) in reference to continuous generation of the

same kind, (2) in reference to the first mover which is of the same kind as the things it moves, (3) as matter;

for that to which the differentia or quality belongs is the substratum, which we call matter.

Those things are said to be 'other in genus' whose proximate substratum is different, and which are not

analysed the one into the other nor both into the same thing (e.g. form and matter are different in genus); and

things which belong to different categories of being (for some of the things that are said to 'be' signify

essence, others a quality, others the other categories we have before distinguished); these also are not

'The false' means (1) that which is false as a thing, and that (a) because it is not put together or cannot be put

together, e.g. 'that the diagonal of a square is commensurate with the side' or 'that you are sitting'; for one of

these is false always, and the other sometimes; it is in these two senses that they are nonexistent. (b) There

are things which exist, but whose nature it is to appear either not to be such as they are or to be things that do

not exist, e.g. a sketch or a dream; for these are something, but are not the things the appearance of which

they produce in us. We call things false in this way, then,either because they themselves do not exist, or

because the appearance which results from them is that of something that does not exist.

(2) A false account is the account of nonexistent objects, in so far as it is false. Hence every account is false

when applied to something other than that of which it is true; e.g. the account of a circle is false when applied

to a triangle. In a sense there is one account of each thing, i.e. the account of its essence, but in a sense there

are many, since the thing itself and the thing itself with an attribute are in a sense the same, e.g. Socrates and

musical Socrates (a false account is not the account of anything, except in a qualified sense). Hence

Antisthenes was too simpleminded when he claimed that nothing could be described except by the account

proper to it,one predicate to one subject; from which the conclusion used to be drawn that there could be no

contradiction, and almost that there could be no error. But it is possible to describe each thing not only by the

account of itself, but also by that of something else. This may be done altogether falsely indeed, but there is

also a way in which it may be done truly; e.g. eight may be described as a double number by the use of the

These things, then, are called false in these senses, but (3) a false man is one who is ready at and fond of such

accounts, not for any other reason but for their own sake, and one who is good at impressing such accounts

on other people, just as we say things are which produce a false appearance. This is why the proof in the

Hippias that the same man is false and true is misleading. For it assumes that he is false who can deceive (i.e.

the man who knows and is wise); and further that he who is willingly bad is better. This is a false result of

inductionfor a man who limps willingly is better than one who does so unwillinglyby 'limping' Plato

means 'mimicking a limp', for if the man were lame willingly, he would presumably be worse in this case as

'Accident' means (1) that which attaches to something and can be truly asserted, but neither of necessity nor

usually, e.g. if some one in digging a hole for a plant has found treasure. Thisthe finding of treasureis for

the man who dug the hole an accident; for neither does the one come of necessity from the other or after the

other, nor, if a man plants, does he usually find treasure. And a musical man might be pale; but since this

does not happen of necessity nor usually, we call it an accident. Therefore since there are attributes and they

attach to subjects, and some of them attach to these only in a particular place and at a particular time,

whatever attaches to a subject, but not because it was this subject, or the time this time, or the place this

place, will be an accident. Therefore, too, there is no definite cause for an accident, but a chance cause, i.e. an

indefinite one. Going to Aegina was an accident for a man, if he went not in order to get there, but because he

was carried out of his way by a storm or captured by pirates. The accident has happened or exists,not in

virtue of the subject's nature, however, but of something else; for the storm was the cause of his coming to a

'Accident' has also (2) another meaning, i.e. all that attaches to each thing in virtue of itself but is not in its

essence, as having its angles equal to two right angles attaches to the triangle. And accidents of this sort may

WE are seeking the principles and the causes of the things that are, and obviously of them qua being. For,

while there is a cause of health and of good condition, and the objects of mathematics have first principles

and elements and causes, and in general every science which is ratiocinative or at all involves reasoning deals

with causes and principles, more or less precise, all these sciences mark off some particular beingsome

genus, and inquire into this, but not into being simply nor qua being, nor do they offer any discussion of the

essence of the things of which they treat; but starting from the essencesome making it plain to the senses,

others assuming it as a hypothesisthey then demonstrate, more or less cogently, the essential attributes of the

genus with which they deal. It is obvious, therefore, that such an induction yields no demonstration of

substance or of the essence, but some other way of exhibiting it. And similarly the sciences omit the question

whether the genus with which they deal exists or does not exist, because it belongs to the same kind of

And since natural science, like other sciences, is in fact about one class of being, i.e. to that sort of substance

which has the principle of its movement and rest present in itself, evidently it is neither practical nor

productive. For in the case of things made the principle is in the makerit is either reason or art or some

faculty, while in the case of things done it is in the doerviz. will, for that which is done and that which is

willed are the same. Therefore, if all thought is either practical or productive or theoretical, physics must be a

theoretical science, but it will theorize about such being as admits of being moved, and about

substanceasdefined for the most part only as not separable from matter. Now, we must not fail to notice the

mode of being of the essence and of its definition, for, without this, inquiry is but idle. Of things defined, i.e.

of 'whats', some are like 'snub', and some like 'concave'. And these differ because 'snub' is bound up with

matter (for what is snub is a concave nose), while concavity is independent of perceptible matter. If then all

natural things are a analogous to the snub in their nature; e.g. nose, eye, face, flesh, bone, and, in general,

animal; leaf, root, bark, and, in general, plant (for none of these can be defined without reference to

movementthey always have matter), it is clear how we must seek and define the 'what' in the case of natural

objects, and also that it belongs to the student of nature to study even soul in a certain sense, i.e. so much of it

That physics, then, is a theoretical science, is plain from these considerations. Mathematics also, however, is

theoretical; but whether its objects are immovable and separable from matter, is not at present clear; still, it is

clear that some mathematical theorems consider them qua immovable and qua separable from matter. But if

there is something which is eternal and immovable and separable, clearly the knowledge of it belongs to a

theoretical science,not, however, to physics (for physics deals with certain movable things) nor to

mathematics, but to a science prior to both. For physics deals with things which exist separately but are not

immovable, and some parts of mathematics deal with things which are immovable but presumably do not

exist separately, but as embodied in matter; while the first science deals with things which both exist

separately and are immovable. Now all causes must be eternal, but especially these; for they are the causes

that operate on so much of the divine as appears to us. There must, then, be three theoretical philosophies,

mathematics, physics, and what we may call theology, since it is obvious that if the divine is present

anywhere, it is present in things of this sort. And the highest science must deal with the highest genus. Thus,

while the theoretical sciences are more to be desired than the other sciences, this is more to be desired than

the other theoretical sciences. For one might raise the question whether first philosophy is universal, or deals

with one genus, i.e. some one kind of being; for not even the mathematical sciences are all alike in this

respect,geometry and astronomy deal with a certain particular kind of thing, while universal mathematics

applies alike to all. We answer that if there is no substance other than those which are formed by nature,

natural science will be the first science; but if there is an immovable substance, the science of this must be

prior and must be first philosophy, and universal in this way, because it is first. And it will belong to this to

consider being qua beingboth what it is and the attributes which belong to it qua being.

But since the unqualified term 'being' has several meanings, of which one was seen' to be the accidental, and

another the true ('nonbeing' being the false), while besides these there are the figures of predication (e.g. the

'what', quality, quantity, place, time, and any similar meanings which 'being' may have), and again besides all

these there is that which 'is' potentially or actually:since 'being' has many meanings, we must say regarding

the accidental, that there can be no scientific treatment of it. This is confirmed by the fact that no science

practical, productive, or theoretical troubles itself about it. For on the one hand he who produces a house does

not produce all the attributes that come into being along with the house; for these are innumerable; the house

that has been made may quite well be pleasant for some people, hurtful for some, and useful to others, and

differentto put it shortly from all things that are; and the science of building does not aim at producing any

of these attributes. And in the same way the geometer does not consider the attributes which attach thus to

figures, nor whether 'triangle' is different from 'triangle whose angles are equal to two right angles'.And this

happens naturally enough; for the accidental is practically a mere name. And so Plato was in a sense not

wrong in ranking sophistic as dealing with that which is not. For the arguments of the sophists deal, we may

say, above all with the accidental; e.g. the question whether 'musical' and 'lettered' are different or the same,

and whether 'musical Coriscus' and 'Coriscus' are the same, and whether 'everything which is, but is not

eternal, has come to be', with the paradoxical conclusion that if one who was musical has come to be lettered,

he must also have been lettered and have come to be musical, and all the other arguments of this sort; the

accidental is obviously akin to nonbeing. And this is clear also from arguments such as the following: things

which are in another sense come into being and pass out of being by a process, but things which are

accidentally do not. But still we must, as far as we can, say further, regarding the accidental, what its nature is

and from what cause it proceeds; for it will perhaps at the same time become clear why there is no science of

Since, among things which are, some are always in the same state and are of necessity (not necessity in the

sense of compulsion but that which we assert of things because they cannot be otherwise), and some are not

of necessity nor always, but for the most part, this is the principle and this the cause of the existence of the

accidental; for that which is neither always nor for the most part, we call accidental. For instance, if in the

dogdays there is wintry and cold weather, we say this is an accident, but not if there is sultry heat, because

the latter is always or for the most part so, but not the former. And it is an accident that a man is pale (for this

is neither always nor for the most part so), but it is not by accident that he is an animal. And that the builder

produces health is an accident, because it is the nature not of the builder but of the doctor to do this,but the

builder happened to be a doctor. Again, a confectioner, aiming at giving pleasure, may make something

wholesome, but not in virtue of the confectioner's art; and therefore we say 'it was an accident', and while

there is a sense in which he makes it, in the unqualified sense he does not. For to other things answer faculties

productive of them, but to accidental results there corresponds no determinate art nor faculty; for of things

which are or come to be by accident, the cause also is accidental. Therefore, since not all things either are or

come to be of necessity and always, but, the majority of things are for the most part, the accidental must exist;

for instance a pale man is not always nor for the most part musical, but since this sometimes happens, it must

be accidental (if not, everything will be of necessity). The matter, therefore, which is capable of being

otherwise than as it usually is, must be the cause of the accidental. And we must take as our startingpoint the

question whether there is nothing that is neither always nor for the most part. Surely this is impossible. There

is, then, besides these something which is fortuitous and accidental. But while the usual exists, can nothing be

said to be always, or are there eternal things? This must be considered later,' but that there is no science of the

accidental is obvious; for all science is either of that which is always or of that which is for the most part.

(For how else is one to learn or to teach another? The thing must be determined as occurring either always or

for the most part, e.g. that honeywater is useful for a patient in a fever is true for the most part.) But that

which is contrary to the usual law science will be unable to state, i.e. when the thing does not happen, e.g.'on

the day of new moon'; for even that which happens on the day of new moon happens then either always or for

the most part; but the accidental is contrary to such laws. We have stated, then, what the accidental is, and

That there are principles and causes which are generable and destructible without ever being in course of

being generated or destroyed, is obvious. For otherwise all things will be of necessity, since that which is

being generated or destroyed must have a cause which is not accidentally its cause. Will A exist or not? It

will if B happens; and if not, not. And B will exist if C happens. And thus if time is constantly subtracted

from a limited extent of time, one will obviously come to the present. This man, then, will die by violence, if

he goes out; and he will do this if he gets thirsty; and he will get thirsty if something else happens; and thus

we shall come to that which is now present, or to some past event. For instance, he will go out if he gets

thirsty; and he will get thirsty if he is eating pungent food; and this is either the case or not; so that he will of

necessity die, or of necessity not die. And similarly if one jumps over to past events, the same account will

hold good; for thisI mean the past conditionis already present in something. Everything, therefore, that will

be, will be of necessity; e.g. it is necessary that he who lives shall one day die; for already some condition has

come into existence, e.g. the presence of contraries in the same body. But whether he is to die by disease or

by violence is not yet determined, but depends on the happening of something else. Clearly then the process

goes back to a certain startingpoint, but this no longer points to something further. This then will be the

startingpoint for the fortuitous, and will have nothing else as cause of its coming to be. But to what sort of

startingpoint and what sort of cause we thus refer the fortuitouswhether to matter or to the purpose or to

Let us dismiss accidental being; for we have sufficiently determined its nature. But since that which is in the

sense of being true, or is not in the sense of being false, depends on combination and separation, and truth and

falsity together depend on the allocation of a pair of contradictory judgements (for the true judgement affirms

where the subject and predicate really are combined, and denies where they are separated, while the false

judgement has the opposite of this allocation; it is another question, how it happens that we think things

together or apart; by 'together' and 'apart' I mean thinking them so that there is no succession in the thoughts

but they become a unity); for falsity and truth are not in thingsit is not as if the good were true, and the bad

were in itself falsebut in thought; while with regard to simple concepts and 'whats' falsity and truth do not

exist even in thoughtthis being so, we must consider later what has to be discussed with regard to that

which is or is not in this sense. But since the combination and the separation are in thought and not in the

things, and that which is in this sense is a different sort of 'being' from the things that are in the full sense (for

the thought attaches or removes either the subject's 'what' or its having a certain quality or quantity or

something else), that which is accidentally and that which is in the sense of being true must be dismissed. For

the cause of the former is indeterminate, and that of the latter is some affection of the thought, and both are

related to the remaining genus of being, and do not indicate the existence of any separate class of being.

Therefore let these be dismissed, and let us consider the causes and the principles of being itself, qua being.

(It was clear in our discussion of the various meanings of terms, that 'being' has several meanings.)

THERE are several senses in which a thing may be said to 'be', as we pointed out previously in our book on

the various senses of words;' for in one sense the 'being' meant is 'what a thing is' or a 'this', and in another

sense it means a quality or quantity or one of the other things that are predicated as these are. While 'being'

has all these senses, obviously that which 'is' primarily is the 'what', which indicates the substance of the

thing. For when we say of what quality a thing is, we say that it is good or bad, not that it is three cubits long

or that it is a man; but when we say what it is, we do not say 'white' or 'hot' or 'three cubits long', but 'a man'

or 'a 'god'. And all other things are said to be because they are, some of them, quantities of that which is in

this primary sense, others qualities of it, others affections of it, and others some other determination of it. And

so one might even raise the question whether the words 'to walk', 'to be healthy', 'to sit' imply that each of

these things is existent, and similarly in any other case of this sort; for none of them is either selfsubsistent

or capable of being separated from substance, but rather, if anything, it is that which walks or sits or is

healthy that is an existent thing. Now these are seen to be more real because there is something definite which

underlies them (i.e. the substance or individual), which is implied in such a predicate; for we never use the

word 'good' or 'sitting' without implying this. Clearly then it is in virtue of this category that each of the

others also is. Therefore that which is primarily, i.e. not in a qualified sense but without qualification, must be

Now there are several senses in which a thing is said to be first; yet substance is first in every sense(1) in

definition, (2) in order of knowledge, (3) in time. For (3) of the other categories none can exist independently,

but only substance. And (1) in definition also this is first; for in the definition of each term the definition of

its substance must be present. And (2) we think we know each thing most fully, when we know what it is, e.g.

what man is or what fire is, rather than when we know its quality, its quantity, or its place; since we know

each of these predicates also, only when we know what the quantity or the quality is.

And indeed the question which was raised of old and is raised now and always, and is always the subject of

doubt, viz. what being is, is just the question, what is substance? For it is this that some assert to be one,

others more than one, and that some assert to be limited in number, others unlimited. And so we also must

consider chiefly and primarily and almost exclusively what that is which is in this sense.

Substance is thought to belong most obviously to bodies; and so we say that not only animals and plants and

their parts are substances, but also natural bodies such as fire and water and earth and everything of the sort,

and all things that are either parts of these or composed of these (either of parts or of the whole bodies), e.g.

the physical universe and its parts, stars and moon and sun. But whether these alone are substances, or there

are also others, or only some of these, or others as well, or none of these but only some other things, are

substances, must be considered. Some think the limits of body, i.e. surface, line, point, and unit, are

Further, some do not think there is anything substantial besides sensible things, but others think there are

eternal substances which are more in number and more real; e.g. Plato posited two kinds of substancethe

Forms and objects of mathematicsas well as a third kind, viz. the substance of sensible bodies. And

Speusippus made still more kinds of substance, beginning with the One, and assuming principles for each

kind of substance, one for numbers, another for spatial magnitudes, and then another for the soul; and by

going on in this way he multiplies the kinds of substance. And some say Forms and numbers have the same

nature, and the other things come after themlines and planesuntil we come to the substance of the material

Regarding these matters, then, we must inquire which of the common statements are right and which are not

right, and what substances there are, and whether there are or are not any besides sensible substances, and

how sensible substances exist, and whether there is a substance capable of separate existence (and if so why

and how) or no such substance, apart from sensible substances; and we must first sketch the nature of

The word 'substance' is applied, if not in more senses, still at least to four main objects; for both the essence

and the universal and the genus, are thought to be the substance of each thing, and fourthly the substratum.

Now the substratum is that of which everything else is predicated, while it is itself not predicated of anything

else. And so we must first determine the nature of this; for that which underlies a thing primarily is thought to

be in the truest sense its substance. And in one sense matter is said to be of the nature of substratum, in

another, shape, and in a third, the compound of these. (By the matter I mean, for instance, the bronze, by the

shape the pattern of its form, and by the compound of these the statue, the concrete whole.) Therefore if the

form is prior to the matter and more real, it will be prior also to the compound of both, for the same reason.

We have now outlined the nature of substance, showing that it is that which is not predicated of a stratum, but

of which all else is predicated. But we must not merely state the matter thus; for this is not enough. The

statement itself is obscure, and further, on this view, matter becomes substance. For if this is not substance, it

baffles us to say what else is. When all else is stripped off evidently nothing but matter remains. For while the

rest are affections, products, and potencies of bodies, length, breadth, and depth are quantities and not

substances (for a quantity is not a substance), but the substance is rather that to which these belong primarily.

But when length and breadth and depth are taken away we see nothing left unless there is something that is

bounded by these; so that to those who consider the question thus matter alone must seem to be substance. By

matter I mean that which in itself is neither a particular thing nor of a certain quantity nor assigned to any

other of the categories by which being is determined. For there is something of which each of these is

predicated, whose being is different from that of each of the predicates (for the predicates other than

substance are predicated of substance, while substance is predicated of matter). Therefore the ultimate

substratum is of itself neither a particular thing nor of a particular quantity nor otherwise positively

characterized; nor yet is it the negations of these, for negations also will belong to it only by accident.

If we adopt this point of view, then, it follows that matter is substance. But this is impossible; for both

separability and 'thisness' are thought to belong chiefly to substance. And so form and the compound of form

and matter would be thought to be substance, rather than matter. The substance compounded of both, i.e. of

matter and shape, may be dismissed; for it is posterior and its nature is obvious. And matter also is in a sense

manifest. But we must inquire into the third kind of substance; for this is the most perplexing.

Some of the sensible substances are generally admitted to be substances, so that we must look first among

these. For it is an advantage to advance to that which is more knowable. For learning proceeds for all in this

waythrough that which is less knowable by nature to that which is more knowable; and just as in conduct

our task is to start from what is good for each and make what is without qualification good good for each, so

it is our task to start from what is more knowable to oneself and make what is knowable by nature knowable

to oneself. Now what is knowable and primary for particular sets of people is often knowable to a very small

extent, and has little or nothing of reality. But yet one must start from that which is barely knowable but

knowable to oneself, and try to know what is knowable without qualification, passing, as has been said, by

Since at the start we distinguished the various marks by which we determine substance, and one of these was

thought to be the essence, we must investigate this. And first let us make some linguistic remarks about it.

The essence of each thing is what it is said to be propter se. For being you is not being musical, since you are

not by your very nature musical. What, then, you are by your very nature is your essence.

Nor yet is the whole of this the essence of a thing; not that which is propter se as white is to a surface,

because being a surface is not identical with being white. But again the combination of both'being a white

surface'is not the essence of surface, because 'surface' itself is added. The formula, therefore, in which the

term itself is not present but its meaning is expressed, this is the formula of the essence of each thing.

Therefore if to be a white surface is to be a smooth surface, to be white and to be smooth are one and the

But since there are also compounds answering to the other categories (for there is a substratum for each

category, e.g. for quality, quantity, time, place, and motion), we must inquire whether there is a formula of

the essence of each of them, i.e. whether to these compounds also there belongs an essence, e.g. 'white man'.

Let the compound be denoted by 'cloak'. What is the essence of cloak? But, it may be said, this also is not a

propter se expression. We reply that there are just two ways in which a predicate may fail to be true of a

subject propter se, and one of these results from the addition, and the other from the omission, of a

determinant. One kind of predicate is not propter se because the term that is being defined is combined with

another determinant, e.g. if in defining the essence of white one were to state the formula of white man; the

other because in the subject another determinant is combined with that which is expressed in the formula, e.g.

if 'cloak' meant 'white man', and one were to define cloak as white; white man is white indeed, but its essence

But is beingacloak an essence at all? Probably not. For the essence is precisely what something is; but

when an attribute is asserted of a subject other than itself, the complex is not precisely what some 'this' is, e.g.

white man is not precisely what some 'this' is, since thisness belongs only to substances. Therefore there is an

essence only of those things whose formula is a definition. But we have a definition not where we have a

word and a formula identical in meaning (for in that case all formulae or sets of words would be definitions;

for there will be some name for any set of words whatever, so that even the Iliad will be a definition), but

where there is a formula of something primary; and primary things are those which do not imply the

predication of one element in them of another element. Nothing, then, which is not a species of a genus will

have an essenceonly species will have it, for these are thought to imply not merely that the subject

participates in the attribute and has it as an affection, or has it by accident; but for ever thing else as well, if it

has a name, there be a formula of its meaningviz. that this attribute belongs to this subject; or instead of a

simple formula we shall be able to give a more accurate one; but there will be no definition nor essence.

Or has 'definition', like 'what a thing is', several meanings? 'What a thing is' in one sense means substance and

the 'this', in another one or other of the predicates, quantity, quality, and the like. For as 'is' belongs to all

things, not however in the same sense, but to one sort of thing primarily and to others in a secondary way, so

too 'what a thing is' belongs in the simple sense to substance, but in a limited sense to the other categories.

For even of a quality we might ask what it is, so that quality also is a 'what a thing is',not in the simple

sense, however, but just as, in the case of that which is not, some say, emphasizing the linguistic form, that

We must no doubt inquire how we should express ourselves on each point, but certainly not more than how

the facts actually stand. And so now also, since it is evident what language we use, essence will belong, just

as 'what a thing is' does, primarily and in the simple sense to substance, and in a secondary way to the other

categories also,not essence in the simple sense, but the essence of a quality or of a quantity. For it must be

either by an equivocation that we say these are, or by adding to and taking from the meaning of 'are' (in the

way in which that which is not known may be said to be known),the truth being that we use the word neither

ambiguously nor in the same sense, but just as we apply the word 'medical' by virtue of a reference to one and

the same thing, not meaning one and the same thing, nor yet speaking ambiguously; for a patient and an

operation and an instrument are called medical neither by an ambiguity nor with a single meaning, but with

reference to a common end. But it does not matter at all in which of the two ways one likes to describe the

facts; this is evident, that definition and essence in the primary and simple sense belong to substances. Still

they belong to other things as well, only not in the primary sense. For if we suppose this it does not follow

that there is a definition of every word which means the same as any formula; it must mean the same as a

particular kind of formula; and this condition is satisfied if it is a formula of something which is one, not by

continuity like the Iliad or the things that are one by being bound together, but in one of the main senses of

'one', which answer to the senses of 'is'; now 'that which is' in one sense denotes a 'this', in another a quantity,

in another a quality. And so there can be a formula or definition even of white man, but not in the sense in

It is a difficult question, if one denies that a formula with an added determinant is a definition, whether any of

the terms that are not simple but coupled will be definable. For we must explain them by adding a

determinant. E.g. there is the nose, and concavity, and snubness, which is compounded out of the two by the

presence of the one in the other, and it is not by accident that the nose has the attribute either of concavity or

of snubness, but in virtue of its nature; nor do they attach to it as whiteness does to Callias, or to man

(because Callias, who happens to be a man, is white), but as 'male' attaches to animal and 'equal' to quantity,

and as all socalled 'attributes propter se' attach to their subjects. And such attributes are those in which is

involved either the formula or the name of the subject of the particular attribute, and which cannot be

explained without this; e.g. white can be explained apart from man, but not female apart from animal.

Therefore there is either no essence and definition of any of these things, or if there is, it is in another sense,

But there is also a second difficulty about them. For if snub nose and concave nose are the same thing, snub

and concave will be the thing; but if snub and concave are not the same (because it is impossible to speak of

snubness apart from the thing of which it is an attribute propter se, for snubness is concavityinanose),

either it is impossible to say 'snub nose' or the same thing will have been said twice, concavenose nose; for

snub nose will be concavenose nose. And so it is absurd that such things should have an essence; if they

have, there will be an infinite regress; for in snubnose nose yet another 'nose' will be involved.

Clearly, then, only substance is definable. For if the other categories also are definable, it must be by addition

of a determinant, e.g. the qualitative is defined thus, and so is the odd, for it cannot be defined apart from

number; nor can female be defined apart from animal. (When I say 'by addition' I mean the expressions in

which it turns out that we are saying the same thing twice, as in these instances.) And if this is true, coupled

terms also, like 'odd number', will not be definable (but this escapes our notice because our formulae are not

accurate.). But if these also are definable, either it is in some other way or, as we definition and essence must

be said to have more than one sense. Therefore in one sense nothing will have a definition and nothing will

have an essence, except substances, but in another sense other things will have them. Clearly, then, definition

is the formula of the essence, and essence belongs to substances either alone or chiefly and primarily and in

We must inquire whether each thing and its essence are the same or different. This is of some use for the

inquiry concerning substance; for each thing is thought to be not different from its substance, and the essence

Now in the case of accidental unities the two would be generally thought to be different, e.g. white man

would be thought to be different from the essence of white man. For if they are the same, the essence of man

and that of white man are also the same; for a man and a white man are the same thing, as people say, so that

the essence of white man and that of man would be also the same. But perhaps it does not follow that the

essence of accidental unities should be the same as that of the simple terms. For the extreme terms are not in

the same way identical with the middle term. But perhaps this might be thought to follow, that the extreme

terms, the accidents, should turn out to be the same, e.g. the essence of white and that of musical; but this is

But in the case of socalled selfsubsistent things, is a thing necessarily the same as its essence? E.g. if there

are some substances which have no other substances nor entities prior to themsubstances such as some

assert the Ideas to be?If the essence of good is to be different from gooditself, and the essence of animal

from animalitself, and the essence of being from beingitself, there will, firstly, be other substances and

entities and Ideas besides those which are asserted, and, secondly, these others will be prior substances, if

essence is substance. And if the posterior substances and the prior are severed from each other, (a) there will

be no knowledge of the former, and (b) the latter will have no being. (By 'severed' I mean, if the gooditself

has not the essence of good, and the latter has not the property of being good.) For (a) there is knowledge of

each thing only when we know its essence. And (b) the case is the same for other things as for the good; so

that if the essence of good is not good, neither is the essence of reality real, nor the essence of unity one. And

all essences alike exist or none of them does; so that if the essence of reality is not real, neither is any of the

others. Again, that to which the essence of good does not belong is not good.The good, then, must be one

with the essence of good, and the beautiful with the essence of beauty, and so with all things which do not

depend on something else but are selfsubsistent and primary. For it is enough if they are this, even if they

are not Forms; or rather, perhaps, even if they are Forms. (At the same time it is clear that if there are Ideas

such as some people say there are, it will not be substratum that is substance; for these must be substances,

but not predicable of a substratum; for if they were they would exist only by being participated in.)

Each thing itself, then, and its essence are one and the same in no merely accidental way, as is evident both

from the preceding arguments and because to know each thing, at least, is just to know its essence, so that

(But of an accidental term, e.g.'the musical' or 'the white', since it has two meanings, it is not true to say that it

itself is identical with its essence; for both that to which the accidental quality belongs, and the accidental

quality, are white, so that in a sense the accident and its essence are the same, and in a sense they are not; for

the essence of white is not the same as the man or the white man, but it is the same as the attribute white.)

The absurdity of the separation would appear also if one were to assign a name to each of the essences; for

there would be yet another essence besides the original one, e.g. to the essence of horse there will belong a

second essence. Yet why should not some things be their essences from the start, since essence is substance?

But indeed not only are a thing and its essence one, but the formula of them is also the same, as is clear even

from what has been said; for it is not by accident that the essence of one, and the one, are one. Further, if they

are to be different, the process will go on to infinity; for we shall have (1) the essence of one, and (2) the one,

Clearly, then, each primary and selfsubsistent thing is one and the same as its essence. The sophistical

objections to this position, and the question whether Socrates and to be Socrates are the same thing, are

obviously answered by the same solution; for there is no difference either in the standpoint from which the

question would be asked, or in that from which one could answer it successfully. We have explained, then, in

Of things that come to be, some come to be by nature, some by art, some spontaneously. Now everything that

comes to be comes to be by the agency of something and from something and comes to be something. And

the something which I say it comes to be may be found in any category; it may come to be either a 'this' or of

Now natural comings to be are the comings to be of those things which come to be by nature; and that out of

which they come to be is what we call matter; and that by which they come to be is something which exists

naturally; and the something which they come to be is a man or a plant or one of the things of this kind,

which we say are substances if anything isall things produced either by nature or by art have matter; for

each of them is capable both of being and of not being, and this capacity is the matter in eachand, in general,

both that from which they are produced is nature, and the type according to which they are produced is nature

(for that which is produced, e.g. a plant or an animal, has a nature), and so is that by which they are

producedthe socalled 'formal' nature, which is specifically the same (though this is in another individual);

Thus, then, are natural products produced; all other productions are called 'makings'. And all makings

proceed either from art or from a faculty or from thought. Some of them happen also spontaneously or by

luck just as natural products sometimes do; for there also the same things sometimes are produced without

seed as well as from seed. Concerning these cases, then, we must inquire later, but from art proceed the things

of which the form is in the soul of the artist. (By form I mean the essence of each thing and its primary

substance.) For even contraries have in a sense the same form; for the substance of a privation is the opposite

substance, e.g. health is the substance of disease (for disease is the absence of health); and health is the

formula in the soul or the knowledge of it. The healthy subject is produced as the result of the following train

of thought:since this is health, if the subject is to be healthy this must first be present, e.g. a uniform state of

body, and if this is to be present, there must be heat; and the physician goes on thinking thus until he reduces

the matter to a final something which he himself can produce. Then the process from this point onward, i.e.

the process towards health, is called a 'making'. Therefore it follows that in a sense health comes from health

and house from house, that with matter from that without matter; for the medical art and the building art are

the form of health and of the house, and when I speak of substance without matter I mean the essence.

Of the productions or processes one part is called thinking and the other making,that which proceeds from

the startingpoint and the form is thinking, and that which proceeds from the final step of the thinking is

making. And each of the other, intermediate, things is produced in the same way. I mean, for instance, if the

subject is to be healthy his bodily state must be made uniform. What then does being made uniform imply?

This or that. And this depends on his being made warm. What does this imply? Something else. And this

something is present potentially; and what is present potentially is already in the physician's power.

The active principle then and the starting point for the process of becoming healthy is, if it happens by art, the

form in the soul, and if spontaneously, it is that, whatever it is, which starts the making, for the man who

makes by art, as in healing the startingpoint is perhaps the production of warmth (and this the physician

produces by rubbing). Warmth in the body, then, is either a part of health or is followed (either directly or

through several intermediate steps) by something similar which is a part of health; and this, viz. that which

produces the part of health, is the limitingpointand so too with a house (the stones are the limitingpoint

here) and in all other cases. Therefore, as the saying goes, it is impossible that anything should be produced if

there were nothing existing before. Obviously then some part of the result will preexist of necessity; for the

matter is a part; for this is present in the process and it is this that becomes something. But is the matter an

element even in the formula? We certainly describe in both ways what brazen circles are; we describe both

the matter by saying it is brass, and the form by saying that it is such and such a figure; and figure is the

proximate genus in which it is placed. The brazen circle, then, has its matter in its formula.

As for that out of which as matter they are produced, some things are said, when they have been produced, to

be not that but 'thaten'; e.g. the statue is not gold but golden. And a healthy man is not said to be that from

which he has come. The reason is that though a thing comes both from its privation and from its substratum,

which we call its matter (e.g. what becomes healthy is both a man and an invalid), it is said to come rather

from its privation (e.g. it is from an invalid rather than from a man that a healthy subject is produced). And so

the healthy subject is not said to he an invalid, but to be a man, and the man is said to be healthy. But as for

the things whose privation is obscure and nameless, e.g. in brass the privation of a particular shape or in

bricks and timber the privation of arrangement as a house, the thing is thought to be produced from these

materials, as in the former case the healthy man is produced from an invalid. And so, as there also a thing is

not said to be that from which it comes, here the statue is not said to be wood but is said by a verbal change to

be wooden, not brass but brazen, not gold but golden, and the house is said to be not bricks but bricken

(though we should not say without qualification, if we looked at the matter carefully, even that a statue is

produced from wood or a house from bricks, because coming to be implies change in that from which a thing

comes to be, and not permanence). It is for this reason, then, that we use this way of speaking.

Since anything which is produced is produced by something (and this I call the startingpoint of the

production), and from something (and let this be taken to be not the privation but the matter; for the meaning

we attach to this has already been explained), and since something is produced (and this is either a sphere or a

circle or whatever else it may chance to be), just as we do not make the substratum (the brass), so we do not

make the sphere, except incidentally, because the brazen sphere is a sphere and we make the forme. For to

make a 'this' is to make a 'this' out of the substratum in the full sense of the word. (I mean that to make the

brass round is not to make the round or the sphere, but something else, i.e. to produce this form in something

different from itself. For if we make the form, we must make it out of something else; for this was assumed.

E.g. we make a brazen sphere; and that in the sense that out of this, which is brass, we make this other, which

is a sphere.) If, then, we also make the substratum itself, clearly we shall make it in the same way, and the

processes of making will regress to infinity. Obviously then the form also, or whatever we ought to call the

shape present in the sensible thing, is not produced, nor is there any production of it, nor is the essence

produced; for this is that which is made to be in something else either by art or by nature or by some faculty.

But that there is a brazen sphere, this we make. For we make it out of brass and the sphere; we bring the form

into this particular matter, and the result is a brazen sphere. But if the essence of sphere in general is to be

produced, something must be produced out of something. For the product will always have to be divisible,

and one part must be this and another that; I mean the one must be matter and the other form. If, then, a

sphere is 'the figure whose circumference is at all points equidistant from the centre', part of this will be the

medium in which the thing made will be, and part will be in that medium, and the whole will be the thing

produced, which corresponds to the brazen sphere. It is obvious, then, from what has been said, that that

which is spoken of as form or substance is not produced, but the concrete thing which gets its name from this

is produced, and that in everything which is generated matter is present, and one part of the thing is matter

Is there, then, a sphere apart from the individual spheres or a house apart from the bricks? Rather we may say

that no 'this' would ever have been coming to be, if this had been so, but that the 'form' means the 'such', and

is not a 'this'a definite thing; but the artist makes, or the father begets, a 'such' out of a 'this'; and when it has

been begotten, it is a 'this such'. And the whole 'this', Callias or Socrates, is analogous to 'this brazen sphere',

but man and animal to 'brazen sphere' in general. Obviously, then, the cause which consists of the Forms

(taken in the sense in which some maintain the existence of the Forms, i.e. if they are something apart from

the individuals) is useless, at least with regard to comingstobe and to substances; and the Forms need not,

for this reason at least, be selfsubsistent substances. In some cases indeed it is even obvious that the begetter

is of the same kind as the begotten (not, however, the same nor one in number, but in form), i.e. in the case of

natural products (for man begets man), unless something happens contrary to nature, e.g. the production of a

mule by a horse. (And even these cases are similar; for that which would be found to be common to horse and

ass, the genus next above them, has not received a name, but it would doubtless be both in fact something

like a mule.) Obviously, therefore, it is quite unnecessary to set up a Form as a pattern (for we should have

looked for Forms in these cases if in any; for these are substances if anything is so); the begetter is adequate

to the making of the product and to the causing of the form in the matter. And when we have the whole, such

and such a form in this flesh and in these bones, this is Callias or Socrates; and they are different in virtue of

their matter (for that is different), but the same in form; for their form is indivisible.

The question might be raised, why some things are produced spontaneously as well as by art, e.g. health,

while others are not, e.g. a house. The reason is that in some cases the matter which governs the production in

the making and producing of any work of art, and in which a part of the product is present,some matter is

such as to be set in motion by itself and some is not of this nature, and of the former kind some can move

itself in the particular way required, while other matter is incapable of this; for many things can be set in

motion by themselves but not in some particular way, e.g. that of dancing. The things, then, whose matter is

of this sort, e.g. stones, cannot be moved in the particular way required, except by something else, but in

another way they can move themselvesand so it is with fire. Therefore some things will not exist apart from

some one who has the art of making them, while others will; for motion will be started by these things which

have not the art but can themselves be moved by other things which have not the art or with a motion starting

And it is clear also from what has been said that in a sense every product of art is produced from a thing

which shares its name (as natural products are produced), or from a part of itself which shares its name (e.g.

the house is produced from a house, qua produced by reason; for the art of building is the form of the house),

or from something which contains a art of it,if we exclude things produced by accident; for the cause of the

thing's producing the product directly per se is a part of the product. The heat in the movement caused heat in

the body, and this is either health, or a part of health, or is followed by a part of health or by health itself. And

so it is said to cause health, because it causes that to which health attaches as a consequence.

Therefore, as in syllogisms, substance is the startingpoint of everything. It is from 'what a thing is' that

syllogisms start; and from it also we now find processes of production to start.

Things which are formed by nature are in the same case as these products of art. For the seed is productive in

the same way as the things that work by art; for it has the form potentially, and that from which the seed

comes has in a sense the same name as the offspring only in a sense, for we must not expect parent and

offspring always to have exactly the same name, as in the production of 'human being' from 'human' for a

'woman' also can be produced by a 'man'unless the offspring be an imperfect form; which is the reason why

the parent of a mule is not a mule. The natural things which (like the artificial objects previously considered)

can be produced spontaneously are those whose matter can be moved even by itself in the way in which the

seed usually moves it; those things which have not such matter cannot be produced except from the parent

But not only regarding substance does our argument prove that its form does not come to be, but the

argument applies to all the primary classes alike, i.e. quantity, quality, and the other categories. For as the

brazen sphere comes to be, but not the sphere nor the brass, and so too in the case of brass itself, if it comes to

be, it is its concrete unity that comes to be (for the matter and the form must always exist before), so is it both

in the case of substance and in that of quality and quantity and the other categories likewise; for the quality

does not come to be, but the wood of that quality, and the quantity does not come to be, but the wood or the

animal of that size. But we may learn from these instances a peculiarity of substance, that there must exist

beforehand in complete reality another substance which produces it, e.g. an animal if an animal is produced;

but it is not necessary that a quality or quantity should preexist otherwise than potentially.

Since a definition is a formula, and every formula has parts, and as the formula is to the thing, so is the part of

the formula to the part of the thing, the question is already being asked whether the formula of the parts must

be present in the formula of the whole or not. For in some cases the formulae of the parts are seen to be

present, and in some not. The formula of the circle does not include that of the segments, but that of the

syllable includes that of the letters; yet the circle is divided into segments as the syllable is into letters.And

further if the parts are prior to the whole, and the acute angle is a part of the right angle and the finger a part

of the animal, the acute angle will be prior to the right angle and finger to the man. But the latter are thought

to be prior; for in formula the parts are explained by reference to them, and in respect also of the power of

Perhaps we should rather say that 'part' is used in several senses. One of these is 'that which measures another

thing in respect of quantity'. But let this sense be set aside; let us inquire about the parts of which substance

consists. If then matter is one thing, form another, the compound of these a third, and both the matter and the

form and the compound are substance even the matter is in a sense called part of a thing, while in a sense it is

not, but only the elements of which the formula of the form consists. E.g. of concavity flesh (for this is the

matter in which it is produced) is not a part, but of snubness it is a part; and the bronze is a part of the

concrete statue, but not of the statue when this is spoken of in the sense of the form. (For the form, or the

thing as having form, should be said to be the thing, but the material element by itself must never be said to

be so.) And so the formula of the circle does not include that of the segments, but the formula of the syllable

includes that of the letters; for the letters are parts of the formula of the form, and not matter, but the

segments are parts in the sense of matter on which the form supervenes; yet they are nearer the form than the

bronze is when roundness is produced in bronze. But in a sense not even every kind of letter will be present

in the formula of the syllable, e.g. particular waxen letters or the letters as movements in the air; for in these

also we have already something that is part of the syllable only in the sense that it is its perceptible matter.

For even if the line when divided passes away into its halves, or the man into bones and muscles and flesh, it

does not follow that they are composed of these as parts of their essence, but rather as matter; and these are

parts of the concrete thing, but not also of the form, i.e. of that to which the formula refers; wherefore also

they are not present in the formulae. In one kind of formula, then, the formula of such parts will be present,

but in another it must not be present, where the formula does not refer to the concrete object. For it is for this

reason that some things have as their constituent principles parts into which they pass away, while some have

not. Those things which are the form and the matter taken together, e.g. the snub, or the bronze circle, pass

away into these materials, and the matter is a part of them; but those things which do not involve matter but

are without matter, and whose formulae are formulae of the form only, do not pass away,either not at all or

at any rate not in this way. Therefore these materials are principles and parts of the concrete things, while of

the form they are neither parts nor principles. And therefore the clay statue is resolved into clay and the ball

into bronze and Callias into flesh and bones, and again the circle into its segments; for there is a sense of

'circle' in which involves matter. For 'circle' is used ambiguously, meaning both the circle, unqualified, and

The truth has indeed now been stated, but still let us state it yet more clearly, taking up the question again.

The parts of the formula, into which the formula is divided, are prior to it, either all or some of them. The

formula of the right angle, however, does not include the formula of the acute, but the formula of the acute

includes that of the right angle; for he who defines the acute uses the right angle; for the acute is 'less than a

right angle'. The circle and the semicircle also are in a like relation; for the semicircle is defined by the circle;

and so is the finger by the whole body, for a finger is 'such and such a part of a man'. Therefore the parts

which are of the nature of matter, and into which as its matter a thing is divided, are posterior; but those

which are of the nature of parts of the formula, and of the substance according to its formula, are prior, either

all or some of them. And since the soul of animals (for this is the substance of a living being) is their

substance according to the formula, i.e. the form and the essence of a body of a certain kind (at least we shall

define each part, if we define it well, not without reference to its function, and this cannot belong to it without

perception), so that the parts of soul are prior, either all or some of them, to the concrete 'animal', and so too

with each individual animal; and the body and parts are posterior to this, the essential substance, and it is not

the substance but the concrete thing that is divided into these parts as its matter:this being so, to the concrete

thing these are in a sense prior, but in a sense they are not. For they cannot even exist if severed from the

whole; for it is not a finger in any and every state that is the finger of a living thing, but a dead finger is a

finger only in name. Some parts are neither prior nor posterior to the whole, i.e. those which are dominant

and in which the formula, i.e. the essential substance, is immediately present, e.g. perhaps the heart or the

brain; for it does not matter in the least which of the two has this quality. But man and horse and terms which

are thus applied to individuals, but universally, are not substance but something composed of this particular

formula and this particular matter treated as universal; and as regards the individual, Socrates already

includes in him ultimate individual matter; and similarly in all other cases. 'A part' may be a part either of the

form (i.e. of the essence), or of the compound of the form and the matter, or of the matter itself. But only the

parts of the form are parts of the formula, and the formula is of the universal; for 'being a circle' is the same as

the circle, and 'being a soul' the same as the soul. But when we come to the concrete thing, e.g. this circle, i.e.

one of the individual circles, whether perceptible or intelligible (I mean by intelligible circles the

mathematical, and by perceptible circles those of bronze and of wood),of these there is no definition, but

they are known by the aid of intuitive thinking or of perception; and when they pass out of this complete

realization it is not clear whether they exist or not; but they are always stated and recognized by means of the

universal formula. But matter is unknowable in itself. And some matter is perceptible and some intelligible,

perceptible matter being for instance bronze and wood and all matter that is changeable, and intelligible

matter being that which is present in perceptible things not qua perceptible, i.e. the objects of mathematics.

We have stated, then, how matters stand with regard to whole and part, and their priority and posteriority. But

when any one asks whether the right angle and the circle and the animal are prior, or the things into which

they are divided and of which they consist, i.e. the parts, we must meet the inquiry by saying that the question

cannot be answered simply. For if even bare soul is the animal or the living thing, or the soul of each

individual is the individual itself, and 'being a circle' is the circle, and 'being a right angle' and the essence of

the right angle is the right angle, then the whole in one sense must be called posterior to the art in one sense,

i.e. to the parts included in the formula and to the parts of the individual right angle (for both the material

right angle which is made of bronze, and that which is formed by individual lines, are posterior to their parts);

while the immaterial right angle is posterior to the parts included in the formula, but prior to those included in

the particular instance, and the question must not be answered simply. If, however, the soul is something

different and is not identical with the animal, even so some parts must, as we have maintained, be called prior

Another question is naturally raised, viz. what sort of parts belong to the form and what sort not to the form,

but to the concrete thing. Yet if this is not plain it is not possible to define any thing; for definition is of the

universal and of the form. If then it is not evident what sort of parts are of the nature of matter and what sort

are not, neither will the formula of the thing be evident. In the case of things which are found to occur in

specifically different materials, as a circle may exist in bronze or stone or wood, it seems plain that these, the

bronze or the stone, are no part of the essence of the circle, since it is found apart from them. Of things which

are not seen to exist apart, there is no reason why the same may not be true, just as if all circles that had ever

been seen were of bronze; for none the less the bronze would be no part of the form; but it is hard to eliminate

it in thought. E.g. the form of man is always found in flesh and bones and parts of this kind; are these then

also parts of the form and the formula? No, they are matter; but because man is not found also in other

Since this is thought to be possible, but it is not clear when it is the case, some people already raise the

question even in the case of the circle and the triangle, thinking that it is not right to define these by reference

to lines and to the continuous, but that all these are to the circle or the triangle as flesh and bones are to man,

and bronze or stone to the statue; and they reduce all things to numbers, and they say the formula of 'line' is

that of 'two'. And of those who assert the Ideas some make 'two' the lineitself, and others make it the Form

of the line; for in some cases they say the Form and that of which it is the Form are the same, e.g. 'two' and

It follows then that there is one Form for many things whose form is evidently different (a conclusion which

confronted the Pythagoreans also); and it is possible to make one thing the Formitself of all, and to hold that

We have pointed out, then, that the question of definitions contains some difficulty, and why this is so. And

so to reduce all things thus to Forms and to eliminate the matter is useless labour; for some things surely are a

particular form in a particular matter, or particular things in a particular state. And the comparison which

Socrates the younger used to make in the case of 'animal' is not sound; for it leads away from the truth, and

makes one suppose that man can possibly exist without his parts, as the circle can without the bronze. But the

case is not similar; for an animal is something perceptible, and it is not possible to define it without reference

to movementnor, therefore, without reference to the parts' being in a certain state. For it is not a hand in any

and every state that is a part of man, but only when it can fulfil its work, and therefore only when it is alive; if

Regarding the objects of mathematics, why are the formulae of the parts not parts of the formulae of the

wholes; e.g. why are not the semicircles included in the formula of the circle? It cannot be said, 'because

these parts are perceptible things'; for they are not. But perhaps this makes no difference; for even some

things which are not perceptible must have matter; indeed there is some matter in everything which is not an

essence and a bare form but a 'this'. The semicircles, then, will not be parts of the universal circle, but will be

parts of the individual circles, as has been said before; for while one kind of matter is perceptible, there is

It is clear also that the soul is the primary substance and the body is matter, and man or animal is the

compound of both taken universally; and 'Socrates' or 'Coriscus', if even the soul of Socrates may be called

Socrates, has two meanings (for some mean by such a term the soul, and others mean the concrete thing), but

if 'Socrates' or 'Coriscus' means simply this particular soul and this particular body, the individual is

Whether there is, apart from the matter of such substances, another kind of matter, and one should look for

some substance other than these, e.g. numbers or something of the sort, must be considered later. For it is for

the sake of this that we are trying to determine the nature of perceptible substances as well, since in a sense

the inquiry about perceptible substances is the work of physics, i.e. of second philosophy; for the physicist

must come to know not only about the matter, but also about the substance expressed in the formula, and

even more than about the other. And in the case of definitions, how the elements in the formula are parts of

the definition, and why the definition is one formula (for clearly the thing is one, but in virtue of what is the

What the essence is and in what sense it is independent, has been stated universally in a way which is true of

every case, and also why the formula of the essence of some things contains the parts of the thing defined,

while that of others does not. And we have stated that in the formula of the substance the material parts will

not be present (for they are not even parts of the substance in that sense, but of the concrete substance; but of

this there is in a sense a formula, and in a sense there is not; for there is no formula of it with its matter, for

this is indefinite, but there is a formula of it with reference to its primary substancee.g. in the case of man

the formula of the soul, for the substance is the indwelling form, from which and the matter the socalled

concrete substance is derived; e.g. concavity is a form of this sort, for from this and the nose arise 'snub nose'

and 'snubness'); but in the concrete substance, e.g. a snub nose or Callias, the matter also will be present. And

we have stated that the essence and the thing itself are in some cases the same; ie. in the case of primary

substances, e.g. curvature and the essence of curvature if this is primary. (By a 'primary' substance I mean one

which does not imply the presence of something in something else, i.e. in something that underlies it which

acts as matter.) But things which are of the nature of matter, or of wholes that include matter, are not the

same as their essences, nor are accidental unities like that of 'Socrates' and 'musical'; for these are the same

Now let us treat first of definition, in so far as we have not treated of it in the Analytics; for the problem

stated in them is useful for our inquiries concerning substance. I mean this problem:wherein can consist the

unity of that, the formula of which we call a definition, as for instance, in the case of man, 'twofooted

animal'; for let this be the formula of man. Why, then, is this one, and not many, viz. 'animal' and

'twofooted'? For in the case of 'man' and 'pale' there is a plurality when one term does not belong to the

other, but a unity when it does belong and the subject, man, has a certain attribute; for then a unity is

produced and we have 'the pale man'. In the present case, on the other hand, one does not share in the other;

the genus is not thought to share in its differentiae (for then the same thing would share in contraries; for the

differentiae by which the genus is divided are contrary). And even if the genus does share in them, the same

argument applies, since the differentiae present in man are many, e.g. endowed with feet, twofooted,

featherless. Why are these one and not many? Not because they are present in one thing; for on this principle

a unity can be made out of all the attributes of a thing. But surely all the attributes in the definition must be

one; for the definition is a single formula and a formula of substance, so that it must be a formula of some one

We must first inquire about definitions reached by the method of divisions. There is nothing in the definition

except the firstnamed and the differentiae. The other genera are the first genus and along with this the

differentiae that are taken with it, e.g. the first may be 'animal', the next 'animal which is twofooted', and

again 'animal which is twofooted and featherless', and similarly if the definition includes more terms. And

in general it makes no difference whether it includes many or few terms,nor, therefore, whether it includes

few or simply two; and of the two the one is differentia and the other genus; e.g. in 'twofooted animal'

If then the genus absolutely does not exist apart from the speciesofagenus, or if it exists but exists as

matter (for the voice is genus and matter, but its differentiae make the species, i.e. the letters, out of it),

But it is also necessary that the division be by the differentia of the diferentia; e.g. 'endowed with feet' is a

differentia of 'animal'; again the differentia of 'animal endowed with feet' must be of it qua endowed with

feet. Therefore we must not say, if we are to speak rightly, that of that which is endowed with feet one part

has feathers and one is featherless (if we do this we do it through incapacity); we must divide it only into

clovenfooted and not cloven; for these are differentiae in the foot; clovenfootedness is a form of

footedness. And the process wants always to go on so till it reaches the species that contain no differences.

And then there will be as many kinds of foot as there are differentiae, and the kinds of animals endowed with

feet will be equal in number to the differentiae. If then this is so, clearly the last differentia will be the

substance of the thing and its definition, since it is not right to state the same things more than once in our

definitions; for it is superfluous. And this does happen; for when we say 'animal endowed with feet and

twofooted' we have said nothing other than 'animal having feet, having two feet'; and if we divide this by the

proper division, we shall be saying the same thing more than onceas many times as there are differentiae.

If then a differentia of a differentia be taken at each step, one differentiathe lastwill be the form and the

substance; but if we divide according to accidental qualities, e.g. if we were to divide that which is endowed

with feet into the white and the black, there will be as many differentiae as there are cuts. Therefore it is plain

that the definition is the formula which contains the differentiae, or, according to the right method, the last of

these. This would be evident, if we were to change the order of such definitions, e.g. of that of man, saying

'animal which is twofooted and endowed with feet'; for 'endowed with feet' is superfluous when

'twofooted' has been said. But there is no order in the substance; for how are we to think the one element

posterior and the other prior? Regarding the definitions, then, which are reached by the method of divisions,

Let us return to the subject of our inquiry, which is substance. As the substratum and the essence and the

compound of these are called substance, so also is the universal. About two of these we have spoken; both

about the essence and about the substratum, of which we have said that it underlies in two senses, either being

a 'this'which is the way in which an animal underlies its attributesor as the matter underlies the complete

reality. The universal also is thought by some to be in the fullest sense a cause, and a principle; therefore let

us attack the discussion of this point also. For it seems impossible that any universal term should be the name

of a substance. For firstly the substance of each thing is that which is peculiar to it, which does not belong to

anything else; but the universal is common, since that is called universal which is such as to belong to more

than one thing. Of which individual then will this be the substance? Either of all or of none; but it cannot be

the substance of all. And if it is to be the substance of one, this one will be the others also; for things whose

Further, substance means that which is not predicable of a subject, but the universal is predicable of some

But perhaps the universal, while it cannot be substance in the way in which the essence is so, can be present

in this; e.g. 'animal' can be present in 'man' and 'horse'. Then clearly it is a formula of the essence. And it

makes no difference even if it is not a formula of everything that is in the substance; for none the less the

universal will be the substance of something, as 'man' is the substance of the individual man in whom it is

present, so that the same result will follow once more; for the universal, e.g. 'animal', will be the substance of

that in which it is present as something peculiar to it. And further it is impossible and absurd that the 'this', i.e.

the substance, if it consists of parts, should not consist of substances nor of what is a 'this', but of quality; for

that which is not substance, i.e. the quality, will then be prior to substance and to the 'this'. Which is

impossible; for neither in formula nor in time nor in coming to be can the modifications be prior to the

substance; for then they will also be separable from it. Further, Socrates will contain a substance present in a

substance, so that this will be the substance of two things. And in general it follows, if man and such things

are substance, that none of the elements in their formulae is the substance of anything, nor does it exist apart

from the species or in anything else; I mean, for instance, that no 'animal' exists apart from the particular

kinds of animal, nor does any other of the elements present in formulae exist apart.

If, then, we view the matter from these standpoints, it is plain that no universal attribute is a substance, and

this is plain also from the fact that no common predicate indicates a 'this', but rather a 'such'. If not, many

The conclusion is evident also from the following consideration. A substance cannot consist of substances

present in it in complete reality; for things that are thus in complete reality two are never in complete reality

one, though if they are potentially two, they can be one (e.g. the double line consists of two

halvespotentially; for the complete realization of the halves divides them from one another); therefore if the

substance is one, it will not consist of substances present in it and present in this way, which Democritus

describes rightly; he says one thing cannot be made out of two nor two out of one; for he identifies substances

with his indivisible magnitudes. It is clear therefore that the same will hold good of number, if number is a

synthesis of units, as is said by some; for two is either not one, or there is no unit present in it in complete

reality. But our result involves a difficulty. If no substance can consist of universals because a universal

indicates a 'such', not a 'this', and if no substance can be composed of substances existing in complete reality,

every substance would be incomposite, so that there would not even be a formula of any substance. But it is

thought by all and was stated long ago that it is either only, or primarily, substance that can defined; yet now

it seems that not even substance can. There cannot, then, be a definition of anything; or in a sense there can

be, and in a sense there cannot. And what we are saying will be plainer from what follows.

It is clear also from these very facts what consequence confronts those who say the Ideas are substances

capable of separate existence, and at the same time make the Form consist of the genus and the differentiae.

For if the Forms exist and 'animal' is present in 'man' and 'horse', it is either one and the same in number, or

different. (In formula it is clearly one; for he who states the formula will go through the formula in either

case.) If then there is a 'maninhimself' who is a 'this' and exists apart, the parts also of which he consists,

e.g. 'animal' and 'twofooted', must indicate 'thises', and be capable of separate existence, and substances;

Now (1) if the 'animal' in 'the horse' and in 'man' is one and the same, as you are with yourself, (a) how will

the one in things that exist apart be one, and how will this 'animal' escape being divided even from itself?

Further, (b) if it is to share in 'twofooted' and 'manyfooted', an impossible conclusion follows; for contrary

attributes will belong at the same time to it although it is one and a 'this'. If it is not to share in them, what is

the relation implied when one says the animal is twofooted or possessed of feet? But perhaps the two things

are 'put together' and are 'in contact', or are 'mixed'. Yet all these expressions are absurd.

But (2) suppose the Form to be different in each species. Then there will be practically an infinite number of

things whose substance is animal'; for it is not by accident that 'man' has 'animal' for one of its elements.

Further, many things will be 'animalitself'. For (i) the 'animal' in each species will be the substance of the

species; for it is after nothing else that the species is called; if it were, that other would be an element in 'man',

i.e. would be the genus of man. And further, (ii) all the elements of which 'man' is composed will be Ideas.

None of them, then, will be the Idea of one thing and the substance of another; this is impossible. The

'animal', then, present in each species of animals will be animalitself. Further, from what is this 'animal' in

each species derived, and how will it be derived from animalitself? Or how can this 'animal', whose essence

Further, (3)in the case of sensible things both these consequences and others still more absurd follow. If, then,

these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some

Since substance is of two kinds, the concrete thing and the formula (I mean that one kind of substance is the

formula taken with the matter, while another kind is the formula in its generality), substances in the former

sense are capable of destruction (for they are capable also of generation), but there is no destruction of the

formula in the sense that it is ever in course of being destroyed (for there is no generation of it either; the

being of house is not generated, but only the being of this house), but without generation and destruction

formulae are and are not; for it has been shown that no one begets nor makes these. For this reason, also,

there is neither definition of nor demonstration about sensible individual substances, because they have

matter whose nature is such that they are capable both of being and of not being; for which reason all the

individual instances of them are destructible. If then demonstration is of necessary truths and definition is a

scientific process, and if, just as knowledge cannot be sometimes knowledge and sometimes ignorance, but

the state which varies thus is opinion, so too demonstration and definition cannot vary thus, but it is opinion

that deals with that which can be otherwise than as it is, clearly there can neither be definition of nor

demonstration about sensible individuals. For perishing things are obscure to those who have the relevant

knowledge, when they have passed from our perception; and though the formulae remain in the soul

unchanged, there will no longer be either definition or demonstration. And so when one of the

definitionmongers defines any individual, he must recognize that his definition may always be overthrown;

Nor is it possible to define any Idea. For the Idea is, as its supporters say, an individual, and can exist apart;

and the formula must consist of words; and he who defines must not invent a word (for it would be

unknown), but the established words are common to all the members of a class; these then must apply to

something besides the thing defined; e.g. if one were defining you, he would say 'an animal which is lean' or

'pale', or something else which will apply also to some one other than you. If any one were to say that perhaps

all the attributes taken apart may belong to many subjects, but together they belong only to this one, we must

reply first that they belong also to both the elements; e.g. 'twofooted animal' belongs to animal and to the

twofooted. (And in the case of eternal entities this is even necessary, since the elements are prior to and

parts of the compound; nay more, they can also exist apart, if 'man' can exist apart. For either neither or both

can. If, then, neither can, the genus will not exist apart from the various species; but if it does, the differentia

will also.) Secondly, we must reply that 'animal' and 'twofooted' are prior in being to 'twofooted animal';

Again, if the Ideas consist of Ideas (as they must, since elements are simpler than the compound), it will be

further necessary that the elements also of which the Idea consists, e.g. 'animal' and 'twofooted', should be

predicated of many subjects. If not, how will they come to be known? For there will then be an Idea which

cannot be predicated of more subjects than one. But this is not thought possibleevery Idea is thought to be

As has been said, then, the impossibility of defining individuals escapes notice in the case of eternal things,

especially those which are unique, like the sun or the moon. For people err not only by adding attributes

whose removal the sun would survive, e.g. 'going round the earth' or 'nighthidden' (for from their view it

follows that if it stands still or is visible, it will no longer be the sun; but it is strange if this is so; for 'the sun'

means a certain substance); but also by the mention of attributes which can belong to another subject; e.g. if

another thing with the stated attributes comes into existence, clearly it will be a sun; the formula therefore is

general. But the sun was supposed to be an individual, like Cleon or Socrates. After all, why does not one of

the supporters of the Ideas produce a definition of an Idea? It would become clear, if they tried, that what has

Evidently even of the things that are thought to be substances, most are only potencies,both the parts of

animals (for none of them exists separately; and when they are separated, then too they exist, all of them,

merely as matter) and earth and fire and air; for none of them is a unity, but as it were a mere heap, till they

are worked up and some unity is made out of them. One might most readily suppose the parts of living things

and the parts of the soul nearly related to them to turn out to be both, i.e. existent in complete reality as well

as in potency, because they have sources of movement in something in their joints; for which reason some

animals live when divided. Yet all the parts must exist only potentially, when they are one and continuous by

nature,not by force or by growing into one, for such a phenomenon is an abnormality.

Since the term 'unity' is used like the term 'being', and the substance of that which is one is one, and things

whose substance is numerically one are numerically one, evidently neither unity nor being can be the

substance of things, just as being an element or a principle cannot be the substance, but we ask what, then, the

principle is, that we may reduce the thing to something more knowable. Now of these concepts 'being' and

'unity' are more substantial than 'principle' or 'element' or 'cause', but not even the former are substance, since

in general nothing that is common is substance; for substance does not belong to anything but to itself and to

that which has it, of which it is the substance. Further, that which is one cannot be in many places at the same

time, but that which is common is present in many places at the same time; so that clearly no universal exists

But those who say the Forms exist, in one respect are right, in giving the Forms separate existence, if they are

substances; but in another respect they are not right, because they say the one over many is a Form. The

reason for their doing this is that they cannot declare what are the substances of this sort, the imperishable

substances which exist apart from the individual and sensible substances. They make them, then, the same in

kind as the perishable things (for this kind of substance we know)'manhimself' and 'horseitself', adding

to the sensible things the word 'itself'. Yet even if we had not seen the stars, none the less, I suppose, would

they have been eternal substances apart from those which we knew; so that now also if we do not know what

nonsensible substances there are, yet it is doubtless necessary that there should he some.Clearly, then, no

universal term is the name of a substance, and no substance is composed of substances.

Let us state what, i.e. what kind of thing, substance should be said to be, taking once more another

startingpoint; for perhaps from this we shall get a clear view also of that substance which exists apart from

sensible substances. Since, then, substance is a principle and a cause, let us pursue it from this startingpoint.

The 'why' is always sought in this form'why does one thing attach to some other?' For to inquire why the

musical man is a musical man, is either to inquireas we have said why the man is musical, or it is

something else. Now 'why a thing is itself' is a meaningless inquiry (for (to give meaning to the question

'why') the fact or the existence of the thing must already be evidente.g. that the moon is eclipsedbut the

fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as

why the man is man, or the musician musical', unless one were to answer 'because each thing is inseparable

from itself, and its being one just meant this'; this, however, is common to all things and is a short and easy

way with the question). But we can inquire why man is an animal of such and such a nature. This, then, is

plain, that we are not inquiring why he who is a man is a man. We are inquiring, then, why something is

predicable of something (that it is predicable must be clear; for if not, the inquiry is an inquiry into nothing).

E.g. why does it thunder? This is the same as 'why is sound produced in the clouds?' Thus the inquiry is about

the predication of one thing of another. And why are these things, i.e. bricks and stones, a house? Plainly we

are seeking the cause. And this is the essence (to speak abstractly), which in some cases is the end, e.g.

perhaps in the case of a house or a bed, and in some cases is the first mover; for this also is a cause. But while

the efficient cause is sought in the case of genesis and destruction, the final cause is sought in the case of

The object of the inquiry is most easily overlooked where one term is not expressly predicated of another

(e.g. when we inquire 'what man is'), because we do not distinguish and do not say definitely that certain

elements make up a certain whole. But we must articulate our meaning before we begin to inquire; if not, the

inquiry is on the borderline between being a search for something and a search for nothing. Since we must

have the existence of the thing as something given, clearly the question is why the matter is some definite

thing; e.g. why are these materials a house? Because that which was the essence of a house is present. And

why is this individual thing, or this body having this form, a man? Therefore what we seek is the cause, i.e.

the form, by reason of which the matter is some definite thing; and this is the substance of the thing.

Evidently, then, in the case of simple terms no inquiry nor teaching is possible; our attitude towards such

Since that which is compounded out of something so that the whole is one, not like a heap but like a

syllablenow the syllable is not its elements, ba is not the same as b and a, nor is flesh fire and earth (for

when these are separated the wholes, i.e. the flesh and the syllable, no longer exist, but the elements of the

syllable exist, and so do fire and earth); the syllable, then, is somethingnot only its elements (the vowel and

the consonant) but also something else, and the flesh is not only fire and earth or the hot and the cold, but also

something else:if, then, that something must itself be either an element or composed of elements, (1) if it is

an element the same argument will again apply; for flesh will consist of this and fire and earth and something

still further, so that the process will go on to infinity. But (2) if it is a compound, clearly it will be a

compound not of one but of more than one (or else that one will be the thing itself), so that again in this case

we can use the same argument as in the case of flesh or of the syllable. But it would seem that this 'other' is

something, and not an element, and that it is the cause which makes this thing flesh and that a syllable. And

similarly in all other cases. And this is the substance of each thing (for this is the primary cause of its being);

and since, while some things are not substances, as many as are substances are formed in accordance with a

nature of their own and by a process of nature, their substance would seem to be this kind of 'nature', which is

not an element but a principle. An element, on the other hand, is that into which a thing is divided and which

WE must reckon up the results arising from what has been said, and compute the sum of them, and put the

finishing touch to our inquiry. We have said that the causes, principles, and elements of substances are the

object of our search. And some substances are recognized by every one, but some have been advocated by

particular schools. Those generally recognized are the natural substances, i.e. fire, earth, water, air, the simple

bodies; second plants and their parts, and animals and the parts of animals; and finally the physical universe

and its parts; while some particular schools say that Forms and the objects of mathematics are substances. But

there are arguments which lead to the conclusion that there are other substances, the essence and the

substratum. Again, in another way the genus seems more substantial than the various spccies, and the

universal than the particulars. And with the universal and the genus the Ideas are connected; it is in virtue of

the same argument that they are thought to be substances. And since the essence is substance, and the

definition is a formula of the essence, for this reason we have discussed definition and essential predication.

Since the definition is a formula, and a formula has parts, we had to consider also with respect to the notion

of 'part', what are parts of the substance and what are not, and whether the parts of the substance are also parts

of the definition. Further, too, neither the universal nor the genus is a substance; we must inquire later into the

Ideas and the objects of mathematics; for some say these are substances as well as the sensible substances.

But now let us resume the discussion of the generally recognized substances. These are the sensible

substances, and sensible substances all have matter. The substratum is substance, and this is in one sense the

matter (and by matter I mean that which, not being a 'this' actually, is potentially a 'this'), and in another sense

the formula or shape (that which being a 'this' can be separately formulated), and thirdly the complex of these

two, which alone is generated and destroyed, and is, without qualification, capable of separate existence; for

of substances completely expressible in a formula some are separable and some are separable and some are

But clearly matter also is substance; for in all the opposite changes that occur there is something which

underlies the changes, e.g. in respect of place that which is now here and again elsewhere, and in respect of

increase that which is now of one size and again less or greater, and in respect of alteration that which is now

healthy and again diseased; and similarly in respect of substance there is something that is now being

generated and again being destroyed, and now underlies the process as a 'this' and again underlies it in respect

of a privation of positive character. And in this change the others are involved. But in either one or two of the

others this is not involved; for it is not necessary if a thing has matter for change of place that it should also

The difference between becoming in the full sense and becoming in a qualified sense has been stated in our

Since the substance which exists as underlying and as matter is generally recognized, and this that which

exists potentially, it remains for us to say what is the substance, in the sense of actuality, of sensible things.

Democritus seems to think there are three kinds of difference between things; the underlying body, the

matter, is one and the same, but they differ either in rhythm, i.e. shape, or in turning, i.e. position, or in

intercontact, i.e. order. But evidently there are many differences; for instance, some things are characterized

by the mode of composition of their matter, e.g. the things formed by blending, such as honeywater; and

others by being bound together, e.g. bundle; and others by being glued together, e.g. a book; and others by

being nailed together, e.g. a casket; and others in more than one of these ways; and others by position, e.g.

threshold and lintel (for these differ by being placed in a certain way); and others by time, e.g. dinner and

breakfast; and others by place, e.g. the winds; and others by the affections proper to sensible things, e.g.

hardness and softness, density and rarity, dryness and wetness; and some things by some of these qualities,

others by them all, and in general some by excess and some by defect. Clearly, then, the word 'is' has just as

many meanings; a thing is a threshold because it lies in such and such a position, and its being means its lying

in that position, while being ice means having been solidified in such and such a way. And the being of some

things will be defined by all these qualities, because some parts of them are mixed, others are blended, others

are bound together, others are solidified, and others use the other differentiae; e.g. the hand or the foot

requires such complex definition. We must grasp, then, the kinds of differentiae (for these will be the

principles of the being of things), e.g. the things characterized by the more and the less, or by the dense and

the rare, and by other such qualities; for all these are forms of excess and defect. And anything that is

characterized by shape or by smoothness and roughness is characterized by the straight and the curved. And

for other things their being will mean their being mixed, and their not being will mean the opposite.

It is clear, then, from these facts that, since its substance is the cause of each thing's being, we must seek in

these differentiae what is the cause of the being of each of these things. Now none of these differentiae is

substance, even when coupled with matter, yet it is what is analogous to substance in each case; and as in

substances that which is predicated of the matter is the actuality itself, in all other definitions also it is what

most resembles full actuality. E.g. if we had to define a threshold, we should say 'wood or stone in such and

such a position', and a house we should define as 'bricks and timbers in such and such a position',(or a

purpose may exist as well in some cases), and if we had to define ice we should say 'water frozen or solidified

in such and such a way', and harmony is 'such and such a blending of high and low'; and similarly in all other

Obviously, then, the actuality or the formula is different when the matter is different; for in some cases it is

the composition, in others the mixing, and in others some other of the attributes we have named. And so, of

the people who go in for defining, those who define a house as stones, bricks, and timbers are speaking of the

potential house, for these are the matter; but those who propose 'a receptacle to shelter chattels and living

beings', or something of the sort, speak of the actuality. Those who combine both of these speak of the third

kind of substance, which is composed of matter and form (for the formula that gives the differentiae seems to

be an account of the form or actuality, while that which gives the components is rather an account of the

matter); and the same is true of the kind of definitions which Archytas used to accept; they are accounts of

the combined form and matter. E.g. what is still weather? Absence of motion in a large expanse of air; air is

the matter, and absence of motion is the actuality and substance. What is a calm? Smoothness of sea; the

material substratum is the sea, and the actuality or shape is smoothness. It is obvious then, from what has

been said, what sensible substance is and how it existsone kind of it as matter, another as form or actuality,

We must not fail to notice that sometimes it is not clear whether a name means the composite substance, or

the actuality or form, e.g. whether 'house' is a sign for the composite thing, 'a covering consisting of bricks

and stones laid thus and thus', or for the actuality or form, 'a covering', and whether a line is 'twoness in

length' or 'twoness', and whether an animal is soul in a body' or 'a soul'; for soul is the substance or actuality

of some body. 'Animal' might even be applied to both, not as something definable by one formula, but as

related to a single thing. But this question, while important for another purpose, is of no importance for the

inquiry into sensible substance; for the essence certainly attaches to the form and the actuality. For 'soul' and

'to be soul' are the same, but 'to be man' and 'man' are not the same, unless even the bare soul is to be called

man; and thus on one interpretation the thing is the same as its essence, and on another it is not.

If we examine we find that the syllable does not consist of the letters + juxtaposition, nor is the house bricks

+ juxtaposition. And this is right; for the juxtaposition or mixing does not consist of those things of which it

is the juxtaposition or mixing. And the same is true in all other cases; e.g. if the threshold is characterized by

its position, the position is not constituted by the threshold, but rather the latter is constituted by the former.

Nor is man animal + biped, but there must be something besides these, if these are matter,something which

is neither an element in the whole nor a compound, but is the substance; but this people eliminate, and state

only the matter. If, then, this is the cause of the thing's being, and if the cause of its being is its substance,

(This, then, must either be eternal or it must be destructible without being ever in course of being destroyed,

and must have come to be without ever being in course of coming to be. But it has been proved and explained

elsewhere that no one makes or begets the form, but it is the individual that is made, i.e. the complex of form

and matter that is generated. Whether the substances of destructible things can exist apart, is not yet at all

clear; except that obviously this is impossible in some casesin the case of things which cannot exist apart

from the individual instances, e.g. house or utensil. Perhaps, indeed, neither these things themselves, nor any

of the other things which are not formed by nature, are substances at all; for one might say that the nature in

Therefore the difficulty which used to be raised by the school of Antisthenes and other such uneducated

people has a certain timeliness. They said that the 'what' cannot be defined (for the definition so called is a

'long rigmarole') but of what sort a thing, e.g. silver, is, they thought it possible actually to explain, not saying

what it is, but that it is like tin. Therefore one kind of substance can be defined and formulated, i.e. the

composite kind, whether it be perceptible or intelligible; but the primary parts of which this consists cannot

be defined, since a definitory formula predicates something of something, and one part of the definition must

It is also obvious that, if substances are in a sense numbers, they are so in this sense and not, as some say, as

numbers of units. For a definition is a sort of number; for (1) it is divisible, and into indivisible parts (for

definitory formulae are not infinite), and number also is of this nature. And (2) as, when one of the parts of

which a number consists has been taken from or added to the number, it is no longer the same number, but a

different one, even if it is the very smallest part that has been taken away or added, so the definition and the

essence will no longer remain when anything has been taken away or added. And (3) the number must be

something in virtue of which it is one, and this these thinkers cannot state, what makes it one, if it is one (for

either it is not one but a sort of heap, or if it is, we ought to say what it is that makes one out of many); and

the definition is one, but similarly they cannot say what makes it one. And this is a natural result; for the

same reason is applicable, and substance is one in the sense which we have explained, and not, as some say,

by being a sort of unit or point; each is a complete reality and a definite nature. And (4) as number does not

admit of the more and the less, neither does substance, in the sense of form, but if any substance does, it is

only the substance which involves matter. Let this, then, suffice for an account of the generation and

destruction of socalled substances in what sense it is possible and in what sense impossibleand of the

Regarding material substance we must not forget that even if all things come from the same first cause or

have the same things for their first causes, and if the same matter serves as startingpoint for their generation,

yet there is a matter proper to each, e.g. for phlegm the sweet or the fat, and for bile the bitter, or something

else; though perhaps these come from the same original matter. And there come to be several matters for the

same thing, when the one matter is matter for the other; e.g. phlegm comes from the fat and from the sweet, if

the fat comes from the sweet; and it comes from bile by analysis of the bile into its ultimate matter. For one

thing comes from another in two senses, either because it will be found at a later stage, or because it is

produced if the other is analysed into its original constituents. When the matter is one, different things may be

produced owing to difference in the moving cause; e.g. from wood may be made both a chest and a bed. But

some different things must have their matter different; e.g. a saw could not be made of wood, nor is this in the

power of the moving cause; for it could not make a saw of wool or of wood. But if, as a matter of fact, the

same thing can be made of different material, clearly the art, i.e. the moving principle, is the same; for if both

When one inquires into the cause of something, one should, since 'causes' are spoken of in several senses,

state all the possible causes. what is the material cause of man? Shall we say 'the menstrual fluid'? What is

moving cause? Shall we say 'the seed'? The formal cause? His essence. The final cause? His end. But perhaps

the latter two are the same.It is the proximate causes we must state. What is the material cause? We must

Regarding the substances that are natural and generable, if the causes are really these and of this number and

we have to learn the causes, we must inquire thus, if we are to inquire rightly. But in the case of natural but

eternal substances another account must be given. For perhaps some have no matter, or not matter of this sort

but only such as can be moved in respect of place. Nor does matter belong to those things which exist by

nature but are not substances; their substratum is the substance. E.g what is the cause of eclipse? What is its

matter? There is none; the moon is that which suffers eclipse. What is the moving cause which extinguished

the light? The earth. The final cause perhaps does not exist. The formal principle is the definitory formula,

but this is obscure if it does not include the cause. E.g. what is eclipse? Deprivation of light. But if we add 'by

the earth's coming in between', this is the formula which includes the cause. In the case of sleep it is not clear

what it is that proximately has this affection. Shall we say that it is the animal? Yes, but the animal in virtue

of what, i.e. what is the proximate subject? The heart or some other part. Next, by what is it produced? Next,

what is the affectionthat of the proximate subject, not of the whole animal? Shall we say that it is

immobility of such and such a kind? Yes, but to what process in the proximate subject is this due?

Since some things are and are not, without coming to be and ceasing to be, e.g. points, if they can be said to

be, and in general forms (for it is not 'white' comes to be, but the wood comes to be white, if everything that

comes to be comes from something and comes to be something), not all contraries can come from one

another, but it is in different senses that a pale man comes from a dark man, and pale comes from dark. Nor

has everything matter, but only those things which come to be and change into one another. Those things

which, without ever being in course of changing, are or are not, have no matter.

There is difficulty in the question how the matter of each thing is related to its contrary states. E.g. if the body

is potentially healthy, and disease is contrary to health, is it potentially both healthy and diseased? And is

water potentially wine and vinegar? We answer that it is the matter of one in virtue of its positive state and its

form, and of the other in virtue of the privation of its positive state and the corruption of it contrary to its

nature. It is also hard to say why wine is not said to be the matter of vinegar nor potentially vinegar (though

vinegar is produced from it), and why a living man is not said to be potentially dead. In fact they are not, but

the corruptions in question are accidental, and it is the matter of the animal that is itself in virtue of its

corruption the potency and matter of a corpse, and it is water that is the matter of vinegar. For the corpse

comes from the animal, and vinegar from wine, as night from day. And all the things which change thus into

one another must go back to their matter; e.g. if from a corpse is produced an animal, the corpse first goes

back to its matter, and only then becomes an animal; and vinegar first goes back to water, and only then

To return to the difficulty which has been stated with respect both to definitions and to numbers, what is the

cause of their unity? In the case of all things which have several parts and in which the totality is not, as it

were, a mere heap, but the whole is something beside the parts, there is a cause; for even in bodies contact is

the cause of unity in some cases, and in others viscosity or some other such quality. And a definition is a set

of words which is one not by being connected together, like the Iliad, but by dealing with one object.What

then, is it that makes man one; why is he one and not many, e.g. animal + biped, especially if there are, as

some say, an animalitself and a bipeditself? Why are not those Forms themselves the man, so that men

would exist by participation not in man, nor inone Form, but in two, animal and biped, and in general man

Clearly, then, if people proceed thus in their usual manner of definition and speech, they cannot explain and

solve the difficulty. But if, as we say, one element is matter and another is form, and one is potentially and

the other actually, the question will no longer be thought a difficulty. For this difficulty is the same as would

arise if 'round bronze' were the definition of 'cloak'; for this word would be a sign of the definitory formula,

so that the question is, what is the cause of the unity of 'round' and 'bronze'? The difficulty disappears,

because the one is matter, the other form. What, then, causes thisthat which was potentially to be

actuallyexcept, in the case of things which are generated, the agent? For there is no other cause of the

potential sphere's becoming actually a sphere, but this was the essence of either. Of matter some is

intelligible, some perceptible, and in a formula there is always an element of matter as well as one of

actuality; e.g. the circle is 'a plane figure'. But of the things which have no matter, either intelligible or

perceptible, each is by its nature essentially a kind of unity, as it is essentially a kind of beingindividual

substance, quality, or quantity (and so neither 'existent' nor 'one' is present in their definitions), and the

essence of each of them is by its very nature a kind of unity as it is a kind of beingand so none of these has

any reason outside itself, for being one, nor for being a kind of being; for each is by its nature a kind of being

and a kind of unity, not as being in the genus 'being' or 'one' nor in the sense that being and unity can exist

Owing to the difficulty about unity some speak of 'participation', and raise the question, what is the cause of

participation and what is it to participate; and others speak of 'communion', as Lycophron says knowledge is a

communion of knowing with the soul; and others say life is a 'composition' or 'connexion' of soul with body.

Yet the same account applies to all cases; for being healthy, too, will on this showing be either a 'communion'

or a 'connexion' or a 'composition' of soul and health, and the fact that the bronze is a triangle will be a

'composition' of bronze and triangle, and the fact that a thing is white will be a 'composition' of surface and

whiteness. The reason is that people look for a unifying formula, and a difference, between potency and

complete reality. But, as has been said, the proximate matter and the form are one and the same thing, the one

potentially, and the other actually. Therefore it is like asking what in general is the cause of unity and of a

thing's being one; for each thing is a unity, and the potential and the actual are somehow one. Therefore there

is no other cause here unless there is something which caused the movement from potency into actuality. And

WE have treated of that which is primarily and to which all the other categories of being are referredi.e. of

substance. For it is in virtue of the concept of substance that the others also are said to bequantity and

quality and the like; for all will be found to involve the concept of substance, as we said in the first part of our

work. And since 'being' is in one way divided into individual thing, quality, and quantity, and is in another

way distinguished in respect of potency and complete reality, and of function, let us now add a discussion of

potency and complete reality. And first let us explain potency in the strictest sense, which is, however, not the

most useful for our present purpose. For potency and actuality extend beyond the cases that involve a

reference to motion. But when we have spoken of this first kind, we shall in our discussions of actuality'

We have pointed out elsewhere that 'potency' and the word 'can' have several senses. Of these we may neglect

all the potencies that are so called by an equivocation. For some are called so by analogy, as in geometry we

say one thing is or is not a 'power' of another by virtue of the presence or absence of some relation between

them. But all potencies that conform to the same type are originative sources of some kind, and are called

potencies in reference to one primary kind of potency, which is an originative source of change in another

thing or in the thing itself qua other. For one kind is a potency of being acted on, i.e. the originative source, in

the very thing acted on, of its being passively changed by another thing or by itself qua other; and another

kind is a state of insusceptibility to change for the worse and to destruction by another thing or by the thing

itself qua other by virtue of an originative source of change. In all these definitions is implied the formula if

potency in the primary sense.And again these socalled potencies are potencies either of merely acting or

being acted on, or of acting or being acted on well, so that even in the formulae of the latter the formulae of

Obviously, then, in a sense the potency of acting and of being acted on is one (for a thing may be 'capable'

either because it can itself be acted on or because something else can be acted on by it), but in a sense the

potencies are different. For the one is in the thing acted on; it is because it contains a certain originative

source, and because even the matter is an originative source, that the thing acted on is acted on, and one thing

by one, another by another; for that which is oily can be burnt, and that which yields in a particular way can

be crushed; and similarly in all other cases. But the other potency is in the agent, e.g. heat and the art of

building are present, one in that which can produce heat and the other in the man who can build. And so, in so

far as a thing is an organic unity, it cannot be acted on by itself; for it is one and not two different things. And

'impotence'and 'impotent' stand for the privation which is contrary to potency of this sort, so that every

potency belongs to the same subject and refers to the same process as a corresponding impotence. Privation

has several senses; for it means (1) that which has not a certain quality and (2) that which might naturally

have it but has not it, either (a) in general or (b) when it might naturally have it, and either (a) in some

particular way, e.g. when it has not it completely, or (b) when it has not it at all. And in certain cases if things

which naturally have a quality lose it by violence, we say they have suffered privation.

Since some such originative sources are present in soulless things, and others in things possessed of soul, and

in soul, and in the rational part of the soul, clearly some potencies will, be nonrational and some will be

nonrational and some will be accompanied by a rational formula. This is why all arts, i.e. all productive

forms of knowledge, are potencies; they are originative sources of change in another thing or in the artist

And each of those which are accompanied by a rational formula is alike capable of contrary effects, but one

nonrational power produces one effect; e.g. the hot is capable only of heating, but the medical art can

produce both disease and health. The reason is that science is a rational formula, and the same rational

formula explains a thing and its privation, only not in the same way; and in a sense it applies to both, but in a

sense it applies rather to the positive fact. Therefore such sciences must deal with contraries, but with one in

virtue of their own nature and with the other not in virtue of their nature; for the rational formula applies to

one object in virtue of that object's nature, and to the other, in a sense, accidentally. For it is by denial and

removal that it exhibits the contrary; for the contrary is the primary privation, and this is the removal of the

positive term. Now since contraries do not occur in the same thing, but science is a potency which depends on

the possession of a rational formula, and the soul possesses an originative source of movement; therefore,

while the wholesome produces only health and the calorific only heat and the frigorific only cold, the

scientific man produces both the contrary effects. For the rational formula is one which applies to both,

though not in the same way, and it is in a soul which possesses an originative source of movement; so that the

soul will start both processes from the same originative source, having linked them up with the same thing.

And so the things whose potency is according to a rational formula act contrariwise to the things whose

potency is nonrational; for the products of the former are included under one originative source, the rational

It is obvious also that the potency of merely doing a thing or having it done to one is implied in that of doing

it or having it done well, but the latter is not always implied in the former: for he who does a thing well must

There are some who say, as the Megaric school does, that a thing 'can' act only when it is acting, and when it

is not acting it 'cannot' act, e.g. that he who is not building cannot build, but only he who is building, when he

is building; and so in all other cases. It is not hard to see the absurdities that attend this view.

For it is clear that on this view a man will not be a builder unless he is building (for to be a builder is to be

able to build), and so with the other arts. If, then, it is impossible to have such arts if one has not at some time

learnt and acquired them, and it is then impossible not to have them if one has not sometime lost them (either

by forgetfulness or by some accident or by time; for it cannot be by the destruction of the object, for that lasts

for ever), a man will not have the art when he has ceased to use it, and yet he may immediately build again;

how then will he have got the art? And similarly with regard to lifeless things; nothing will be either cold or

hot or sweet or perceptible at all if people are not perceiving it; so that the upholders of this view will have to

maintain the doctrine of Protagoras. But, indeed, nothing will even have perception if it is not perceiving, i.e.

exercising its perception. If, then, that is blind which has not sight though it would naturally have it, when it

would naturally have it and when it still exists, the same people will be blind many times in the dayand deaf

Again, if that which is deprived of potency is incapable, that which is not happening will be incapable of

happening; but he who says of that which is incapable of happening either that it is or that it will be will say

what is untrue; for this is what incapacity meant. Therefore these views do away with both movement and

becoming. For that which stands will always stand, and that which sits will always sit, since if it is sitting it

will not get up; for that which, as we are told, cannot get up will be incapable of getting up. But we cannot

say this, so that evidently potency and actuality are different (but these views make potency and actuality the

same, and so it is no small thing they are seeking to annihilate), so that it is possible that a thing may be

capable of being and not he, and capable of not being and yet he, and similarly with the other kinds of

predicate; it may be capable of walking and yet not walk, or capable of not walking and yet walk. And a thing

is capable of doing something if there will be nothing impossible in its having the actuality of that of which it

is said to have the capacity. I mean, for instance, if a thing is capable of sitting and it is open to it to sit, there

will be nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving, or

of standing or making to stand, or of being or coming to be, or of not being or not coming to be.

The word 'actuality', which we connect with 'complete reality', has, in the main, been extended from

movements to other things; for actuality in the strict sense is thought to be identical with movement. And so

people do not assign movement to nonexistent things, though they do assign some other predicates. E.g.

they say that nonexistent things are objects of thought and desire, but not that they are moved; and this

because, while ex hypothesi they do not actually exist, they would have to exist actually if they were moved.

For of nonexistent things some exist potentially; but they do not exist, because they do not exist in complete

If what we have described is identical with the capable or convertible with it, evidently it cannot be true to

say 'this is capable of being but will not be', which would imply that the things incapable of being would on

this showing vanish. Suppose, for instance, that a manone who did not take account of that which is

incapable of beingwere to say that the diagonal of the square is capable of being measured but will not be

measured, because a thing may well be capable of being or coming to be, and yet not be or be about to be.

But from the premisses this necessarily follows, that if we actually supposed that which is not, but is capable

of being, to be or to have come to be, there will be nothing impossible in this; but the result will be

impossible, for the measuring of the diagonal is impossible. For the false and the impossible are not the same;

that you are standing now is false, but that you should be standing is not impossible.

At the same time it is clear that if, when A is real, B must be real, then, when A is possible, B also must be

possible. For if B need not be possible, there is nothing to prevent its not being possible. Now let A be

supposed possible. Then, when A was possible, we agreed that nothing impossible followed if A were

supposed to be real; and then B must of course be real. But we supposed B to be impossible. Let it be

impossible then. If, then, B is impossible, A also must be so. But the first was supposed impossible; therefore

the second also is impossible. If, then, A is possible, B also will be possible, if they were so related that if

A,is real, B must be real. If, then, A and B being thus related, B is not possible on this condition, and B will

not be related as was supposed. And if when A is possible, B must be possible, then if A is real, B also must

be real. For to say that B must be possible, if A is possible, means this, that if A is real both at the time when

and in the way in which it was supposed capable of being real, B also must then and in that way be real.

As all potencies are either innate, like the senses, or come by practice, like the power of playing the flute, or

by learning, like artistic power, those which come by practice or by rational formula we must acquire by

previous exercise but this is not necessary with those which are not of this nature and which imply passivity.

Since that which is 'capable' is capable of something and at some time in some way (with all the other

qualifications which must be present in the definition), and since some things can produce change according

to a rational formula and their potencies involve such a formula, while other things are nonrational and their

potencies are nonrational, and the former potencies must be in a living thing, while the latter can be both in

the living and in the lifeless; as regards potencies of the latter kind, when the agent and the patient meet in the

way appropriate to the potency in question, the one must act and the other be acted on, but with the former

kind of potency this is not necessary. For the nonrational potencies are all productive of one effect each, but

the rational produce contrary effects, so that if they produced their effects necessarily they would produce

contrary effects at the same time; but this is impossible. There must, then, be something else that decides; I

mean by this, desire or will. For whichever of two things the animal desires decisively, it will do, when it is

present, and meets the passive object, in the way appropriate to the potency in question. Therefore everything

which has a rational potency, when it desires that for which it has a potency and in the circumstances in

which it has the potency, must do this. And it has the potency in question when the passive object is present

and is in a certain state; if not it will not be able to act. (To add the qualification 'if nothing external prevents

it' is not further necessary; for it has the potency on the terms on which this is a potency of acting, and it is

this not in all circumstances but on certain conditions, among which will be the exclusion of external

hindrances; for these are barred by some of the positive qualifications.) And so even if one has a rational

wish, or an appetite, to do two things or contrary things at the same time, one will not do them; for it is not on

these terms that one has the potency for them, nor is it a potency of doing both at the same time, since one

will do the things which it is a potency of doing, on the terms on which one has the potency.

Since we have treated of the kind of potency which is related to movement, let us discuss actualitywhat, and

what kind of thing, actuality is. For in the course of our analysis it will also become clear, with regard to the

potential, that we not only ascribe potency to that whose nature it is to move something else, or to be moved

by something else, either without qualification or in some particular way, but also use the word in another

sense, which is the reason of the inquiry in the course of which we have discussed these previous senses also.

Actuality, then, is the existence of a thing not in the way which we express by 'potentially'; we say that

potentially, for instance, a statue of Hermes is in the block of wood and the halfline is in the whole, because

it might be separated out, and we call even the man who is not studying a man of science, if he is capable of

studying; the thing that stands in contrast to each of these exists actually. Our meaning can be seen in the

particular cases by induction, and we must not seek a definition of everything but be content to grasp the

analogy, that it is as that which is building is to that which is capable of building, and the waking to the

sleeping, and that which is seeing to that which has its eyes shut but has sight, and that which has been

shaped out of the matter to the matter, and that which has been wrought up to the unwrought. Let actuality be

defined by one member of this antithesis, and the potential by the other. But all things are not said in the

same sense to exist actually, but only by analogyas A is in B or to B, C is in D or to D; for some are as

But also the infinite and the void and all similar things are said to exist potentially and actually in a different

sense from that which applies to many other things, e.g. to that which sees or walks or is seen. For of the

latter class these predicates can at some time be also truly asserted without qualification; for the seen is so

called sometimes because it is being seen, sometimes because it is capable of being seen. But the infinite does

not exist potentially in the sense that it will ever actually have separate existence; it exists potentially only for

knowledge. For the fact that the process of dividing never comes to an end ensures that this activity exists

Since of the actions which have a limit none is an end but all are relative to the end, e.g. the removing of fat,

or fatremoval, and the bodily parts themselves when one is making them thin are in movement in this way

(i.e. without being already that at which the movement aims), this is not an action or at least not a complete

one (for it is not an end); but that movement in which the end is present is an action. E.g. at the same time we

are seeing and have seen, are understanding and have understood, are thinking and have thought (while it is

not true that at the same time we are learning and have learnt, or are being cured and have been cured). At the

same time we are living well and have lived well, and are happy and have been happy. If not, the process

would have had sometime to cease, as the process of making thin ceases: but, as things are, it does not cease;

we are living and have lived. Of these processes, then, we must call the one set movements, and the other

actualities. For every movement is incompletemaking thin, learning, walking, building; these are

movements, and incomplete at that. For it is not true that at the same time a thing is walking and has walked,

or is building and has built, or is coming to be and has come to be, or is being moved and has been moved,

but what is being moved is different from what has been moved, and what is moving from what has moved.

But it is the same thing that at the same time has seen and is seeing, seeing, or is thinking and has thought.

The latter sort of process, then, I call an actuality, and the former a movement.

What, and what kind of thing, the actual is, may be taken as explained by these and similar considerations.

But we must distinguish when a thing exists potentially and when it does not; for it is not at any and every

time. E.g. is earth potentially a man? Nobut rather when it has already become seed, and perhaps not even

then. It is just as it is with being healed; not everything can be healed by the medical art or by luck, but there

is a certain kind of thing which is capable of it, and only this is potentially healthy. And (1) the delimiting

mark of that which as a result of thought comes to exist in complete reality from having existed potentially is

that if the agent has willed it it comes to pass if nothing external hinders, while the condition on the other

sideviz. in that which is healedis that nothing in it hinders the result. It is on similar terms that we have

what is potentially a house; if nothing in the thing acted oni.e. in the matterprevents it from becoming a

house, and if there is nothing which must be added or taken away or changed, this is potentially a house; and

the same is true of all other things the source of whose becoming is external. And (2) in the cases in which

the source of the becoming is in the very thing which comes to be, a thing is potentially all those things which

it will be of itself if nothing external hinders it. E.g. the seed is not yet potentially a man; for it must be

deposited in something other than itself and undergo a change. But when through its own motive principle it

has already got such and such attributes, in this state it is already potentially a man; while in the former state

it needs another motive principle, just as earth is not yet potentially a statue (for it must first change in order

It seems that when we call a thing not something else but 'thaten'e.g. a casket is not 'wood' but 'wooden', and

wood is not 'earth' but 'earthen', and again earth will illustrate our point if it is similarly not something else

but 'thaten'that other thing is always potentially (in the full sense of that word) the thing which comes after it

in this series. E.g. a casket is not 'earthen' nor 'earth', but 'wooden'; for this is potentially a casket and this is

the matter of a casket, wood in general of a casket in general, and this particular wood of this particular

casket. And if there is a first thing, which is no longer, in reference to something else, called 'thaten', this is

prime matter; e.g. if earth is 'airy' and air is not 'fire' but 'fiery', fire is prime matter, which is not a 'this'. For

the subject or substratum is differentiated by being a 'this' or not being one; i.e. the substratum of

modifications is, e.g. a man, i.e. a body and a soul, while the modification is 'musical' or 'pale'. (The subject is

called, when music comes to be present in it, not 'music' but 'musical', and the man is not 'paleness' but 'pale',

and not 'ambulation' or 'movement' but 'walking' or 'moving',which is akin to the 'thaten'.) Wherever this is

so, then, the ultimate subject is a substance; but when this is not so but the predicate is a form and a 'this', the

ultimate subject is matter and material substance. And it is only right that 'thaten' should be used with

We have stated, then, when a thing is to be said to exist potentially and when it is not.

From our discussion of the various senses of 'prior', it is clear that actuality is prior to potency. And I mean by

potency not only that definite kind which is said to be a principle of change in another thing or in the thing

itself regarded as other, but in general every principle of movement or of rest. For nature also is in the same

genus as potency; for it is a principle of movementnot, however, in something else but in the thing itself qua

itself. To all such potency, then, actuality is prior both in formula and in substantiality; and in time it is prior

(1) Clearly it is prior in formula; for that which is in the primary sense potential is potential because it is

possible for it to become active; e.g. I mean by 'capable of building' that which can build, and by 'capable of

seeing' that which can see, and by 'visible' that which can be seen. And the same account applies to all other

cases, so that the formula and the knowledge of the one must precede the knowledge of the other.

(2) In time it is prior in this sense: the actual which is identical in species though not in number with a

potentially existing thing is to it. I mean that to this particular man who now exists actually and to the corn

and to the seeing subject the matter and the seed and that which is capable of seeing, which are potentially a

man and corn and seeing, but not yet actually so, are prior in time; but prior in time to these are other actually

existing things, from which they were produced. For from the potentially existing the actually existing is

always produced by an actually existing thing, e.g. man from man, musician by musician; there is always a

first mover, and the mover already exists actually. We have said in our account of substance that everything

that is produced is something produced from something and by something, and that the same in species as it.

This is why it is thought impossible to be a builder if one has built nothing or a harper if one has never played

the harp; for he who learns to play the harp learns to play it by playing it, and all other learners do similarly.

And thence arose the sophistical quibble, that one who does not possess a science will be doing that which is

the object of the science; for he who is learning it does not possess it. But since, of that which is coming to

be, some part must have come to be, and, of that which, in general, is changing, some part must have changed

(this is shown in the treatise on movement), he who is learning must, it would seem, possess some part of the

science. But here too, then, it is clear that actuality is in this sense also, viz. in order of generation and of

But (3) it is also prior in substantiality; firstly, (a) because the things that are posterior in becoming are prior

in form and in substantiality (e.g. man is prior to boy and human being to seed; for the one already has its

form, and the other has not), and because everything that comes to be moves towards a principle, i.e. an end

(for that for the sake of which a thing is, is its principle, and the becoming is for the sake of the end), and the

actuality is the end, and it is for the sake of this that the potency is acquired. For animals do not see in order

that they may have sight, but they have sight that they may see. And similarly men have the art of building

that they may build, and theoretical science that they may theorize; but they do not theorize that they may

have theoretical science, except those who are learning by practice; and these do not theorize except in a

limited sense, or because they have no need to theorize. Further, matter exists in a potential state, just because

it may come to its form; and when it exists actually, then it is in its form. And the same holds good in all

cases, even those in which the end is a movement. And so, as teachers think they have achieved their end

when they have exhibited the pupil at work, nature does likewise. For if this is not the case, we shall have

Pauson's Hermes over again, since it will be hard to say about the knowledge, as about the figure in the

picture, whether it is within or without. For the action is the end, and the actuality is the action. And so even

the word 'actuality' is derived from 'action', and points to the complete reality.

And while in some cases the exercise is the ultimate thing (e.g. in sight the ultimate thing is seeing, and no

other product besides this results from sight), but from some things a product follows (e.g. from the art of

building there results a house as well as the act of building), yet none the less the act is in the former case the

end and in the latter more of an end than the potency is. For the act of building is realized in the thing that is

Where, then, the result is something apart from the exercise, the actuality is in the thing that is being made,

e.g. the act of building is in the thing that is being built and that of weaving in the thing that is being woven,

and similarly in all other cases, and in general the movement is in the thing that is being moved; but where

there is no product apart from the actuality, the actuality is present in the agents, e.g. the act of seeing is in the

seeing subject and that of theorizing in the theorizing subject and the life is in the soul (and therefore

Obviously, therefore, the substance or form is actuality. According to this argument, then, it is obvious that

actuality is prior in substantial being to potency; and as we have said, one actuality always precedes another

But (b) actuality is prior in a stricter sense also; for eternal things are prior in substance to perishable things,

and no eternal thing exists potentially. The reason is this. Every potency is at one and the same time a

potency of the opposite; for, while that which is not capable of being present in a subject cannot be present,

everything that is capable of being may possibly not be actual. That, then, which is capable of being may

either be or not be; the same thing, then, is capable both of being and of not being. And that which is capable

of not being may possibly not be; and that which may possibly not be is perishable, either in the full sense, or

in the precise sense in which it is said that it possibly may not be, i.e. in respect either of place or of quantity

or quality; 'in the full sense' means 'in respect of substance'. Nothing, then, which is in the full sense

imperishable is in the full sense potentially existent (though there is nothing to prevent its being so in some

respect, e.g. potentially of a certain quality or in a certain place); all imperishable things, then, exist actually.

Nor can anything which is of necessity exist potentially; yet these things are primary; for if these did not

exist, nothing would exist. Nor does eternal movement, if there be such, exist potentially; and, if there is an

eternal mobile, it is not in motion in virtue of a potentiality, except in respect of 'whence' and 'whither' (there

is nothing to prevent its having matter which makes it capable of movement in various directions). And so the

sun and the stars and the whole heaven are ever active, and there is no fear that they may sometime stand still,

as the natural philosophers fear they may. Nor do they tire in this activity; for movement is not for them, as it

is for perishable things, connected with the potentiality for opposites, so that the continuity of the movement

should be laborious; for it is that kind of substance which is matter and potency, not actuality, that causes

Imperishable things are imitated by those that are involved in change, e.g. earth and fire. For these also are

ever active; for they have their movement of themselves and in themselves. But the other potencies,

according to our previous discussion, are all potencies for opposites; for that which can move another in this

way can also move it not in this way, i.e. if it acts according to a rational formula; and the same nonrational

If, then, there are any entities or substances such as the dialecticians say the Ideas are, there must be

something much more scientific than scienceitself and something more mobile than movementitself; for

these will be more of the nature of actualities, while scienceitself and movementitself are potencies for

Obviously, then, actuality is prior both to potency and to every principle of change.

That the actuality is also better and more valuable than the good potency is evident from the following

argument. Everything of which we say that it can do something, is alike capable of contraries, e.g. that of

which we say that it can be well is the same as that which can be ill, and has both potencies at once; for the

same potency is a potency of health and illness, of rest and motion, of building and throwing down, of being

built and being thrown down. The capacity for contraries, then, is present at the same time; but contraries

cannot be present at the same time, and the actualities also cannot be present at the same time, e.g. health and

illness. Therefore, while the good must be one of them, the capacity is both alike, or neither; the actuality,

then, is better. Also in the case of bad things the end or actuality must be worse than the potency; for that

which 'can' is both contraries alike. Clearly, then, the bad does not exist apart from bad things; for the bad is

in its nature posterior to the potency. And therefore we may also say that in the things which are from the

beginning, i.e. in eternal things, there is nothing bad, nothing defective, nothing perverted (for perversion is

It is an activity also that geometrical constructions are discovered; for we find them by dividing. If the figures

had been already divided, the constructions would have been obvious; but as it is they are present only

potentially. Why are the angles of the triangle equal to two right angles? Because the angles about one point

are equal to two right angles. If, then, the line parallel to the side had been already drawn upwards, the reason

would have been evident to any one as soon as he saw the figure. Why is the angle in a semicircle in all cases

a right angle? If three lines are equal the two which form the base, and the perpendicular from the centrethe

conclusion is evident at a glance to one who knows the former proposition. Obviously, therefore, the

potentially existing constructions are discovered by being brought to actuality; the reason is that the

geometer's thinking is an actuality; so that the potency proceeds from an actuality; and therefore it is by

making constructions that people come to know them (though the single actuality is later in generation than

The terms 'being' and 'nonbeing' are employed firstly with reference to the categories, and secondly with

reference to the potency or actuality of these or their nonpotency or nonactuality, and thirdly in the sense of

true and false. This depends, on the side of the objects, on their being combined or separated, so that he who

thinks the separated to be separated and the combined to be combined has the truth, while he whose thought

is in a state contrary to that of the objects is in error. This being so, when is what is called truth or falsity

present, and when is it not? We must consider what we mean by these terms. It is not because we think truly

that you are pale, that you are pale, but because you are pale we who say this have the truth. If, then, some

things are always combined and cannot be separated, and others are always separated and cannot be

combined, while others are capable either of combination or of separation, 'being' is being combined and one,

and 'not being' is being not combined but more than one. Regarding contingent facts, then, the same opinion

or the same statement comes to be false and true, and it is possible for it to be at one time correct and at

another erroneous; but regarding things that cannot be otherwise opinions are not at one time true and at

But with regard to incomposites, what is being or not being, and truth or falsity? A thing of this sort is not

composite, so as to 'be' when it is compounded, and not to 'be' if it is separated, like 'that the wood is white' or

'that the diagonal is incommensurable'; nor will truth and falsity be still present in the same way as in the

previous cases. In fact, as truth is not the same in these cases, so also being is not the same; but (a) truth or

falsity is as followscontact and assertion are truth (assertion not being the same as affirmation), and

ignorance is noncontact. For it is not possible to be in error regarding the question what a thing is, save in an

accidental sense; and the same holds good regarding noncomposite substances (for it is not possible to be in

error about them). And they all exist actually, not potentially; for otherwise they would have come to be and

ceased to be; but, as it is, being itself does not come to be (nor cease to be); for if it had done so it would have

had to come out of something. About the things, then, which are essences and actualities, it is not possible to

be in error, but only to know them or not to know them. But we do inquire what they are, viz. whether they

(b) As regards the 'being' that answers to truth and the 'nonbeing' that answers to falsity, in one case there is

truth if the subject and the attribute are really combined, and falsity if they are not combined; in the other

case, if the object is existent it exists in a particular way, and if it does not exist in this way does not exist at

all. And truth means knowing these objects, and falsity does not exist, nor error, but only ignoranceand not

an ignorance which is like blindness; for blindness is akin to a total absence of the faculty of thinking.

It is evident also that about unchangeable things there can be no error in respect of time, if we assume them to

be unchangeable. E.g. if we suppose that the triangle does not change, we shall not suppose that at one time

its angles are equal to two right angles while at another time they are not (for that would imply change). It is

possible, however, to suppose that one member of such a class has a certain attribute and another has not; e.g.

while we may suppose that no even number is prime, we may suppose that some are and some are not. But

regarding a numerically single number not even this form of error is possible; for we cannot in this case

suppose that one instance has an attribute and another has not, but whether our judgement be true or false, it

WE have said previously, in our distinction of the various meanings of words, that 'one' has several

meanings; the things that are directly and of their own nature and not accidentally called one may be

summarized under four heads, though the word is used in more senses. (1) There is the continuous, either in

general, or especially that which is continuous by nature and not by contact nor by being together; and of

these, that has more unity and is prior, whose movement is more indivisible and simpler. (2) That which is a

whole and has a certain shape and form is one in a still higher degree; and especially if a thing is of this sort

by nature, and not by force like the things which are unified by glue or nails or by being tied together, i.e. if it

has in itself the cause of its continuity. A thing is of this sort because its movement is one and indivisible in

place and time; so that evidently if a thing has by nature a principle of movement that is of the first kind (i.e.

local movement) and the first in that kind (i.e. circular movement), this is in the primary sense one extended

thing. Some things, then, are one in this way, qua continuous or whole, and the other things that are one are

those whose definition is one. Of this sort are the things the thought of which is one, i.e. those the thought of

which is indivisible; and it is indivisible if the thing is indivisible in kind or in number. (3) In number, then,

the individual is indivisible, and (4) in kind, that which in intelligibility and in knowledge is indivisible, so

that that which causes substances to be one must be one in the primary sense. 'One', then, has all these

meaningsthe naturally continuous and the whole, and the individual and the universal. And all these are one

because in some cases the movement, in others the thought or the definition is indivisible.

But it must be observed that the questions, what sort of things are said to be one, and what it is to be one and

what is the definition of it, should not be assumed to be the same. 'One' has all these meanings, and each of

the things to which one of these kinds of unity belongs will be one; but 'to be one' will sometimes mean being

one of these things, and sometimes being something else which is even nearer to the meaning of the word

'one' while these other things approximate to its application. This is also true of 'element' or 'cause', if one had

both to specify the things of which it is predicable and to render the definition of the word. For in a sense fire

is an element (and doubtless also 'the indefinite' or something else of the sort is by its own nature the

element), but in a sense it is not; for it is not the same thing to be fire and to be an element, but while as a

particular thing with a nature of its own fire is an element, the name 'element' means that it has this attribute,

that there is something which is made of it as a primary constituent. And so with 'cause' and 'one' and all such

terms. For this reason, too, 'to be one' means 'to be indivisible, being essentially one means a "this" and

capable of being isolated either in place, or in form or thought'; or perhaps 'to be whole and indivisible'; but it

means especially 'to be the first measure of a kind', and most strictly of quantity; for it is from this that it has

been extended to the other categories. For measure is that by which quantity is known; and quantity qua

quantity is known either by a 'one' or by a number, and all number is known by a 'one'. Therefore all quantity

qua quantity is known by the one, and that by which quantities are primarily known is the one itself; and so

the one is the startingpoint of number qua number. And hence in the other classes too 'measure' means that

by which each is first known, and the measure of each is a unitin length, in breadth, in depth, in weight, in

speed. (The words 'weight' and 'speed' are common to both contraries; for each of them has two

meanings'weight' means both that which has any amount of gravity and that which has an excess of gravity,

and 'speed' both that which has any amount of movement and that which has an excess of movement; for

even the slow has a certain speed and the comparatively light a certain weight.)

In all these, then, the measure and startingpoint is something one and indivisible, since even in lines we treat

as indivisible the line a foot long. For everywhere we seek as the measure something one and indivisible; and

this is that which is simple either in quality or in quantity. Now where it is thought impossible to take away or

to add, there the measure is exact (hence that of number is most exact; for we posit the unit as indivisible in

every respect); but in all other cases we imitate this sort of measure. For in the case of a furlong or a talent or

of anything comparatively large any addition or subtraction might more easily escape our notice than in the

case of something smaller; so that the first thing from which, as far as our perception goes, nothing can be

subtracted, all men make the measure, whether of liquids or of solids, whether of weight or of size; and they

think they know the quantity when they know it by means of this measure. And indeed they know movement

too by the simple movement and the quickest; for this occupies least time. And so in astronomy a 'one' of this

sort is the startingpoint and measure (for they assume the movement of the heavens to be uniform and the

quickest, and judge the others by reference to it), and in music the quartertone (because it is the least

interval), and in speech the letter. And all these are ones in this sensenot that 'one' is something predicable

But the measure is not always one in numbersometimes there are several; e.g. the quartertones (not to the

ear, but as determined by the ratios) are two, and the articulate sounds by which we measure are more than

one, and the diagonal of the square and its side are measured by two quantities, and all spatial magnitudes

reveal similar varieties of unit. Thus, then, the one is the measure of all things, because we come to know the

elements in the substance by dividing the things either in respect of quantity or in respect of kind. And the

one is indivisible just because the first of each class of things is indivisible. But it is not in the same way that

every 'one' is indivisible e.g. a foot and a unit; the latter is indivisible in every respect, while the former must

be placed among things which are undivided to perception, as has been said alreadyonly to perception, for

The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial

magnitude, and in particular that of length is a length, that of breadth a breadth, that of articulate sound an

articulate sound, that of weight a weight, that of units a unit. (For we must state the matter so, and not say that

the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of

words, but the claim does not really correspondit is as if one claimed that the measure of units is units and

Knowledge, also, and perception, we call the measure of things for the same reason, because we come to

know something by themwhile as a matter of fact they are measured rather than measure other things. But it

is with us as if some one else measured us and we came to know how big we are by seeing that he applied the

cubitmeasure to such and such a fraction of us. But Protagoras says 'man is the measure of all things', as if

he had said 'the man who knows' or 'the man who perceives'; and these because they have respectively

knowledge and perception, which we say are the measures of objects. Such thinkers are saying nothing, then,

Evidently, then, unity in the strictest sense, if we define it according to the meaning of the word, is a measure,

and most properly of quantity, and secondly of quality. And some things will be one if they are indivisible in

quantity, and others if they are indivisible in quality; and so that which is one is indivisible, either absolutely

With regard to the substance and nature of the one we must ask in which of two ways it exists. This is the

very question that we reviewed in our discussion of problems, viz. what the one is and how we must conceive

of it, whether we must take the one itself as being a substance (as both the Pythagoreans say in earlier and

Plato in later times), or there is, rather, an underlying nature and the one should be described more intelligibly

and more in the manner of the physical philosophers, of whom one says the one is love, another says it is air,

If, then, no universal can be a substance, as has been said our discussion of substance and being, and if being

itself cannot be a substance in the sense of a one apart from the many (for it is common to the many), but is

only a predicate, clearly unity also cannot be a substance; for being and unity are the most universal of all

predicates. Therefore, on the one hand, genera are not certain entities and substances separable from other

things; and on the other hand the one cannot be a genus, for the same reasons for which being and substance

Further, the position must be similar in all the kinds of unity. Now 'unity' has just as many meanings as

'being'; so that since in the sphere of qualities the one is something definitesome particular kind of

thingand similarly in the sphere of quantities, clearly we must in every category ask what the one is, as we

must ask what the existent is, since it is not enough to say that its nature is just to be one or existent. But in

colours the one is a colour, e.g. white, and then the other colours are observed to be produced out of this and

black, and black is the privation of white, as darkness of light. Therefore if all existent things were colours,

existent things would have been a number, indeed, but of what? Clearly of colours; and the 'one' would have

been a particular 'one', i.e. white. And similarly if all existing things were tunes, they would have been a

number, but a number of quartertones, and their essence would not have been number; and the one would

have been something whose substance was not to be one but to be the quartertone. And similarly if all

existent things had been articulate sounds, they would have been a number of letters, and the one would have

been a vowel. And if all existent things were rectilinear figures, they would have been a number of figures,

and the one would have been the triangle. And the same argument applies to all other classes. Since,

therefore, while there are numbers and a one both in affections and in qualities and in quantities and in

movement, in all cases the number is a number of particular things and the one is one something, and its

substance is not just to be one, the same must be true of substances also; for it is true of all cases alike.

That the one, then, in every class is a definite thing, and in no case is its nature just this, unity, is evident; but

as in colours the oneitself which we must seek is one colour, so too in substance the oneitself is one

substance. That in a sense unity means the same as being is clear from the facts that its meanings correspond

to the categories one to one, and it is not comprised within any category (e.g. it is comprised neither in 'what

a thing is' nor in quality, but is related to them just as being is); that in 'one man' nothing more is predicated

than in 'man' (just as being is nothing apart from substance or quality or quantity); and that to be one is just to

The one and the many are opposed in several ways, of which one is the opposition of the one and plurality as

indivisible and divisible; for that which is either divided or divisible is called a plurality, and that which is

indivisible or not divided is called one. Now since opposition is of four kinds, and one of these two terms is

privative in meaning, they must be contraries, and neither contradictory nor correlative in meaning. And the

one derives its name and its explanation from its contrary, the indivisible from the divisible, because plurality

and the divisible is more perceptible than the indivisible, so that in definition plurality is prior to the

To the one belong, as we indicated graphically in our distinction of the contraries, the same and the like and

the equal, and to plurality belong the other and the unlike and the unequal. 'The same' has several meanings;

(1) we sometimes mean 'the same numerically'; again, (2) we call a thing the same if it is one both in

definition and in number, e.g. you are one with yourself both in form and in matter; and again, (3) if the

definition of its primary essence is one; e.g. equal straight lines are the same, and so are equal and

equalangled quadrilaterals; there are many such, but in these equality constitutes unity.

Things are like if, not being absolutely the same, nor without difference in respect of their concrete substance,

they are the same in form; e.g. the larger square is like the smaller, and unequal straight lines are like; they

are like, but not absolutely the same. Other things are like, if, having the same form, and being things in

which difference of degree is possible, they have no difference of degree. Other things, if they have a quality

that is in form one and samee.g. whitenessin a greater or less degree, are called like because their form is

one. Other things are called like if the qualities they have in common are more numerous than those in which

they differeither the qualities in general or the prominent qualities; e.g. tin is like silver, qua white, and gold

Evidently, then, 'other' and 'unlike' also have several meanings. And the other in one sense is the opposite of

the same (so that everything is either the same as or other than everything else). In another sense things are

other unless both their matter and their definition are one (so that you are other than your neighbour). The

other in the third sense is exemplified in the objects of mathematics. 'Other or the same' can therefore be

predicated of everything with regard to everything elsebut only if the things are one and existent, for 'other'

is not the contradictory of 'the same'; which is why it is not predicated of nonexistent things (while 'not the

same' is so predicated). It is predicated of all existing things; for everything that is existent and one is by its

The other, then, and the same are thus opposed. But difference is not the same as otherness. For the other and

that which it is other than need not be other in some definite respect (for everything that is existent is either

other or the same), but that which is different is different from some particular thing in some particular

respect, so that there must be something identical whereby they differ. And this identical thing is genus or

species; for everything that differs differs either in genus or in species, in genus if the things have not their

matter in common and are not generated out of each other (i.e. if they belong to different figures of

predication), and in species if they have the same genus ('genus' meaning that identical thing which is

Contraries are different, and contrariety is a kind of difference. That we are right in this supposition is shown

by induction. For all of these too are seen to be different; they are not merely other, but some are other in

genus, and others are in the same line of predication, and therefore in the same genus, and the same in genus.

We have distinguished elsewhere what sort of things are the same or other in genus.

Since things which differ may differ from one another more or less, there is also a greatest difference, and

this I call contrariety. That contrariety is the greatest difference is made clear by induction. For things which

differ in genus have no way to one another, but are too far distant and are not comparable; and for things that

differ in species the extremes from which generation takes place are the contraries, and the distance between

But surely that which is greatest in each class is complete. For that is greatest which cannot be exceeded, and

that is complete beyond which nothing can be found. For the complete difference marks the end of a series

(just as the other things which are called complete are so called because they have attained an end), and

beyond the end there is nothing; for in everything it is the extreme and includes all else, and therefore there is

nothing beyond the end, and the complete needs nothing further. From this, then, it is clear that contrariety is

complete difference; and as contraries are so called in several senses, their modes of completeness will

This being so, it is clear that one thing have more than one contrary (for neither can there be anything more

extreme than the extreme, nor can there be more than two extremes for the one interval), and, to put the

matter generally, this is clear if contrariety is a difference, and if difference, and therefore also the complete

And the other commonly accepted definitions of contraries are also necessarily true. For not only is (1) the

complete difference the greatest difference (for we can get no difference beyond it of things differing either in

genus or in species; for it has been shown that there is no 'difference' between anything and the things outside

its genus, and among the things which differ in species the complete difference is the greatest); but also (2)

the things in the same genus which differ most are contrary (for the complete difference is the greatest

difference between species of the same genus); and (3) the things in the same receptive material which differ

most are contrary (for the matter is the same for contraries); and (4) of the things which fall under the same

faculty the most different are contrary (for one science deals with one class of things, and in these the

The primary contrariety is that between positive state and privationnot every privation, however (for

'privation' has several meanings), but that which is complete. And the other contraries must be called so with

reference to these, some because they possess these, others because they produce or tend to produce them,

others because they are acquisitions or losses of these or of other contraries. Now if the kinds of opposition

are contradiction and privation and contrariety and relation, and of these the first is contradiction, and

contradiction admits of no intermediate, while contraries admit of one, clearly contradiction and contrariety

are not the same. But privation is a kind of contradiction; for what suffers privation, either in general or in

some determinate way, either that which is quite incapable of having some attribute or that which, being of

such a nature as to have it, has it not; here we have already a variety of meanings, which have been

distinguished elsewhere. Privation, therefore, is a contradiction or incapacity which is determinate or taken

along with the receptive material. This is the reason why, while contradiction does not admit of an

intermediate, privation sometimes does; for everything is equal or not equal, but not everything is equal or

unequal, or if it is, it is only within the sphere of that which is receptive of equality. If, then, the

comingstobe which happen to the matter start from the contraries, and proceed either from the form and

the possession of the form or from a privation of the form or shape, clearly all contrariety must be privation,

but presumably not all privation is contrariety (the reason being that that has suffered privation may have

suffered it in several ways); for it is only the extremes from which changes proceed that are contraries.

And this is obvious also by induction. For every contrariety involves, as one of its terms, a privation, but not

all cases are alike; inequality is the privation of equality and unlikeness of likeness, and on the other hand

vice is the privation of virtue. But the cases differ in a way already described; in one case we mean simply

that the thing has suffered privation, in another case that it has done so either at a certain time or in a certain

part (e.g. at a certain age or in the dominant part), or throughout. This is why in some cases there is a mean

(there are men who are neither good nor bad), and in others there is not (a number must be either odd or

even). Further, some contraries have their subject defined, others have not. Therefore it is evident that one of

the contraries is always privative; but it is enough if this is true of the firsti.e. the genericcontraries, e.g. the

Since one thing has one contrary, we might raise the question how the one is opposed to the many, and the

equal to the great and the small. For if we used the word 'whether' only in an antithesis such as 'whether it is

white or black', or 'whether it is white or not white' (we do not ask 'whether it is a man or white'), unless we

are proceeding on a prior assumption and asking something such as 'whether it was Cleon or Socrates that

came' as this is not a necessary disjunction in any class of things; yet even this is an extension from the case

of opposites; for opposites alone cannot be present together; and we assume this incompatibility here too in

asking which of the two came; for if they might both have come, the question would have been absurd; but if

they might, even so this falls just as much into an antithesis, that of the 'one or many', i.e. 'whether both came

or one of the two':if, then, the question 'whether' is always concerned with opposites, and we can ask

'whether it is greater or less or equal', what is the opposition of the equal to the other two? It is not contrary

either to one alone or to both; for why should it be contrary to the greater rather than to the less? Further, the

equal is contrary to the unequal. Therefore if it is contrary to the greater and the less, it will be contrary to

more things than one. But if the unequal means the same as both the greater and the less together, the equal

will be opposite to both (and the difficulty supports those who say the unequal is a 'two'), but it follows that

one thing is contrary to two others, which is impossible. Again, the equal is evidently intermediate between

the great and the small, but no contrariety is either observed to be intermediate, or, from its definition, can be

so; for it would not be complete if it were intermediate between any two things, but rather it always has

It remains, then, that it is opposed either as negation or as privation. It cannot be the negation or privation of

one of the two; for why of the great rather than of the small? It is, then, the privative negation of both. This is

why 'whether' is said with reference to both, not to one of the two (e.g. 'whether it is greater or equal' or

'whether it is equal or less'); there are always three cases. But it is not a necessary privation; for not

everything which is not greater or less is equal, but only the things which are of such a nature as to have these

The equal, then, is that which is neither great nor small but is naturally fitted to be either great or small; and it

is opposed to both as a privative negation (and therefore is also intermediate). And that which is neither good

nor bad is opposed to both, but has no name; for each of these has several meanings and the recipient subject

is not one; but that which is neither white nor black has more claim to unity. Yet even this has not one name,

though the colours of which this negation is privatively predicated are in a way limited; for they must be

either grey or yellow or something else of the kind. Therefore it is an incorrect criticism that is passed by

those who think that all such phrases are used in the same way, so that that which is neither a shoe nor a hand

would be intermediate between a shoe and a hand, since that which is neither good nor bad is intermediate

between the good and the badas if there must be an intermediate in all cases. But this does not necessarily

follow. For the one phrase is a joint denial of opposites between which there is an intermediate and a certain

natural interval; but between the other two there is no 'difference'; for the things, the denials of which are

We might raise similar questions about the one and the many. For if the many are absolutely opposed to the

one, certain impossible results follow. One will then be few, whether few be treated here as singular or plural;

for the many are opposed also to the few. Further, two will be many, since the double is multiple and 'double'

derives its meaning from 'two'; therefore one will be few; for what is that in comparison with which two are

many, except one, which must therefore be few? For there is nothing fewer. Further, if the much and the little

are in plurality what the long and the short are in length, and whatever is much is also many, and the many

are much (unless, indeed, there is a difference in the case of an easilybounded continuum), the little (or few)

will be a plurality. Therefore one is a plurality if it is few; and this it must be, if two are many. But perhaps,

while the 'many' are in a sense said to be also 'much', it is with a difference; e.g. water is much but not many.

But 'many' is applied to the things that are divisible; in the one sense it means a plurality which is excessive

either absolutely or relatively (while 'few' is similarly a plurality which is deficient), and in another sense it

means number, in which sense alone it is opposed to the one. For we say 'one or many', just as if one were to

say 'one and ones' or 'white thing and white things', or to compare the things that have been measured with

the measure. It is in this sense also that multiples are so called. For each number is said to be many because it

consists of ones and because each number is measurable by one; and it is 'many' as that which is opposed to

one, not to the few. In this sense, then, even two is manynot, however, in the sense of a plurality which is

excessive either relatively or absolutely; it is the first plurality. But without qualification two is few; for it is

first plurality which is deficient (for this reason Anaxagoras was not right in leaving the subject with the

statement that 'all things were together, boundless both in plurality and in smallness'where for 'and in

smallness' he should have said 'and in fewness'; for they could not have been boundless in fewness), since it

The one is opposed then to the many in numbers as measure to thing measurable; and these are opposed as

are the relatives which are not from their very nature relatives. We have distinguished elsewhere the two

senses in which relatives are so called:(1) as contraries; (2) as knowledge to thing known, a term being

called relative because another is relative to it. There is nothing to prevent one from being fewer than

something, e.g. than two; for if one is fewer, it is not therefore few. Plurality is as it were the class to which

number belongs; for number is plurality measurable by one, and one and number are in a sense opposed, not

as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the

other measurable, they are opposed. This is why not everything that is one is a number; i.e. if the thing is

indivisible it is not a number. But though knowledge is similarly spoken of as relative to the knowable, the

relation does not work out similarly; for while knowledge might be thought to be the measure, and the

knowable the thing measured, the fact that all knowledge is knowable, but not all that is knowable is

knowledge, because in a sense knowledge is measured by the knowable.Plurality is contrary neither to the

few (the many being contrary to this as excessive plurality to plurality exceeded), nor to the one in every

sense; but in the one sense these are contrary, as has been said, because the former is divisible and the latter

indivisible, while in another sense they are relative as knowledge is to knowable, if plurality is number and

Since contraries admit of an intermediate and in some cases have it, intermediates must be composed of the

contraries. For (1) all intermediates are in the same genus as the things between which they stand. For we call

those things intermediates, into which that which changes must change first; e.g. if we were to pass from the

highest string to the lowest by the smallest intervals, we should come sooner to the intermediate notes, and in

colours if we were to pass from white to black, we should come sooner to crimson and grey than to black;

and similarly in all other cases. But to change from one genus to another genus is not possible except in an

incidental way, as from colour to figure. Intermediates, then, must be in the same genus both as one another

But (2) all intermediates stand between opposites of some kind; for only between these can change take place

in virtue of their own nature (so that an intermediate is impossible between things which are not opposite; for

then there would be change which was not from one opposite towards the other). Of opposites,

contradictories admit of no middle term; for this is what contradiction isan opposition, one or other side of

which must attach to anything whatever, i.e. which has no intermediate. Of other opposites, some are relative,

others privative, others contrary. Of relative terms, those which are not contrary have no intermediate; the

reason is that they are not in the same genus. For what intermediate could there be between knowledge and

(3) If intermediates are in the same genus, as has been shown, and stand between contraries, they must be

composed of these contraries. For either there will be a genus including the contraries or there will be none.

And if (a) there is to be a genus in such a way that it is something prior to the contraries, the differentiae

which constituted the contrary speciesofagenus will be contraries prior to the species; for species are

composed of the genus and the differentiae. (E.g. if white and black are contraries, and one is a piercing

colour and the other a compressing colour, these differentiae'piercing' and 'compressing'are prior; so that

these are prior contraries of one another.) But, again, the species which differ contrariwise are the more truly

contrary species. And the other.species, i.e. the intermediates, must be composed of their genus and their

differentiae. (E.g. all colours which are between white and black must be said to be composed of the genus,

i.e. colour, and certain differentiae. But these differentiae will not be the primary contraries; otherwise every

colour would be either white or black. They are different, then, from the primary contraries; and therefore

they will be between the primary contraries; the primary differentiae are 'piercing' and 'compressing'.)

Therefore it is (b) with regard to these contraries which do not fall within a genus that we must first ask of

what their intermediates are composed. (For things which are in the same genus must be composed of terms

in which the genus is not an element, or else be themselves incomposite.) Now contraries do not involve one

another in their composition, and are therefore first principles; but the intermediates are either all

incomposite, or none of them. But there is something compounded out of the contraries, so that there can be a

change from a contrary to it sooner than to the other contrary; for it will have less of the quality in question

than the one contrary and more than the other. This also, then, will come between the contraries. All the other

intermediates also, therefore, are composite; for that which has more of a quality than one thing and less than

another is compounded somehow out of the things than which it is said to have more and less respectively of

the quality. And since there are no other things prior to the contraries and homogeneous with the

intermediates, all intermediates must be compounded out of the contraries. Therefore also all the inferior

classes, both the contraries and their intermediates, will be compounded out of the primary contraries.

Clearly, then, intermediates are (1) all in the same genus and (2) intermediate between contraries, and (3) all

That which is other in species is other than something in something, and this must belong to both; e.g. if it is

an animal other in species, both are animals. The things, then, which are other in species must be in the same

genus. For by genus I mean that one identical thing which is predicated of both and is differentiated in no

merely accidental way, whether conceived as matter or otherwise. For not only must the common nature

attach to the different things, e.g. not only must both be animals, but this very animality must also be

different for each (e.g. in the one case equinity, in the other humanity), and so this common nature is

specifically different for each from what it is for the other. One, then, will be in virtue of its own nature one

sort of animal, and the other another, e.g. one a horse and the other a man. This difference, then, must be an

otherness of the genus. For I give the name of 'difference in the genus' an otherness which makes the genus

This, then, will be a contrariety (as can be shown also by induction). For all things are divided by opposites,

and it has been proved that contraries are in the same genus. For contrariety was seen to be complete

difference; and all difference in species is a difference from something in something; so that this is the same

for both and is their genus. (Hence also all contraries which are different in species and not in genus are in the

same line of predication, and other than one another in the highest degreefor the difference is complete,

and cannot be present along with one another.) The difference, then, is a contrariety.

This, then, is what it is to be 'other in species'to have a contrariety, being in the same genus and being

indivisible (and those things are the same in species which have no contrariety, being indivisible); we say

'being indivisible', for in the process of division contrarieties arise in the intermediate stages before we come

to the indivisibles. Evidently, therefore, with reference to that which is called the genus, none of the

speciesofagenus is either the same as it or other than it in species (and this is fitting; for the matter is

indicated by negation, and the genus is the matter of that of which it is called the genus, not in the sense in

which we speak of the genus or family of the Heraclidae, but in that in which the genus is an element in a

thing's nature), nor is it so with reference to things which are not in the same genus, but it will differ in genus

from them, and in species from things in the same genus. For a thing's difference from that from which it

differs in species must be a contrariety; and this belongs only to things in the same genus.

One might raise the question, why woman does not differ from man in species, when female and male are

contrary and their difference is a contrariety; and why a female and a male animal are not different in species,

though this difference belongs to animal in virtue of its own nature, and not as paleness or darkness does;

both 'female' and 'male' belong to it qua animal. This question is almost the same as the other, why one

contrariety makes things different in species and another does not, e.g. 'with feet' and 'with wings' do, but

paleness and darkness do not. Perhaps it is because the former are modifications peculiar to the genus, and

the latter are less so. And since one element is definition and one is matter, contrarieties which are in the

definition make a difference in species, but those which are in the thing taken as including its matter do not

make one. And so paleness in a man, or darkness, does not make one, nor is there a difference in species

between the pale man and the dark man, not even if each of them be denoted by one word. For man is here

being considered on his material side, and matter does not create a difference; for it does not make individual

men species of man, though the flesh and the bones of which this man and that man consist are other. The

concrete thing is other, but not other in species, because in the definition there is no contrariety. This is the

ultimate indivisible kind. Callias is definition + matter, the pale man, then, is so also, because it is the

individual Callias that is pale; man, then, is pale only incidentally. Neither do a brazen and a wooden circle,

then, differ in species; and if a brazen triangle and a wooden circle differ in species, it is not because of the

matter, but because there is a contrariety in the definition. But does the matter not make things other in

species, when it is other in a certain way, or is there a sense in which it does? For why is this horse other than

this man in species, although their matter is included with their definitions? Doubtless because there is a

contrariety in the definition. For while there is a contrariety also between pale man and dark horse, and it is a

contrariety in species, it does not depend on the paleness of the one and the darkness of the other, since even

if both had been pale, yet they would have been other in species. But male and female, while they are

modifications peculiar to 'animal', are so not in virtue of its essence but in the matter, ie. the body. This is

why the same seed becomes female or male by being acted on in a certain way. We have stated, then, what it

is to be other in species, and why some things differ in species and others do not.

Since contraries are other in form, and the perishable and the imperishable are contraries (for privation is a

determinate incapacity), the perishable and the imperishable must be different in kind.

Now so far we have spoken of the general terms themselves, so that it might be thought not to be necessary

that every imperishable thing should be different from every perishable thing in form, just as not every pale

thing is different in form from every dark thing. For the same thing can be both, and even at the same time if

it is a universal (e.g. man can be both pale and dark), and if it is an individual it can still be both; for the same

man can be, though not at the same time, pale and dark. Yet pale is contrary to dark.

But while some contraries belong to certain things by accident (e.g. both those now mentioned and many

others), others cannot, and among these are 'perishable' and 'imperishable'. For nothing is by accident

perishable. For what is accidental is capable of not being present, but perishableness is one of the attributes

that belong of necessity to the things to which they belong; or else one and the same thing may be perishable

and imperishable, if perishableness is capable of not belonging to it. Perishableness then must either be the

essence or be present in the essence of each perishable thing. The same account holds good for

imperishableness also; for both are attributes which are present of necessity. The characteristics, then, in

respect of which and in direct consequence of which one thing is perishable and another imperishable, are

Evidently, then, there cannot be Forms such as some maintain, for then one man would be perishable and

another imperishable. Yet the Forms are said to be the same in form with the individuals and not merely to

have the same name; but things which differ in kind are farther apart than those which differ in form.

THAT Wisdom is a science of first principles is evident from the introductory chapters, in which we have

raised objections to the statements of others about the first principles; but one might ask the question whether

Wisdom is to be conceived as one science or as several. If as one, it may be objected that one science always

deals with contraries, but the first principles are not contrary. If it is not one, what sort of sciences are those

Further, is it the business of one science, or of more than one, to examine the first principles of

demonstration? If of one, why of this rather than of any other? If of more, what sort of sciences must these be

Further, does Wisdom investigate all substances or not? If not all, it is hard to say which; but if, being one, it

investigates them all, it is doubtful how the same science can embrace several subjectmatters.

Further, does it deal with substances only or also with their attributes? If in the case of attributes

demonstration is possible, in that of substances it is not. But if the two sciences are different, what is each of

them and which is Wisdom? If we think of it as demonstrative, the science of the attributes is Wisdom, but if

But again the science we are looking for must not be supposed to deal with the causes which have been

mentioned in the Physics. For (A) it does not deal with the final cause (for that is the nature of the good, and

this is found in the field of action and movement; and it is the first moverfor that is the nature of the endbut

in the case of things unmovable there is nothing that moved them first), and (B) in general it is hard to say

whether perchance the science we are now looking for deals with perceptible substances or not with them, but

with certain others. If with others, it must deal either with the Forms or with the objects of mathematics. Now

(a) evidently the Forms do not exist. (But it is hard to say, even if one suppose them to exist, why in the

world the same is not true of the other things of which there are Forms, as of the objects of mathematics. I

mean that these thinkers place the objects of mathematics between the Forms and perceptible things, as a kind

of third set of things apart both from the Forms and from the things in this world; but there is not a third man

or horse besides the ideal and the individuals. If on the other hand it is not as they say, with what sort of

things must the mathematician be supposed to deal? Certainly not with the things in this world; for none of

these is the sort of thing which the mathematical sciences demand.) Nor (b) does the science which we are

now seeking treat of the objects of mathematics; for none of them can exist separately. But again it does not

In general one might raise the question, to what kind of science it belongs to discuss the difficulties about the

matter of the objects of mathematics. Neither to physics (because the whole inquiry of the physicist is about

the things that have in themselves a principle. of movement and rest), nor yet to the science which inquires

into demonstration and science; for this is just the subject which it investigates. It remains then that it is the

One might discuss the question whether the science we are seeking should be said to deal with the principles

which are by some called elements; all men suppose these to be present in composite things. But it might be

thought that the science we seek should treat rather of universals; for every definition and every science is of

universals and not of infimae species, so that as far as this goes it would deal with the highest genera. These

would turn out to be being and unity; for these might most of all be supposed to contain all things that are,

and to be most like principles because they are by nature; for if they perish all other things are destroyed with

them; for everything is and is one. But inasmuch as, if one is to suppose them to be genera, they must be

predicable of their differentiae, and no genus is predicable of any of its differentiae, in this way it would seem

that we should not make them genera nor principles. Further, if the simpler is more of a principle than the less

simple, and the ultimate members of the genus are simpler than the genera (for they are indivisible, but the

genera are divided into many and differing species), the species might seem to be the principles, rather than

the genera. But inasmuch as the species are involved in the destruction of the genera, the genera are more like

principles; for that which involves another in its destruction is a principle of it. These and others of the kind

Further, must we suppose something apart from individual things, or is it these that the science we are

seeking treats of? But these are infinite in number. Yet the things that are apart from the individuals are

genera or species; but the science we now seek treats of neither of these. The reason why this is impossible

has been stated. Indeed, it is in general hard to say whether one must assume that there is a separable

substance besides the sensible substances (i.e. the substances in this world), or that these are the real things

and Wisdom is concerned with them. For we seem to seek another kind of substance, and this is our problem,

i.e. to see if there is something which can exist apart by itself and belongs to no sensible thing.Further, if

there is another substance apart from and corresponding to sensible substances, which kinds of sensible

substance must be supposed to have this corresponding to them? Why should one suppose men or horses to

have it, more than either the other animals or even all lifeless things? On the other hand to set up other and

eternal substances equal in number to the sensible and perishable substances would seem to fall beyond the

bounds of probability.But if the principle we now seek is not separable from corporeal things, what has a

better claim to the name matter? This, however, does not exist in actuality, but exists in potency. And it

would seem rather that the form or shape is a more important principle than this; but the form is perishable,

so that there is no eternal substance at all which can exist apart and independent. But this is paradoxical; for

such a principle and substance seems to exist and is sought by nearly all the most refined thinkers as

something that exists; for how is there to be order unless there is something eternal and independent and

Further, if there is a substance or principle of such a nature as that which we are now seeking, and if this is

one for all things, and the same for eternal and for perishable things, it is hard to say why in the world, if

there is the same principle, some of the things that fall under the principle are eternal, and others are not

eternal; this is paradoxical. But if there is one principle of perishable and another of eternal things, we shall

be in a like difficulty if the principle of perishable things, as well as that of eternal, is eternal; for why, if the

principle is eternal, are not the things that fall under the principle also eternal? But if it is perishable another

principle is involved to account for it, and another to account for that, and this will go on to infinity.

If on the other hand we are to set up what are thought to be the most unchangeable principles, being and

unity, firstly, if each of these does not indicate a 'this' or substance, how will they be separable and

independent? Yet we expect the eternal and primary principles to be so. But if each of them does signify a

'this' or substance, all things that are are substances; for being is predicated of all things (and unity also of

some); but that all things that are are substance is false. Further, how can they be right who say that the first

principle is unity and this is substance, and generate number as the first product from unity and from matter,

assert that number is substance? How are we to think of 'two', and each of the other numbers composed of

units, as one? On this point neither do they say anything nor is it easy to say anything. But if we are to

suppose lines or what comes after these (I mean the primary surfaces) to be principles, these at least are not

separable substances, but sections and divisionsthe former of surfaces, the latter of bodies (while points are

sections and divisions of lines); and further they are limits of these same things; and all these are in other

things and none is separable. Further, how are we to suppose that there is a substance of unity and the point?

Every substance comes into being by a gradual process, but a point does not; for the point is a division.

A further difficulty is raised by the fact that all knowledge is of universals and of the 'such', but substance is

not a universal, but is rather a 'this'a separable thing, so that if there is knowledge about the first principles,

Further, is there anything apart from the concrete thing (by which I mean the matter and that which is joined

with it), or not? If not, we are met by the objection that all things that are in matter are perishable. But if there

is something, it must be the form or shape. Now it is hard to determine in which cases this exists apart and in

which it does not; for in some cases the form is evidently not separable, e.g. in the case of a house.

Further, are the principles the same in kind or in number? If they are one in number, all things will be the

Since the science of the philosopher treats of being qua being universally and not in respect of a part of it, and

'being' has many senses and is not used in one only, it follows that if the word is used equivocally and in

virtue of nothing common to its various uses, being does not fall under one science (for the meanings of an

equivocal term do not form one genus); but if the word is used in virtue of something common, being will fall

under one science. The term seems to be used in the way we have mentioned, like 'medical' and 'healthy'. For

each of these also we use in many senses. Terms are used in this way by virtue of some kind of reference, in

the one case to medical science, in the other to health, in others to something else, but in each case to one

identical concept. For a discussion and a knife are called medical because the former proceeds from medical

science, and the latter is useful to it. And a thing is called healthy in a similar way; one thing because it is

indicative of health, another because it is productive of it. And the same is true in the other cases. Everything

that is, then, is said to 'be' in this same way; each thing that is is said to 'be' because it is a modification of

being qua being or a permanent or a transient state or a movement of it, or something else of the sort. And

since everything that is may be referred to something single and common, each of the contrarieties also may

be referred to the first differences and contrarieties of being, whether the first differences of being are

plurality and unity, or likeness and unlikeness, or some other differences; let these be taken as already

discussed. It makes no difference whether that which is be referred to being or to unity. For even if they are

not the same but different, at least they are convertible; for that which is one is also somehow being, and that

But since every pair of contraries falls to be examined by one and the same science, and in each pair one term

is the privative of the other though one might regarding some contraries raise the question, how they can be

privately related, viz. those which have an intermediate, e.g. unjust and justin all such cases one must

maintain that the privation is not of the whole definition, but of the infima species. if the just man is 'by virtue

of some permanent disposition obedient to the laws', the unjust man will not in every case have the whole

definition denied of him, but may be merely 'in some respect deficient in obedience to the laws', and in this

As the mathematician investigates abstractions (for before beginning his investigation he strips off all the

sensible qualities, e.g. weight and lightness, hardness and its contrary, and also heat and cold and the other

sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two,

sometimes in three dimensions, and the attributes of these qua quantitative and continuous, and does not

consider them in any other respect, and examines the relative positions of some and the attributes of these,

and the commensurabilities and incommensurabilities of others, and the ratios of others; but yet we posit one

and the same science of all these thingsgeometry)the same is true with regard to being. For the

attributes of this in so far as it is being, and the contrarieties in it qua being, it is the business of no other

science than philosophy to investigate; for to physics one would assign the study of things not qua being, but

rather qua sharing in movement; while dialectic and sophistic deal with the attributes of things that are, but

not of things qua being, and not with being itself in so far as it is being; therefore it remains that it is the

philosopher who studies the things we have named, in so far as they are being. Since all that is is to 'be' in

virtue of something single and common, though the term has many meanings, and contraries are in the same

case (for they are referred to the first contrarieties and differences of being), and things of this sort can fall

under one science, the difficulty we stated at the beginning appears to be solved,I mean the question how

Since even the mathematician uses the common axioms only in a special application, it must be the business

of first philosophy to examine the principles of mathematics also. That when equals are taken from equals the

remainders are equal, is common to all quantities, but mathematics studies a part of its proper matter which it

has detached, e.g. lines or angles or numbers or some other kind of quantitynot, however, qua being but in

so far as each of them is continuous in one or two or three dimensions; but philosophy does not inquire about

particular subjects in so far as each of them has some attribute or other, but speculates about being, in so far

as each particular thing is.Physics is in the same position as mathematics; for physics studies the attributes

and the principles of the things that are, qua moving and not qua being (whereas the primary science, we have

said, deals with these, only in so far as the underlying subjects are existent, and not in virtue of any other

character); and so both physics and mathematics must be classed as parts of Wisdom.

There is a principle in things, about which we cannot be deceived, but must always, on the contrary recognize

the truth,viz. that the same thing cannot at one and the same time be and not be, or admit any other similar

pair of opposites. About such matters there is no proof in the full sense, though there is proof ad hominem.

For it is not possible to infer this truth itself from a more certain principle, yet this is necessary if there is to

be completed proof of it in the full sense. But he who wants to prove to the asserter of opposites that he is

wrong must get from him an admission which shall be identical with the principle that the same thing cannot

be and not be at one and the same time, but shall not seem to be identical; for thus alone can his thesis be

demonstrated to the man who asserts that opposite statements can be truly made about the same subject.

Those, then, who are to join in argument with one another must to some extent understand one another; for if

this does not happen how are they to join in argument with one another? Therefore every word must be

intelligible and indicate something, and not many things but only one; and if it signifies more than one thing,

it must be made plain to which of these the word is being applied. He, then, who says 'this is and is not'

denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible.

Therefore if 'this is' signifies something, one cannot truly assert its contradictory.

Further, if the word signifies something and this is asserted truly, this connexion must be necessary; and it is

not possible that that which necessarily is should ever not be; it is not possible therefore to make the opposed

affirmations and negations truly of the same subject. Further, if the affirmation is no more true than the

negation, he who says 'man' will be no more right than he who says 'notman'. It would seem also that in

saying the man is not a horse one would be either more or not less right than in saying he is not a man, so that

one will also be right in saying that the same person is a horse; for it was assumed to be possible to make

opposite statements equally truly. It follows then that the same person is a man and a horse, or any other

While, then, there is no proof of these things in the full sense, there is a proof which may suffice against one

who will make these suppositions. And perhaps if one had questioned Heraclitus himself in this way one

might have forced him to confess that opposite statements can never be true of the same subjects. But, as it is,

he adopted this opinion without understanding what his statement involves. But in any case if what is said by

him is true, not even this itself will be trueviz. that the same thing can at one and the same time both be and

not be. For as, when the statements are separated, the affirmation is no more true than the negation, in the

same waythe combined and complex statement being like a single affirmationthe whole taken as an

affirmation will be no more true than the negation. Further, if it is not possible to affirm anything truly, this

itself will be falsethe assertion that there is no true affirmation. But if a true affirmation exists, this appears

to refute what is said by those who raise such objections and utterly destroy rational discourse.

The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things,

meaning simply that that which seems to each man also assuredly is. If this is so, it follows that the same

thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true,

because often a particular thing appears beautiful to some and the contrary of beautiful to others, and that

which appears to each man is the measure. This difficulty may be solved by considering the source of this

opinion. It seems to have arisen in some cases from the doctrine of the natural philosophers, and in others

from the fact that all men have not the same views about the same things, but a particular thing appears

That nothing comes to be out of that which is not, but everything out of that which is, is a dogma common to

nearly all the natural philosophers. Since, then, white cannot come to be if the perfectly white and in no

respect notwhite existed before, that which becomes white must come from that which is not white; so that

it must come to be out of that which is not (so they argue), unless the same thing was at the beginning white

and notwhite. But it is not hard to solve this difficulty; for we have said in our works on physics in what

sense things that come to be come to be from that which is not, and in what sense from that which is.

But to attend equally to the opinions and the fancies of disputing parties is childish; for clearly one of them

must be mistaken. And this is evident from what happens in respect of sensation; for the same thing never

appears sweet to some and the contrary of sweet to others, unless in the one case the senseorgan which

discriminates the aforesaid flavours has been perverted and injured. And if this is so the one party must be

taken to be the measure, and the other must not. And say the same of good and bad, and beautiful and ugly,

and all other such qualities. For to maintain the view we are opposing is just like maintaining that the things

that appear to people who put their finger under their eye and make the object appear two instead of one must

be two (because they appear to be of that number) and again one (for to those who do not interfere with their

In general, it is absurd to make the fact that the things of this earth are observed to change and never to

remain in the same state, the basis of our judgement about the truth. For in pursuing the truth one must start

from the things that are always in the same state and suffer no change. Such are the heavenly bodies; for these

do not appear to be now of one nature and again of another, but are manifestly always the same and share in

Further, if there is movement, there is also something moved, and everything is moved out of something and

into something; it follows that that that which is moved must first be in that out of which it is to be moved,

and then not be in it, and move into the other and come to be in it, and that the contradictory statements are

And if the things of this earth continuously flow and move in respect of quantityif one were to suppose this,

although it is not truewhy should they not endure in respect of quality? For the assertion of contradictory

statements about the same thing seems to have arisen largely from the belief that the quantity of bodies does

not endure, which, our opponents hold, justifies them in saying that the same thing both is and is not four

cubits long. But essence depends on quality, and this is of determinate nature, though quantity is of

Further, when the doctor orders people to take some particular food, why do they take it? In what respect is

'this is bread' truer than 'this is not bread'? And so it would make no difference whether one ate or not. But as

a matter of fact they take the food which is ordered, assuming that they know the truth about it and that it is

bread. Yet they should not, if there were no fixed constant nature in sensible things, but all natures moved

Again, if we are always changing and never remain the same, what wonder is it if to us, as to the sick, things

never appear the same? (For to them also, because they are not in the same condition as when they were well,

sensible qualities do not appear alike; yet, for all that, the sensible things themselves need not share in any

change, though they produce different, and not identical, sensations in the sick. And the same must surely

happen to the healthy if the aforesaid change takes place.) But if we do not change but remain the same,

As for those to whom the difficulties mentioned are suggested by reasoning, it is not easy to solve the

difficulties to their satisfaction, unless they will posit something and no longer demand a reason for it; for it is

only thus that all reasoning and all proof is accomplished; if they posit nothing, they destroy discussion and

all reasoning. Therefore with such men there is no reasoning. But as for those who are perplexed by the

traditional difficulties, it is easy to meet them and to dissipate the causes of their perplexity. This is evident

It is manifest, therefore, from these arguments that contradictory statements cannot be truly made about the

same subject at one time, nor can contrary statements, because every contrariety depends on privation. This is

Similarly, no intermediate between contraries can be predicated of one and the same subject, of which one of

the contraries is predicated. If the subject is white we shall be wrong in saying it is neither black nor white,

for then it follows that it is and is not white; for the second of the two terms we have put together is true of it,

We could not be right, then, in accepting the views either of Heraclitus or of Anaxagoras. If we were, it

would follow that contraries would be predicated of the same subject; for when Anaxagoras says that in

everything there is a part of everything, he says nothing is sweet any more than it is bitter, and so with any

other pair of contraries, since in everything everything is present not potentially only, but actually and

separately. And similarly all statements cannot be false nor all true, both because of many other difficulties

which might be adduced as arising from this position, and because if all are false it will not be true to say

Every science seeks certain principles and causes for each of its objectse.g. medicine and gymnastics and

each of the other sciences, whether productive or mathematical. For each of these marks off a certain class of

things for itself and busies itself about this as about something existing and real,not however qua real; the

science that does this is another distinct from these. Of the sciences mentioned each gets somehow the 'what'

in some class of things and tries to prove the other truths, with more or less precision. Some get the 'what'

through perception, others by hypothesis; so that it is clear from an induction of this sort that there is no

There is a science of nature, and evidently it must be different both from practical and from productive

science. For in the case of productive science the principle of movement is in the producer and not in the

product, and is either an art or some other faculty. And similarly in practical science the movement is not in

the thing done, but rather in the doers. But the science of the natural philosopher deals with the things that

have in themselves a principle of movement. It is clear from these facts, then, that natural science must be

neither practical nor productive, but theoretical (for it must fall into some one of these classes). And since

each of the sciences must somehow know the 'what' and use this as a principle, we must not fall to observe

how the natural philosopher should define things and how he should state the definition of the

essencewhether as akin to 'snub' or rather to 'concave'. For of these the definition of 'snub' includes the

matter of the thing, but that of 'concave' is independent of the matter; for snubness is found in a nose, so that

we look for its definition without eliminating the nose, for what is snub is a concave nose. Evidently then the

definition of flesh also and of the eye and of the other parts must always be stated without eliminating the

Since there is a science of being qua being and capable of existing apart, we must consider whether this is to

be regarded as the same as physics or rather as different. Physics deals with the things that have a principle of

movement in themselves; mathematics is theoretical, and is a science that deals with things that are at rest,

but its subjects cannot exist apart. Therefore about that which can exist apart and is unmovable there is a

science different from both of these, if there is a substance of this nature (I mean separable and unmovable),

as we shall try to prove there is. And if there is such a kind of thing in the world, here must surely be the

divine, and this must be the first and most dominant principle. Evidently, then, there are three kinds of

theoretical sciencesphysics, mathematics, theology. The class of theoretical sciences is the best, and of these

themselves the last named is best; for it deals with the highest of existing things, and each science is called

One might raise the question whether the science of being qua being is to be regarded as universal or not.

Each of the mathematical sciences deals with some one determinate class of things, but universal

mathematics applies alike to all. Now if natural substances are the first of existing things, physics must be the

first of sciences; but if there is another entity and substance, separable and unmovable, the knowledge of it

Since 'being' in general has several senses, of which one is 'being by accident', we must consider first that

which 'is' in this sense. Evidently none of the traditional sciences busies itself about the accidental. For

neither does architecture consider what will happen to those who are to use the house (e.g. whether they have

a painful life in it or not), nor does weaving, or shoemaking, or the confectioner's art, do the like; but each of

these sciences considers only what is peculiar to it, i.e. its proper end. And as for the argument that 'when he

who is musical becomes lettered he'll be both at once, not having been both before; and that which is, not

always having been, must have come to be; therefore he must have at once become musical and lettered',this

none of the recognized sciences considers, but only sophistic; for this alone busies itself about the accidental,

so that Plato is not far wrong when he says that the sophist spends his time on nonbeing.

That a science of the accidental is not even possible will be evident if we try to see what the accidental really

is. We say that everything either is always and of necessity (necessity not in the sense of violence, but that

which we appeal to in demonstrations), or is for the most part, or is neither for the most part, nor always and

of necessity, but merely as it chances; e.g. there might be cold in the dogdays, but this occurs neither always

and of necessity, nor for the most part, though it might happen sometimes. The accidental, then, is what

occurs, but not always nor of necessity, nor for the most part. Now we have said what the accidental is, and it

is obvious why there is no science of such a thing; for all science is of that which is always or for the most

Evidently there are not causes and principles of the accidental, of the same kind as there are of the essential;

for if there were, everything would be of necessity. If A is when B is, and B is when C is, and if C exists not

by chance but of necessity, that also of which C was cause will exist of necessity, down to the last causatum

as it is called (but this was supposed to be accidental). Therefore all things will be of necessity, and chance

and the possibility of a thing's either occurring or not occurring are removed entirely from the range of

events. And if the cause be supposed not to exist but to be coming to be, the same results will follow;

everything will occur of necessity. For tomorrow's eclipse will occur if A occurs, and A if B occurs, and B

if C occurs; and in this way if we subtract time from the limited time between now and tomorrow we shall

come sometime to the already existing condition. Therefore since this exists, everything after this will occur

As to that which 'is' in the sense of being true or of being by accident, the former depends on a combination

in thought and is an affection of thought (which is the reason why it is the principles, not of that which 'is' in

this sense, but of that which is outside and can exist apart, that are sought); and the latter is not necessary but

indeterminate (I mean the accidental); and of such a thing the causes are unordered and indefinite.

Adaptation to an end is found in events that happen by nature or as the result of thought. It is 'luck' when one

of these events happens by accident. For as a thing may exist, so it may be a cause, either by its own nature or

by accident. Luck is an accidental cause at work in such events adapted to an end as are usually effected in

accordance with purpose. And so luck and thought are concerned with the same sphere; for purpose cannot

exist without thought. The causes from which lucky results might happen are indeterminate; and so luck is

obscure to human calculation and is a cause by accident, but in the unqualified sense a cause of nothing. It is

good or bad luck when the result is good or evil; and prosperity or misfortune when the scale of the results is

Since nothing accidental is prior to the essential, neither are accidental causes prior. If, then, luck or

spontaneity is a cause of the material universe, reason and nature are causes before it.

Some things are only actually, some potentially, some potentially and actually, what they are, viz. in one case

a particular reality, in another, characterized by a particular quantity, or the like. There is no movement apart

from things; for change is always according to the categories of being, and there is nothing common to these

and in no one category. But each of the categories belongs to all its subjects in either of two ways (e.g.

'thisness'for one kind of it is 'positive form', and the other is 'privation'; and as regards quality one kind is

'white' and the other 'black', and as regards quantity one kind is 'complete' and the other 'incomplete', and as

regards spatial movement one is 'upwards' and the other 'downwards', or one thing is 'light' and another

'heavy'); so that there are as many kinds of movement and change as of being. There being a distinction in

each class of things between the potential and the completely real, I call the actuality of the potential as such,

movement. That what we say is true, is plain from the following facts. When the 'buildable', in so far as it is

what we mean by 'buildable', exists actually, it is being built, and this is the process of building. Similarly

with learning, healing, walking, leaping, ageing, ripening. Movement takes when the complete reality itself

exists, and neither earlier nor later. The complete reality, then, of that which exists potentially, when it is

completely real and actual, not qua itself, but qua movable, is movement. By qua I mean this: bronze is

potentially a statue; but yet it is not the complete reality of bronze qua bronze that is movement. For it is not

the same thing to be bronze and to be a certain potency. If it were absolutely the same in its definition, the

complete reality of bronze would have been a movement. But it is not the same. (This is evident in the case of

contraries; for to be capable of being well and to be capable of being ill are not the samefor if they were,

being well and being ill would have been the sameit is that which underlies and is healthy or diseased,

whether it is moisture or blood, that is one and the same.) And since it is not. the same, as colour and the

visible are not the same, it is the complete reality of the potential, and as potential, that is movement. That it

is this, and that movement takes place when the complete reality itself exists, and neither earlier nor later, is

evident. For each thing is capable of being sometimes actual, sometimes not, e.g. the buildable qua buildable;

and the actuality of the buildable qua buildable is building. For the actuality is either thisthe act of

buildingor the house. But when the house exists, it is no longer buildable; the buildable is what is being

built. The actuality, then, must be the act of building, and this is a movement. And the same account applies

That what we have said is right is evident from what all others say about movement, and from the fact that it

is not easy to define it otherwise. For firstly one cannot put it in any class. This is evident from what people

say. Some call it otherness and inequality and the unreal; none of these, however, is necessarily moved, and

further, change is not either to these or from these any more than from their opposites. The reason why people

put movement in these classes is that it is thought to be something indefinite, and the principles in one of the

two 'columns of contraries' are indefinite because they are privative, for none of them is either a 'this' or a

'such' or in any of the other categories. And the reason why movement is thought to be indefinite is that it

cannot be classed either with the potency of things or with their actuality; for neither that which is capable of

being of a certain quantity, nor that which is actually of a certain quantity, is of necessity moved, and

movement is thought to be an actuality, but incomplete; the reason is that the potential, whose actuality it is,

is incomplete. And therefore it is hard to grasp what movement is; for it must be classed either under

privation or under potency or under absolute actuality, but evidently none of these is possible. Therefore what

remains is that it must be what we saidboth actuality and the actuality we have describedwhich is hard to

And evidently movement is in the movable; for it is the complete realization of this by that which is capable

of causing movement. And the actuality of that which is capable of causing movement is no other than that of

the movable. For it must be the complete reality of both. For while a thing is capable of causing movement

because it can do this, it is a mover because it is active; but it is on the movable that it is capable of acting, so

that the actuality of both is one, just as there is the same interval from one to two as from two to one, and as

the steep ascent and the steep descent are one, but the being of them is not one; the case of the mover and the

The infinite is either that which is incapable of being traversed because it is not its nature to be traversed (this

corresponds to the sense in which the voice is 'invisible'), or that which admits only of incomplete traverse or

scarcely admits of traverse, or that which, though it naturally admits of traverse, is not traversed or limited;

further, a thing may be infinite in respect of addition or of subtraction, or both. The infinite cannot be a

separate, independent thing. For if it is neither a spatial magnitude nor a plurality, but infinity itself is its

substance and not an accident of it, it will be indivisible; for the divisible is either magnitude or plurality. But

if indivisible, it is not infinite, except as the voice is invisible; but people do not mean this, nor are we

examining this sort of infinite, but the infinite as untraversable. Further, how can an infinite exist by itself,

unless number and magnitude also exist by themselvesssince infinity is an attribute of these? Further, if the

infinite is an accident of something else, it cannot be qua infinite an element in things, as the invisible is not

an element in speech, though the voice is invisible. And evidently the infinite cannot exist actually. For then

any part of it that might be taken would be infinite (for 'to be infinite' and 'the infinite' are the same, if the

infinite is substance and not predicated of a subject). Therefore it is either indivisible, or if it is partible, it is

divisible into infinites; but the same thing cannot be many infinites (as a part of air is air, so a part of the

infinite would be infinite, if the infinite is substance and a principle). Therefore it must be impartible and

indivisible. But the actually infinite cannot be indivisible; for it must be of a certain quantity. Therefore

infinity belongs to its subject incidentally. But if so, then (as we have said) it cannot be it that is a principle,

This inquiry is universal; but that the infinite is not among sensible things, is evident from the following

argument. If the definition of a body is 'that which is bounded by planes', there cannot be an infinite body

either sensible or intelligible; nor a separate and infinite number, for number or that which has a number is

numerable. Concretely, the truth is evident from the following argument. The infinite can neither be

composite nor simple. For (a) it cannot be a composite body, since the elements are limited in multitude. For

the contraries must be equal and no one of them must be infinite; for if one of the two bodies falls at all short

of the other in potency, the finite will be destroyed by the infinite. And that each should be infinite is

impossible. For body is that which has extension in all directions, and the infinite is the boundlessly

extended, so that if the infinite is a body it will be infinite in every direction. Nor (b) can the infinite body be

one and simpleneither, as some say, something apart from the elements, from which they generate these (for

there is no such body apart from the elements; for everything can be resolved into that of which it consists,

but no such product of analysis is observed except the simple bodies), nor fire nor any other of the elements.

For apart from the question how any of them could be infinite, the All, even if it is finite, cannot either be or

become any one of them, as Heraclitus says all things sometime become fire. The same argument applies to

this as to the One which the natural philosophers posit besides the elements. For everything changes from

Further, a sensible body is somewhere, and whole and part have the same proper place, e.g. the whole earth

and part of the earth. Therefore if (a) the infinite body is homogeneous, it will be unmovable or it will be

always moving. But this is impossible; for why should it rather rest, or move, down, up, or anywhere, rather

than anywhere else? E.g. if there were a clod which were part of an infinite body, where will this move or

rest? The proper place of the body which is homogeneous with it is infinite. Will the clod occupy the whole

place, then? And how? (This is impossible.) What then is its rest or its movement? It will either rest

everywhere, and then it cannot move; or it will move everywhere, and then it cannot be still. But (b) if the All

has unlike parts, the proper places of the parts are unlike also, and, firstly, the body of the All is not one

except by contact, and, secondly, the parts will be either finite or infinite in variety of kind. Finite they cannot

be; for then those of one kind will be infinite in quantity and those of another will not (if the All is infinite),

e.g. fire or water would be infinite, but such an infinite element would be destruction to the contrary

elements. But if the parts are infinite and simple, their places also are infinite and there will be an infinite

number of elements; and if this is impossible, and the places are finite, the All also must be limited.

In general, there cannot be an infinite body and also a proper place for bodies, if every sensible body has

either weight or lightness. For it must move either towards the middle or upwards, and the infinite either the

whole or the half of itcannot do either; for how will you divide it? Or how will part of the infinite be down

and part up, or part extreme and part middle? Further, every sensible body is in a place, and there are six

kinds of place, but these cannot exist in an infinite body. In general, if there cannot be an infinite place, there

cannot be an infinite body; (and there cannot be an infinite place,) for that which is in a place is somewhere,

and this means either up or down or in one of the other directions, and each of these is a limit.

The infinite is not the same in the sense that it is a single thing whether exhibited in distance or in movement

or in time, but the posterior among these is called infinite in virtue of its relation to the prior; i.e. a movement

is called infinite in virtue of the distance covered by the spatial movement or alteration or growth, and a time

Of things which change, some change in an accidental sense, like that in which 'the musical' may be said to

walk, and others are said, without qualification, to change, because something in them changes, i.e. the things

that change in parts; the body becomes healthy, because the eye does. But there is something which is by its

own nature moved directly, and this is the essentially movable. The same distinction is found in the case of

the mover; for it causes movement either in an accidental sense or in respect of a part of itself or essentially.

There is something that directly causes movement; and there is something that is moved, also the time in

which it is moved, and that from which and that into which it is moved. But the forms and the affections and

the place, which are the terminals of the movement of moving things, are unmovable, e.g. knowledge or heat;

it is not heat that is a movement, but heating. Change which is not accidental is found not in all things, but

between contraries, and their intermediates, and between contradictories. We may convince ourselves of this

That which changes changes either from positive into positive, or from negative into negative, or from

positive into negative, or from negative into positive. (By positive I mean that which is expressed by an

affirmative term.) Therefore there must be three changes; that from negative into negative is not change,

because (since the terms are neither contraries nor contradictories) there is no opposition. The change from

the negative into the positive which is its contradictory is generationabsolute change absolute generation,

and partial change partial generation; and the change from positive to negative is destructionabsolute change

absolute destruction, and partial change partial destruction. If, then, 'that which is not' has several senses, and

movement can attach neither to that which implies putting together or separating, nor to that which implies

potency and is opposed to that which is in the full sense (true, the notwhite or notgood can be moved

incidentally, for the notwhite might be a man; but that which is not a particular thing at all can in no wise be

moved), that which is not cannot be moved (and if this is so, generation cannot be movement; for that which

is not is generated; for even if we admit to the full that its generation is accidental, yet it is true to say that

'notbeing' is predicable of that which is generated absolutely). Similarly rest cannot be long to that which is

not. These consequences, then, turn out to be awkward, and also this, that everything that is moved is in a

place, but that which is not is not in a place; for then it would be somewhere. Nor is destruction movement;

for the contrary of movement is rest, but the contrary of destruction is generation. Since every movement is a

change, and the kinds of change are the three named above, and of these those in the way of generation and

destruction are not movements, and these are the changes from a thing to its contradictory, it follows that

only the change from positive into positive is movement. And the positives are either contrary or intermediate

(for even privation must be regarded as contrary), and are expressed by an affirmative term, e.g. 'naked' or

If the categories are classified as substance, quality, place, acting or being acted on, relation, quantity, there

must be three kinds of movementof quality, of quantity, of place. There is no movement in respect of

substance (because there is nothing contrary to substance), nor of relation (for it is possible that if one of two

things in relation changes, the relative term which was true of the other thing ceases to be true, though this

other does not change at all,so that their movement is accidental), nor of agent and patient, or mover and

moved, because there is no movement of movement nor generation of generation, nor, in general, change of

change. For there might be movement of movement in two senses; (1) movement might be the subject

moved, as a man is moved because he changes from pale to dark,so that on this showing movement, too,

may be either heated or cooled or change its place or increase. But this is impossible; for change is not a

subject. Or (2) some other subject might change from change into some other form of existence (e.g. a man

from disease into health). But this also is not possible except incidentally. For every movement is change

from something into something. (And so are generation and destruction; only, these are changes into things

opposed in certain ways while the other, movement, is into things opposed in another way.) A thing changes,

then, at the same time from health into illness, and from this change itself into another. Clearly, then, if it has

become ill, it will have changed into whatever may be the other change concerned (though it may be at rest),

and, further, into a determinate change each time; and that new change will be from something definite into

some other definite thing; therefore it will be the opposite change, that of growing well. We answer that this

happens only incidentally; e.g. there is a change from the process of recollection to that of forgetting, only

because that to which the process attaches is changing, now into a state of knowledge, now into one of

Further, the process will go on to infinity, if there is to be change of change and coming to be of coming to

be. What is true of the later, then, must be true of the earlier; e.g. if the simple coming to be was once coming

to be, that which comes to be something was also once coming to be; therefore that which simply comes to be

something was not yet in existence, but something which was coming to be coming to be something was

already in existence. And this was once coming to be, so that at that time it was not yet coming to be

something else. Now since of an infinite number of terms there is not a first, the first in this series will not

exist, and therefore no following term exist. Nothing, then, can either come term wi to be or move or change.

Further, that which is capable of a movement is also capable of the contrary movement and rest, and that

which comes to be also ceases to be. Therefore that which is coming to be is ceasing to be when it has come

to be coming to be; for it cannot cease to be as soon as it is coming to be coming to be, nor after it has come

to be; for that which is ceasing to be must be. Further, there must be a matter underlying that which comes to

be and changes. What will this be, then,what is it that becomes movement or becoming, as body or soul is

that which suffers alteration? And; again, what is it that they move into? For it must be the movement or

becoming of something from something into something. How, then, can this condition be fulfilled? There can

be no learning of learning, and therefore no becoming of becoming. Since there is not movement either of

substance or of relation or of activity and passivity, it remains that movement is in respect of quality and

quantity and place; for each of these admits of contrariety. By quality I mean not that which is in the

substance (for even the differentia is a quality), but the passive quality, in virtue of which a thing is said to be

acted on or to be incapable of being acted on. The immobile is either that which is wholly incapable of being

moved, or that which is moved with difficulty in a long time or begins slowly, or that which is of a nature to

be moved and can be moved but is not moved when and where and as it would naturally be moved. This

alone among immobiles I describe as being at rest; for rest is contrary to movement, so that it must be a

Things which are in one proximate place are together in place, and things which are in different places are

apart: things whose extremes are together touch: that at which a changing thing, if it changes continuously

according to its nature, naturally arrives before it arrives at the extreme into which it is changing, is between.

That which is most distant in a straight line is contrary in place. That is successive which is after the

beginning (the order being determined by position or form or in some other way) and has nothing of the same

class between it and that which it succeeds, e.g. lines in the case of a line, units in that of a unit, or a house in

that of a house. (There is nothing to prevent a thing of some other class from being between.) For the

successive succeeds something and is something later; 'one' does not succeed 'two', nor the first day of the

month the second. That which, being successive, touches, is contiguous. (Since all change is between

opposites, and these are either contraries or contradictories, and there is no middle term for contradictories,

clearly that which is between is between contraries.) The continuous is a species of the contiguous. I call two

things continuous when the limits of each, with which they touch and by which they are kept together,

become one and the same, so that plainly the continuous is found in the things out of which a unity naturally

arises in virtue of their contact. And plainly the successive is the first of these concepts (for the successive

does not necessarily touch, but that which touches is successive; and if a thing is continuous, it touches, but if

it touches, it is not necessarily continuous; and in things in which there is no touching, there is no organic

unity); therefore a point is not the same as a unit; for contact belongs to points, but not to units, which have

only succession; and there is something between two of the former, but not between two of the latter.

The subject of our inquiry is substance; for the principles and the causes we are seeking are those of

substances. For if the universe is of the nature of a whole, substance is its first part; and if it coheres merely

by virtue of serial succession, on this view also substance is first, and is succeeded by quality, and then by

quantity. At the same time these latter are not even being in the full sense, but are qualities and movements of

it,or else even the notwhite and the notstraight would be being; at least we say even these are, e.g. 'there

is a notwhite'. Further, none of the categories other than substance can exist apart. And the early

philosophers also in practice testify to the primacy of substance; for it was of substance that they sought the

principles and elements and causes. The thinkers of the present day tend to rank universals as substances (for

genera are universals, and these they tend to describe as principles and substances, owing to the abstract

nature of their inquiry); but the thinkers of old ranked particular things as substances, e.g. fire and earth, not

There are three kinds of substanceone that is sensible (of which one subdivision is eternal and another is

perishable; the latter is recognized by all men, and includes e.g. plants and animals), of which we must grasp

the elements, whether one or many; and another that is immovable, and this certain thinkers assert to be

capable of existing apart, some dividing it into two, others identifying the Forms and the objects of

mathematics, and others positing, of these two, only the objects of mathematics. The former two kinds of

substance are the subject of physics (for they imply movement); but the third kind belongs to another science,

Sensible substance is changeable. Now if change proceeds from opposites or from intermediates, and not

from all opposites (for the voice is notwhite, (but it does not therefore change to white)), but from the

contrary, there must be something underlying which changes into the contrary state; for the contraries do not

change. Further, something persists, but the contrary does not persist; there is, then, some third thing besides

the contraries, viz. the matter. Now since changes are of four kindseither in respect of the 'what' or of the

quality or of the quantity or of the place, and change in respect of 'thisness' is simple generation and

destruction, and change in quantity is increase and diminution, and change in respect of an affection is

alteration, and change of place is motion, changes will be from given states into those contrary to them in

these several respects. The matter, then, which changes must be capable of both states. And since that which

'is' has two senses, we must say that everything changes from that which is potentially to that which is

actually, e.g. from potentially white to actually white, and similarly in the case of increase and diminution.

Therefore not only can a thing come to be, incidentally, out of that which is not, but also all things come to be

out of that which is, but is potentially, and is not actually. And this is the 'One' of Anaxagoras; for instead of

'all things were together'and the 'Mixture' of Empedocles and Anaximander and the account given by

Democritusit is better to say 'all things were together potentially but not actually'. Therefore these thinkers

seem to have had some notion of matter. Now all things that change have matter, but different matter; and of

eternal things those which are not generable but are movable in space have matternot matter for generation,

One might raise the question from what sort of nonbeing generation proceeds; for 'nonbeing' has three

senses. If, then, one form of nonbeing exists potentially, still it is not by virtue of a potentiality for any and

every thing, but different things come from different things; nor is it satisfactory to say that 'all things were

together'; for they differ in their matter, since otherwise why did an infinity of things come to be, and not one

thing? For 'reason' is one, so that if matter also were one, that must have come to be in actuality which the

matter was in potency. The causes and the principles, then, are three, two being the pair of contraries of

which one is definition and form and the other is privation, and the third being the matter.

Note, next, that neither the matter nor the form comes to beand I mean the last matter and form. For

everything that changes is something and is changed by something and into something. That by which it is

changed is the immediate mover; that which is changed, the matter; that into which it is changed, the form.

The process, then, will go on to infinity, if not only the bronze comes to be round but also the round or the

Note, next, that each substance comes into being out of something that shares its name. (Natural objects and

other things both rank as substances.) For things come into being either by art or by nature or by luck or by

spontaneity. Now art is a principle of movement in something other than the thing moved, nature is a

principle in the thing itself (for man begets man), and the other causes are privations of these two.

There are three kinds of substancethe matter, which is a 'this' in appearance (for all things that are

characterized by contact and not, by organic unity are matter and substratum, e.g. fire, flesh, head; for these

are all matter, and the last matter is the matter of that which is in the full sense substance); the nature, which

is a 'this' or positive state towards which movement takes place; and again, thirdly, the particular substance

which is composed of these two, e.g. Socrates or Callias. Now in some cases the 'this' does not exist apart

from the composite substance, e.g. the form of house does not so exist, unless the art of building exists apart

(nor is there generation and destruction of these forms, but it is in another way that the house apart from its

matter, and health, and all ideals of art, exist and do not exist); but if the 'this' exists apart from the concrete

thing, it is only in the case of natural objects. And so Plato was not far wrong when he said that there are as

many Forms as there are kinds of natural object (if there are Forms distinct from the things of this earth). The

moving causes exist as things preceding the effects, but causes in the sense of definitions are simultaneous

with their effects. For when a man is healthy, then health also exists; and the shape of a bronze sphere exists

at the same time as the bronze sphere. (But we must examine whether any form also survives afterwards. For

in some cases there is nothing to prevent this; e.g. the soul may be of this sortnot all soul but the reason; for

presumably it is impossible that all soul should survive.) Evidently then there is no necessity, on this ground

at least, for the existence of the Ideas. For man is begotten by man, a given man by an individual father; and

The causes and the principles of different things are in a sense different, but in a sense, if one speaks

universally and analogically, they are the same for all. For one might raise the question whether the principles

and elements are different or the same for substances and for relative terms, and similarly in the case of each

of the categories. But it would be paradoxical if they were the same for all. For then from the same elements

will proceed relative terms and substances. What then will this common element be? For (1) (a) there is

nothing common to and distinct from substance and the other categories, viz. those which are predicated; but

an element is prior to the things of which it is an element. But again (b) substance is not an element in

relative terms, nor is any of these an element in substance. Further, (2) how can all things have the same

elements? For none of the elements can be the same as that which is composed of elements, e.g. b or a cannot

be the same as ba. (None, therefore, of the intelligibles, e.g. being or unity, is an element; for these are

predicable of each of the compounds as well.) None of the elements, then, will be either a substance or a

relative term; but it must be one or other. All things, then, have not the same elements.

Or, as we are wont to put it, in a sense they have and in a sense they have not; e.g. perhaps the elements of

perceptible bodies are, as form, the hot, and in another sense the cold, which is the privation; and, as matter,

that which directly and of itself potentially has these attributes; and substances comprise both these and the

things composed of these, of which these are the principles, or any unity which is produced out of the hot and

the cold, e.g. flesh or bone; for the product must be different from the elements. These things then have the

same elements and principles (though specifically different things have specifically different elements); but

all things have not the same elements in this sense, but only analogically; i.e. one might say that there are

three principlesthe form, the privation, and the matter. But each of these is different for each class; e.g. in

colour they are white, black, and surface, and in day and night they are light, darkness, and air.

Since not only the elements present in a thing are causes, but also something external, i.e. the moving cause,

clearly while 'principle' and 'element' are different both are causes, and 'principle' is divided into these two

kinds; and that which acts as producing movement or rest is a principle and a substance. Therefore

analogically there are three elements, and four causes and principles; but the elements are different in

different things, and the proximate moving cause is different for different things. Health, disease, body; the

moving cause is the medical art. Form, disorder of a particular kind, bricks; the moving cause is the building

art. And since the moving cause in the case of natural things isfor man, for instance, man, and in the

products of thought the form or its contrary, there will be in a sense three causes, while in a sense there are

four. For the medical art is in some sense health, and the building art is the form of the house, and man begets

man; further, besides these there is that which as first of all things moves all things.

Some things can exist apart and some cannot, and it is the former that are substances. And therefore all things

have the same causes, because, without substances, modifications and movements do not exist. Further, these

And in yet another way, analogically identical things are principles, i.e. actuality and potency; but these also

are not only different for different things but also apply in different ways to them. For in some cases the same

thing exists at one time actually and at another potentially, e.g. wine or flesh or man does so. (And these too

fall under the abovenamed causes. For the form exists actually, if it can exist apart, and so does the complex

of form and matter, and the privation, e.g. darkness or disease; but the matter exists potentially; for this is that

which can become qualified either by the form or by the privation.) But the distinction of actuality and

potentiality applies in another way to cases where the matter of cause and of effect is not the same, in some of

which cases the form is not the same but different; e.g. the cause of man is (1) the elements in man (viz. fire

and earth as matter, and the peculiar form), and further (2) something else outside, i.e. the father, and (3)

besides these the sun and its oblique course, which are neither matter nor form nor privation of man nor of the

Further, one must observe that some causes can be expressed in universal terms, and some cannot. The

proximate principles of all things are the 'this' which is proximate in actuality, and another which is proximate

in potentiality. The universal causes, then, of which we spoke do not exist. For it is the individual that is the

originative principle of the individuals. For while man is the originative principle of man universally, there is

no universal man, but Peleus is the originative principle of Achilles, and your father of you, and this

particular b of this particular ba, though b in general is the originative principle of ba taken without

Further, if the causes of substances are the causes of all things, yet different things have different causes and

elements, as was said; the causes of things that are not in the same class, e.g. of colours and sounds, of

substances and quantities, are different except in an analogical sense; and those of things in the same species

are different, not in species, but in the sense that the causes of different individuals are different, your matter

and form and moving cause being different from mine, while in their universal definition they are the same.

And if we inquire what are the principles or elements of substances and relations and qualitieswhether they

are the same or differentclearly when the names of the causes are used in several senses the causes of each

are the same, but when the senses are distinguished the causes are not the same but different, except that in

the following senses the causes of all are the same. They are (1) the same or analogous in this sense, that

matter, form, privation, and the moving cause are common to all things; and (2) the causes of substances may

be treated as causes of all things in this sense, that when substances are removed all things are removed;

further, (3) that which is first in respect of complete reality is the cause of all things. But in another sense

there are different first causes, viz. all the contraries which are neither generic nor ambiguous terms; and,

further, the matters of different things are different. We have stated, then, what are the principles of sensible

things and how many they are, and in what sense they are the same and in what sense different.

Since there were three kinds of substance, two of them physical and one unmovable, regarding the latter we

must assert that it is necessary that there should be an eternal unmovable substance. For substances are the

first of existing things, and if they are all destructible, all things are destructible. But it is impossible that

movement should either have come into being or cease to be (for it must always have existed), or that time

should. For there could not be a before and an after if time did not exist. Movement also is continuous, then,

in the sense in which time is; for time is either the same thing as movement or an attribute of movement. And

there is no continuous movement except movement in place, and of this only that which is circular is

But if there is something which is capable of moving things or acting on them, but is not actually doing so,

there will not necessarily be movement; for that which has a potency need not exercise it. Nothing, then, is

gained even if we suppose eternal substances, as the believers in the Forms do, unless there is to be in them

some principle which can cause change; nay, even this is not enough, nor is another substance besides the

Forms enough; for if it is not to act, there will be no movement. Further even if it acts, this will not be

enough, if its essence is potency; for there will not be eternal movement, since that which is potentially may

possibly not be. There must, then, be such a principle, whose very essence is actuality. Further, then, these

substances must be without matter; for they must be eternal, if anything is eternal. Therefore they must be

Yet there is a difficulty; for it is thought that everything that acts is able to act, but that not everything that is

able to act acts, so that the potency is prior. But if this is so, nothing that is need be; for it is possible for all

Yet if we follow the theologians who generate the world from night, or the natural philosophers who say that

'all things were together', the same impossible result ensues. For how will there be movement, if there is no

actually existing cause? Wood will surely not move itselfthe carpenter's art must act on it; nor will the

menstrual blood nor the earth set themselves in motion, but the seeds must act on the earth and the semen on

This is why some suppose eternal actualitye.g. Leucippus and Plato; for they say there is always movement.

But why and what this movement is they do say, nor, if the world moves in this way or that, do they tell us

the cause of its doing so. Now nothing is moved at random, but there must always be something present to

move it; e.g. as a matter of fact a thing moves in one way by nature, and in another by force or through the

influence of reason or something else. (Further, what sort of movement is primary? This makes a vast

difference.) But again for Plato, at least, it is not permissible to name here that which he sometimes supposes

to be the source of movementthat which moves itself; for the soul is later, and coeval with the heavens,

according to his account. To suppose potency prior to actuality, then, is in a sense right, and in a sense not;

and we have specified these senses. That actuality is prior is testified by Anaxagoras (for his 'reason' is

actuality) and by Empedocles in his doctrine of love and strife, and by those who say that there is always

movement, e.g. Leucippus. Therefore chaos or night did not exist for an infinite time, but the same things

have always existed (either passing through a cycle of changes or obeying some other law), since actuality is

prior to potency. If, then, there is a constant cycle, something must always remain, acting in the same way.

And if there is to be generation and destruction, there must be something else which is always acting in

different ways. This must, then, act in one way in virtue of itself, and in another in virtue of something

elseeither of a third agent, therefore, or of the first. Now it must be in virtue of the first. For otherwise this

again causes the motion both of the second agent and of the third. Therefore it is better to say 'the first'. For it

was the cause of eternal uniformity; and something else is the cause of variety, and evidently both together

are the cause of eternal variety. This, accordingly, is the character which the motions actually exhibit. What

Since (1) this is a possible account of the matter, and (2) if it were not true, the world would have proceeded

out of night and 'all things together' and out of nonbeing, these difficulties may be taken as solved. There is,

then, something which is always moved with an unceasing motion, which is motion in a circle; and this is

plain not in theory only but in fact. Therefore the first heaven must be eternal. There is therefore also

something which moves it. And since that which moves and is moved is intermediate, there is something

which moves without being moved, being eternal, substance, and actuality. And the object of desire and the

object of thought move in this way; they move without being moved. The primary objects of desire and of

thought are the same. For the apparent good is the object of appetite, and the real good is the primary object

of rational wish. But desire is consequent on opinion rather than opinion on desire; for the thinking is the

startingpoint. And thought is moved by the object of thought, and one of the two columns of opposites is in

itself the object of thought; and in this, substance is first, and in substance, that which is simple and exists

actually. (The one and the simple are not the same; for 'one' means a measure, but 'simple' means that the

thing itself has a certain nature.) But the beautiful, also, and that which is in itself desirable are in the same

That a final cause may exist among unchangeable entities is shown by the distinction of its meanings. For the

final cause is (a) some being for whose good an action is done, and (b) something at which the action aims;

and of these the latter exists among unchangeable entities though the former does not. The final cause, then,

produces motion as being loved, but all other things move by being moved. Now if something is moved it is

capable of being otherwise than as it is. Therefore if its actuality is the primary form of spatial motion, then in

so far as it is subject to change, in this respect it is capable of being otherwise,in place, even if not in

substance. But since there is something which moves while itself unmoved, existing actually, this can in no

way be otherwise than as it is. For motion in space is the first of the kinds of change, and motion in a circle

the first kind of spatial motion; and this the first mover produces. The first mover, then, exists of necessity;

and in so far as it exists by necessity, its mode of being is good, and it is in this sense a first principle. For the

necessary has all these sensesthat which is necessary perforce because it is contrary to the natural impulse,

that without which the good is impossible, and that which cannot be otherwise but can exist only in a single

On such a principle, then, depend the heavens and the world of nature. And it is a life such as the best which

we enjoy, and enjoy for but a short time (for it is ever in this state, which we cannot be), since its actuality is

also pleasure. (And for this reason are waking, perception, and thinking most pleasant, and hopes and

memories are so on account of these.) And thinking in itself deals with that which is best in itself, and that

which is thinking in the fullest sense with that which is best in the fullest sense. And thought thinks on itself

because it shares the nature of the object of thought; for it becomes an object of thought in coming into

contact with and thinking its objects, so that thought and object of thought are the same. For that which is

capable of receiving the object of thought, i.e. the essence, is thought. But it is active when it possesses this

object. Therefore the possession rather than the receptivity is the divine element which thought seems to

contain, and the act of contemplation is what is most pleasant and best. If, then, God is always in that good

state in which we sometimes are, this compels our wonder; and if in a better this compels it yet more. And

God is in a better state. And life also belongs to God; for the actuality of thought is life, and God is that

actuality; and God's selfdependent actuality is life most good and eternal. We say therefore that God is a

living being, eternal, most good, so that life and duration continuous and eternal belong to God; for this is

Those who suppose, as the Pythagoreans and Speusippus do, that supreme beauty and goodness are not

present in the beginning, because the beginnings both of plants and of animals are causes, but beauty and

completeness are in the effects of these, are wrong in their opinion. For the seed comes from other individuals

which are prior and complete, and the first thing is not seed but the complete being; e.g. we must say that

before the seed there is a man,not the man produced from the seed, but another from whom the seed comes.

It is clear then from what has been said that there is a substance which is eternal and unmovable and separate

from sensible things. It has been shown also that this substance cannot have any magnitude, but is without

parts and indivisible (for it produces movement through infinite time, but nothing finite has infinite power;

and, while every magnitude is either infinite or finite, it cannot, for the above reason, have finite magnitude,

and it cannot have infinite magnitude because there is no infinite magnitude at all). But it has also been

shown that it is impassive and unalterable; for all the other changes are posterior to change of place.

It is clear, then, why these things are as they are. But we must not ignore the question whether we have to

suppose one such substance or more than one, and if the latter, how many; we must also mention, regarding

the opinions expressed by others, that they have said nothing about the number of the substances that can

even be clearly stated. For the theory of Ideas has no special discussion of the subject; for those who speak of

Ideas say the Ideas are numbers, and they speak of numbers now as unlimited, now as limited by the number

10; but as for the reason why there should be just so many numbers, nothing is said with any demonstrative

exactness. We however must discuss the subject, starting from the presuppositions and distinctions we have

mentioned. The first principle or primary being is not movable either in itself or accidentally, but produces

the primary eternal and single movement. But since that which is moved must be moved by something, and

the first mover must be in itself unmovable, and eternal movement must be produced by something eternal

and a single movement by a single thing, and since we see that besides the simple spatial movement of the

universe, which we say the first and unmovable substance produces, there are other spatial movementsthose

of the planetswhich are eternal (for a body which moves in a circle is eternal and unresting; we have proved

these points in the physical treatises), each of these movements also must be caused by a substance both

unmovable in itself and eternal. For the nature of the stars is eternal just because it is a certain kind of

substance, and the mover is eternal and prior to the moved, and that which is prior to a substance must be a

substance. Evidently, then, there must be substances which are of the same number as the movements of the

stars, and in their nature eternal, and in themselves unmovable, and without magnitude, for the reason before

mentioned. That the movers are substances, then, and that one of these is first and another second according

to the same order as the movements of the stars, is evident. But in the number of the movements we reach a

problem which must be treated from the standpoint of that one of the mathematical sciences which is most

akin to philosophyviz. of astronomy; for this science speculates about substance which is perceptible but

eternal, but the other mathematical sciences, i.e. arithmetic and geometry, treat of no substance. That the

movements are more numerous than the bodies that are moved is evident to those who have given even

moderate attention to the matter; for each of the planets has more than one movement. But as to the actual

number of these movements, we nowto give some notion of the subjectquote what some of the

mathematicians say, that our thought may have some definite number to grasp; but, for the rest, we must

partly investigate for ourselves, Partly learn from other investigators, and if those who study this subject form

an opinion contrary to what we have now stated, we must esteem both parties indeed, but follow the more

Eudoxus supposed that the motion of the sun or of the moon involves, in either case, three spheres, of which

the first is the sphere of the fixed stars, and the second moves in the circle which runs along the middle of the

zodiac, and the third in the circle which is inclined across the breadth of the zodiac; but the circle in which

the moon moves is inclined at a greater angle than that in which the sun moves. And the motion of the planets

involves, in each case, four spheres, and of these also the first and second are the same as the first two

mentioned above (for the sphere of the fixed stars is that which moves all the other spheres, and that which is

placed beneath this and has its movement in the circle which bisects the zodiac is common to all), but the

poles of the third sphere of each planet are in the circle which bisects the zodiac, and the motion of the fourth

sphere is in the circle which is inclined at an angle to the equator of the third sphere; and the poles of the third

sphere are different for each of the other planets, but those of Venus and Mercury are the same.

Callippus made the position of the spheres the same as Eudoxus did, but while he assigned the same number

as Eudoxus did to Jupiter and to Saturn, he thought two more spheres should be added to the sun and two to

the moon, if one is to explain the observed facts; and one more to each of the other planets.

But it is necessary, if all the spheres combined are to explain the observed facts, that for each of the planets

there should be other spheres (one fewer than those hitherto assigned) which counteract those already

mentioned and bring back to the same position the outermost sphere of the star which in each case is situated

below the star in question; for only thus can all the forces at work produce the observed motion of the planets.

Since, then, the spheres involved in the movement of the planets themselves areeight for Saturn and Jupiter

and twentyfive for the others, and of these only those involved in the movement of the lowestsituated

planet need not be counteracted the spheres which counteract those of the outermost two planets will be six in

number, and the spheres which counteract those of the next four planets will be sixteen; therefore the number

of all the spheresboth those which move the planets and those which counteract thesewill be fiftyfive.

And if one were not to add to the moon and to the sun the movements we mentioned, the whole set of spheres

Let this, then, be taken as the number of the spheres, so that the unmovable substances and principles also

may probably be taken as just so many; the assertion of necessity must be left to more powerful thinkers. But

if there can be no spatial movement which does not conduce to the moving of a star, and if further every

being and every substance which is immune from change and in virtue of itself has attained to the best must

be considered an end, there can be no other being apart from these we have named, but this must be the

number of the substances. For if there are others, they will cause change as being a final cause of movement;

but there cannot he other movements besides those mentioned. And it is reasonable to infer this from a

consideration of the bodies that are moved; for if everything that moves is for the sake of that which is

moved, and every movement belongs to something that is moved, no movement can be for the sake of itself

or of another movement, but all the movements must be for the sake of the stars. For if there is to be a

movement for the sake of a movement, this latter also will have to be for the sake of something else; so that

since there cannot be an infinite regress, the end of every movement will be one of the divine bodies which

(Evidently there is but one heaven. For if there are many heavens as there are many men, the moving

principles, of which each heaven will have one, will be one in form but in number many. But all things that

are many in number have matter; for one and the same definition, e.g. that of man, applies to many things,

while Socrates is one. But the primary essence has not matter; for it is complete reality. So the unmovable

first mover is one both in definition and in number; so too, therefore, is that which is moved always and

continuously; therefore there is one heaven alone.) Our forefathers in the most remote ages have handed

down to their posterity a tradition, in the form of a myth, that these bodies are gods, and that the divine

encloses the whole of nature. The rest of the tradition has been added later in mythical form with a view to

the persuasion of the multitude and to its legal and utilitarian expediency; they say these gods are in the form

of men or like some of the other animals, and they say other things consequent on and similar to these which

we have mentioned. But if one were to separate the first point from these additions and take it alonethat they

thought the first substances to be gods, one must regard this as an inspired utterance, and reflect that, while

probably each art and each science has often been developed as far as possible and has again perished, these

opinions, with others, have been preserved until the present like relics of the ancient treasure. Only thus far,

then, is the opinion of our ancestors and of our earliest predecessors clear to us.

The nature of the divine thought involves certain problems; for while thought is held to be the most divine of

things observed by us, the question how it must be situated in order to have that character involves

difficulties. For if it thinks of nothing, what is there here of dignity? It is just like one who sleeps. And if it

thinks, but this depends on something else, then (since that which is its substance is not the act of thinking,

but a potency) it cannot be the best substance; for it is through thinking that its value belongs to it. Further,

whether its substance is the faculty of thought or the act of thinking, what does it think of? Either of itself or

of something else; and if of something else, either of the same thing always or of something different. Does it

matter, then, or not, whether it thinks of the good or of any chance thing? Are there not some things about

which it is incredible that it should think? Evidently, then, it thinks of that which is most divine and precious,

and it does not change; for change would be change for the worse, and this would be already a movement.

First, then, if 'thought' is not the act of thinking but a potency, it would be reasonable to suppose that the

continuity of its thinking is wearisome to it. Secondly, there would evidently be something else more

precious than thought, viz. that which is thought of. For both thinking and the act of thought will belong even

to one who thinks of the worst thing in the world, so that if this ought to be avoided (and it ought, for there

are even some things which it is better not to see than to see), the act of thinking cannot be the best of things.

Therefore it must be of itself that the divine thought thinks (since it is the most excellent of things), and its

But evidently knowledge and perception and opinion and understanding have always something else as their

object, and themselves only by the way. Further, if thinking and being thought of are different, in respect of

which does goodness belong to thought? For to he an act of thinking and to he an object of thought are not

the same thing. We answer that in some cases the knowledge is the object. In the productive sciences it is the

substance or essence of the object, matter omitted, and in the theoretical sciences the definition or the act of

thinking is the object. Since, then, thought and the object of thought are not different in the case of things that

have not matter, the divine thought and its object will be the same, i.e. the thinking will be one with the

A further question is leftwhether the object of the divine thought is composite; for if it were, thought would

change in passing from part to part of the whole. We answer that everything which has not matter is

indivisibleas human thought, or rather the thought of composite beings, is in a certain period of time (for it

does not possess the good at this moment or at that, but its best, being something different from it, is attained

only in a whole period of time), so throughout eternity is the thought which has itself for its object.

We must consider also in which of two ways the nature of the universe contains the good, and the highest

good, whether as something separate and by itself, or as the order of the parts. Probably in both ways, as an

army does; for its good is found both in its order and in its leader, and more in the latter; for he does not

depend on the order but it depends on him. And all things are ordered together somehow, but not all

alike,both fishes and fowls and plants; and the world is not such that one thing has nothing to do with

another, but they are connected. For all are ordered together to one end, but it is as in a house, where the

freemen are least at liberty to act at random, but all things or most things are already ordained for them, while

the slaves and the animals do little for the common good, and for the most part live at random; for this is the

sort of principle that constitutes the nature of each. I mean, for instance, that all must at least come to be

dissolved into their elements, and there are other functions similarly in which all share for the good of the

We must not fail to observe how many impossible or paradoxical results confront those who hold different

views from our own, and what are the views of the subtler thinkers, and which views are attended by fewest

difficulties. All make all things out of contraries. But neither 'all things' nor 'out of contraries' is right; nor do

these thinkers tell us how all the things in which the contraries are present can be made out of the contraries;

for contraries are not affected by one another. Now for us this difficulty is solved naturally by the fact that

there is a third element. These thinkers however make one of the two contraries matter; this is done for

instance by those who make the unequal matter for the equal, or the many matter for the one. But this also is

refuted in the same way; for the one matter which underlies any pair of contraries is contrary to nothing.

Further, all things, except the one, will, on the view we are criticizing, partake of evil; for the bad itself is one

of the two elements. But the other school does not treat the good and the bad even as principles; yet in all

things the good is in the highest degree a principle. The school we first mentioned is right in saying that it is a

principle, but how the good is a principle they do not saywhether as end or as mover or as form.

Empedocles also has a paradoxical view; for he identifies the good with love, but this is a principle both as

mover (for it brings things together) and as matter (for it is part of the mixture). Now even if it happens that

the same thing is a principle both as matter and as mover, still the being, at least, of the two is not the same.

In which respect then is love a principle? It is paradoxical also that strife should be imperishable; the nature

Anaxagoras makes the good a motive principle; for his 'reason' moves things. But it moves them for an end,

which must be something other than it, except according to our way of stating the case; for, on our view, the

medical art is in a sense health. It is paradoxical also not to suppose a contrary to the good, i.e. to reason. But

all who speak of the contraries make no use of the contraries, unless we bring their views into shape. And

why some things are perishable and others imperishable, no one tells us; for they make all existing things out

of the same principles. Further, some make existing things out of the nonexistent; and others to avoid the

Further, why should there always be becoming, and what is the cause of becoming?this no one tells us. And

those who suppose two principles must suppose another, a superior principle, and so must those who believe

in the Forms; for why did things come to participate, or why do they participate, in the Forms? And all other

thinkers are confronted by the necessary consequence that there is something contrary to Wisdom, i.e. to the

highest knowledge; but we are not. For there is nothing contrary to that which is primary; for all contraries

have matter, and things that have matter exist only potentially; and the ignorance which is contrary to any

knowledge leads to an object contrary to the object of the knowledge; but what is primary has no contrary.

Again, if besides sensible things no others exist, there will be no first principle, no order, no becoming, no

heavenly bodies, but each principle will have a principle before it, as in the accounts of the theologians and

all the natural philosophers. But if the Forms or the numbers are to exist, they will be causes of nothing; or if

not that, at least not of movement. Further, how is extension, i.e. a continuum, to be produced out of

unextended parts? For number will not, either as mover or as form, produce a continuum. But again there

cannot be any contrary that is also essentially a productive or moving principle; for it would be possible for it

not to be. Or at least its action would be posterior to its potency. The world, then, would not be eternal. But it

is; one of these premisses, then, must be denied. And we have said how this must be done. Further, in virtue

of what the numbers, or the soul and the body, or in general the form and the thing, are oneof this no one

tells us anything; nor can any one tell, unless he says, as we do, that the mover makes them one. And those

who say mathematical number is first and go on to generate one kind of substance after another and give

different principles for each, make the substance of the universe a mere series of episodes (for one substance

has no influence on another by its existence or nonexistence), and they give us many governing principles;

WE have stated what is the substance of sensible things, dealing in the treatise on physics with matter, and

later with the substance which has actual existence. Now since our inquiry is whether there is or is not

besides the sensible substances any which is immovable and eternal, and, if there is, what it is, we must first

consider what is said by others, so that, if there is anything which they say wrongly, we may not be liable to

the same objections, while, if there is any opinion common to them and us, we shall have no private

grievance against ourselves on that account; for one must be content to state some points better than one's

Two opinions are held on this subject; it is said that the objects of mathematicsi.e. numbers and lines and

the likeare substances, and again that the Ideas are substances. And (1) since some recognize these as two

different classesthe Ideas and the mathematical numbers, and (2) some recognize both as having one nature,

while (3) some others say that the mathematical substances are the only substances, we must consider first the

objects of mathematics, not qualifying them by any other characteristicnot asking, for instance, whether

they are in fact Ideas or not, or whether they are the principles and substances of existing things or not, but

only whether as objects of mathematics they exist or not, and if they exist, how they exist. Then after this we

must separately consider the Ideas themselves in a general way, and only as far as the accepted mode of

treatment demands; for most of the points have been repeatedly made even by the discussions outside our

school, and, further, the greater part of our account must finish by throwing light on that inquiry, viz. when

we examine whether the substances and the principles of existing things are numbers and Ideas; for after the

If the objects of mathematics exist, they must exist either in sensible objects, as some say, or separate from

sensible objects (and this also is said by some); or if they exist in neither of these ways, either they do not

exist, or they exist only in some special sense. So that the subject of our discussion will be not whether they

That it is impossible for mathematical objects to exist in sensible things, and at the same time that the

doctrine in question is an artificial one, has been said already in our discussion of difficulties we have pointed

out that it is impossible for two solids to be in the same place, and also that according to the same argument

the other powers and characteristics also should exist in sensible things and none of them separately. This we

have said already. But, further, it is obvious that on this theory it is impossible for any body whatever to be

divided; for it would have to be divided at a plane, and the plane at a line, and the line at a point, so that if the

point cannot be divided, neither can the line, and if the line cannot, neither can the plane nor the solid. What

difference, then, does it make whether sensible things are such indivisible entities, or, without being so

themselves, have indivisible entities in them? The result will be the same; if the sensible entities are divided

the others will be divided too, or else not even the sensible entities can be divided.

But, again, it is not possible that such entities should exist separately. For if besides the sensible solids there

are to be other solids which are separate from them and prior to the sensible solids, it is plain that besides the

planes also there must be other and separate planes and points and lines; for consistency requires this. But if

these exist, again besides the planes and lines and points of the mathematical solid there must be others which

are separate. (For incomposites are prior to compounds; and if there are, prior to the sensible bodies, bodies

which are not sensible, by the same argument the planes which exist by themselves must be prior to those

which are in the motionless solids. Therefore these will be planes and lines other than those that exist along

with the mathematical solids to which these thinkers assign separate existence; for the latter exist along with

the mathematical solids, while the others are prior to the mathematical solids.) Again, therefore, there will be,

belonging to these planes, lines, and prior to them there will have to be, by the same argument, other lines

and points; and prior to these points in the prior lines there will have to be other points, though there will be

no others prior to these. Now (1) the accumulation becomes absurd; for we find ourselves with one set of

solids apart from the sensible solids; three sets of planes apart from the sensible planesthose which exist

apart from the sensible planes, and those in the mathematical solids, and those which exist apart from those in

the mathematical solids; four sets of lines, and five sets of points. With which of these, then, will the

mathematical sciences deal? Certainly not with the planes and lines and points in the motionless solid; for

science always deals with what is prior. And (the same account will apply also to numbers; for there will be a

different set of units apart from each set of points, and also apart from each set of realities, from the objects of

sense and again from those of thought; so that there will be various classes of mathematical numbers.

Again, how is it possible to solve the questions which we have already enumerated in our discussion of

difficulties? For the objects of astronomy will exist apart from sensible things just as the objects of geometry

will; but how is it possible that a heaven and its partsor anything else which has movementshould exist

apart? Similarly also the objects of optics and of harmonics will exist apart; for there will be both voice and

sight besides the sensible or individual voices and sights. Therefore it is plain that the other senses as well,

and the other objects of sense, will exist apart; for why should one set of them do so and another not? And if

this is so, there will also be animals existing apart, since there will be senses.

Again, there are certain mathematical theorems that are universal, extending beyond these substances. Here

then we shall have another intermediate substance separate both from the Ideas and from the intermediates,a

substance which is neither number nor points nor spatial magnitude nor time. And if this is impossible,

plainly it is also impossible that the former entities should exist separate from sensible things.

And, in general, conclusion contrary alike to the truth and to the usual views follow, if one is to suppose the

objects of mathematics to exist thus as separate entities. For because they exist thus they must be prior to

sensible spatial magnitudes, but in truth they must be posterior; for the incomplete spatial magnitude is in the

order of generation prior, but in the order of substance posterior, as the lifeless is to the living.

Again, by virtue of what, and when, will mathematical magnitudes be one? For things in our perceptible

world are one in virtue of soul, or of a part of soul, or of something else that is reasonable enough; when

these are not present, the thing is a plurality, and splits up into parts. But in the case of the subjects of

mathematics, which are divisible and are quantities, what is the cause of their being one and holding

Again, the modes of generation of the objects of mathematics show that we are right. For the dimension first

generated is length, then comes breadth, lastly depth, and the process is complete. If, then, that which is

posterior in the order of generation is prior in the order of substantiality, the solid will be prior to the plane

and the line. And in this way also it is both more complete and more whole, because it can become animate.

How, on the other hand, could a line or a plane be animate? The supposition passes the power of our senses.

Again, the solid is a sort of substance; for it already has in a sense completeness. But how can lines be

substances? Neither as a form or shape, as the soul perhaps is, nor as matter, like the solid; for we have no

experience of anything that can be put together out of lines or planes or points, while if these had been a sort

of material substance, we should have observed things which could be put together out of them.

Grant, then, that they are prior in definition. Still not all things that are prior in definition are also prior in

substantiality. For those things are prior in substantiality which when separated from other things surpass

them in the power of independent existence, but things are prior in definition to those whose definitions are

compounded out of their definitions; and these two properties are not coextensive. For if attributes do not

exist apart from the substances (e.g. a 'mobile' or a pale'), pale is prior to the pale man in definition, but not in

substantiality. For it cannot exist separately, but is always along with the concrete thing; and by the concrete

thing I mean the pale man. Therefore it is plain that neither is the result of abstraction prior nor that which is

produced by adding determinants posterior; for it is by adding a determinant to pale that we speak of the pale

It has, then, been sufficiently pointed out that the objects of mathematics are not substances in a higher

degree than bodies are, and that they are not prior to sensibles in being, but only in definition, and that they

cannot exist somewhere apart. But since it was not possible for them to exist in sensibles either, it is plain that

they either do not exist at all or exist in a special sense and therefore do not 'exist' without qualification. For

For just as the universal propositions of mathematics deal not with objects which exist separately, apart from

extended magnitudes and from numbers, but with magnitudes and numbers, not however qua such as to have

magnitude or to be divisible, clearly it is possible that there should also be both propositions and

demonstrations about sensible magnitudes, not however qua sensible but qua possessed of certain definite

qualities. For as there are many propositions about things merely considered as in motion, apart from what

each such thing is and from their accidents, and as it is not therefore necessary that there should be either a

mobile separate from sensibles, or a distinct mobile entity in the sensibles, so too in the case of mobiles there

will be propositions and sciences, which treat them however not qua mobile but only qua bodies, or again

only qua planes, or only qua lines, or qua divisibles, or qua indivisibles having position, or only qua

indivisibles. Thus since it is true to say without qualification that not only things which are separable but also

things which are inseparable exist (for instance, that mobiles exist), it is true also to say without qualification

that the objects of mathematics exist, and with the character ascribed to them by mathematicians. And as it is

true to say of the other sciences too, without qualification, that they deal with such and such a subjectnot

with what is accidental to it (e.g. not with the pale, if the healthy thing is pale, and the science has the healthy

as its subject), but with that which is the subject of each sciencewith the healthy if it treats its object qua

healthy, with man if qua man:so too is it with geometry; if its subjects happen to be sensible, though it does

not treat them qua sensible, the mathematical sciences will not for that reason be sciences of sensiblesnor,

on the other hand, of other things separate from sensibles. Many properties attach to things in virtue of their

own nature as possessed of each such character; e.g. there are attributes peculiar to the animal qua female or

qua male (yet there is no 'female' nor 'male' separate from animals); so that there are also attributes which

belong to things merely as lengths or as planes. And in proportion as we are dealing with things which are

prior in definition and simpler, our knowledge has more accuracy, i.e. simplicity. Therefore a science which

abstracts from spatial magnitude is more precise than one which takes it into account; and a science is most

precise if it abstracts from movement, but if it takes account of movement, it is most precise if it deals with

the primary movement, for this is the simplest; and of this again uniform movement is the simplest form.

The same account may be given of harmonics and optics; for neither considers its objects qua sight or qua

voice, but qua lines and numbers; but the latter are attributes proper to the former. And mechanics too

proceeds in the same way. Therefore if we suppose attributes separated from their fellow attributes and make

any inquiry concerning them as such, we shall not for this reason be in error, any more than when one draws

a line on the ground and calls it a foot long when it is not; for the error is not included in the premisses.

Each question will be best investigated in this wayby setting up by an act of separation what is not separate,

as the arithmetician and the geometer do. For a man qua man is one indivisible thing; and the arithmetician

supposed one indivisible thing, and then considered whether any attribute belongs to a man qua indivisible.

But the geometer treats him neither qua man nor qua indivisible, but as a solid. For evidently the properties

which would have belonged to him even if perchance he had not been indivisible, can belong to him even

apart from these attributes. Thus, then, geometers speak correctly; they talk about existing things, and their

subjects do exist; for being has two formsit exists not only in complete reality but also materially.

Now since the good and the beautiful are different (for the former always implies conduct as its subject, while

the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing

of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do

not expressly mention them, but prove attributes which are their results or their definitions, it is not true to

say that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness,

which the mathematical sciences demonstrate in a special degree. And since these (e.g. order and

definiteness) are obviously causes of many things, evidently these sciences must treat this sort of causative

principle also (i.e. the beautiful) as in some sense a cause. But we shall speak more plainly elsewhere about

So much then for the objects of mathematics; we have said that they exist and in what sense they exist, and in

what sense they are prior and in what sense not prior. Now, regarding the Ideas, we must first examine the

ideal theory itself, not connecting it in any way with the nature of numbers, but treating it in the form in

which it was originally understood by those who first maintained the existence of the Ideas. The supporters of

the ideal theory were led to it because on the question about the truth of things they accepted the Heraclitean

sayings which describe all sensible things as ever passing away, so that if knowledge or thought is to have an

object, there must be some other and permanent entities, apart from those which are sensible; for there could

be no knowledge of things which were in a state of flux. But when Socrates was occupying himself with the

excellences of character, and in connexion with them became the first to raise the problem of universal

definition (for of the physicists Democritus only touched on the subject to a small extent, and defined, after a

fashion, the hot and the cold; while the Pythagoreans had before this treated of a few things, whose

definitionse.g. those of opportunity, justice, or marriagethey connected with numbers; but it was natural

that Socrates should be seeking the essence, for he was seeking to syllogize, and 'what a thing is' is the

startingpoint of syllogisms; for there was as yet none of the dialectical power which enables people even

without knowledge of the essence to speculate about contraries and inquire whether the same science deals

with contraries; for two things may be fairly ascribed to Socratesinductive arguments and universal

definition, both of which are concerned with the startingpoint of science):but Socrates did not make the

universals or the definitions exist apart: they, however, gave them separate existence, and this was the kind of

thing they called Ideas. Therefore it followed for them, almost by the same argument, that there must be Ideas

of all things that are spoken of universally, and it was almost as if a man wished to count certain things, and

while they were few thought he would not be able to count them, but made more of them and then counted

them; for the Forms are, one may say, more numerous than the particular sensible things, yet it was in

seeking the causes of these that they proceeded from them to the Forms. For to each thing there answers an

entity which has the same name and exists apart from the substances, and so also in the case of all other

Again, of the ways in which it is proved that the Forms exist, none is convincing; for from some no inference

necessarily follows, and from some arise Forms even of things of which they think there are no Forms. For

according to the arguments from the sciences there will be Forms of all things of which there are sciences,

and according to the argument of the 'one over many' there will be Forms even of negations, and according to

the argument that thought has an object when the individual object has perished, there will be Forms of

perishable things; for we have an image of these. Again, of the most accurate arguments, some lead to Ideas

of relations, of which they say there is no independent class, and others introduce the 'third man'.

And in general the arguments for the Forms destroy things for whose existence the believers in Forms are

more zealous than for the existence of the Ideas; for it follows that not the dyad but number is first, and that

prior to number is the relative, and that this is prior to the absolutebesides all the other points on which

certain people, by following out the opinions held about the Forms, came into conflict with the principles of

Again, according to the assumption on the belief in the Ideas rests, there will be Forms not only of substances

but also of many other things; for the concept is single not only in the case of substances, but also in that of

nonsubstances, and there are sciences of other things than substance; and a thousand other such difficulties

confront them. But according to the necessities of the case and the opinions about the Forms, if they can be

shared in there must be Ideas of substances only. For they are not shared in incidentally, but each Form must

be shared in as something not predicated of a subject. (By 'being shared in incidentally' I mean that if a thing

shares in 'double itself', it shares also in 'eternal', but incidentally; for 'the double' happens to be eternal.)

Therefore the Forms will be substance. But the same names indicate substance in this and in the ideal world

(or what will be the meaning of saying that there is something apart from the particularsthe one over

many?). And if the Ideas and the things that share in them have the same form, there will be something

common: for why should '2' be one and the same in the perishable 2's, or in the 2's which are many but

eternal, and not the same in the '2 itself' as in the individual 2? But if they have not the same form, they will

have only the name in common, and it is as if one were to call both Callias and a piece of wood a 'man',

But if we are to suppose that in other respects the common definitions apply to the Forms, e.g. that 'plane

figure' and the other parts of the definition apply to the circle itself, but 'what really is' has to be added, we

must inquire whether this is not absolutely meaningless. For to what is this to be added? To 'centre' or to

'plane' or to all the parts of the definition? For all the elements in the essence are Ideas, e.g. 'animal' and

'twofooted'. Further, there must be some Ideal answering to 'plane' above, some nature which will be present

Above all one might discuss the question what in the world the Forms contribute to sensible things, either to

those that are eternal or to those that come into being and cease to be; for they cause neither movement nor

any change in them. But again they help in no wise either towards the knowledge of other things (for they are

not even the substance of these, else they would have been in them), or towards their being, if they are not in

the individuals which share in them; though if they were, they might be thought to be causes, as white causes

whiteness in a white object by entering into its composition. But this argument, which was used first by

Anaxagoras, and later by Eudoxus in his discussion of difficulties and by certain others, is very easily upset;

But, further, all other things cannot come from the Forms in any of the usual senses of 'from'. And to say that

they are patterns and the other things share in them is to use empty words and poetical metaphors. For what is

it that works, looking to the Ideas? And any thing can both be and come into being without being copied from

something else, so that, whether Socrates exists or not, a man like Socrates might come to be. And evidently

this might be so even if Socrates were eternal. And there will be several patterns of the same thing, and

therefore several Forms; e.g. 'animal' and 'twofooted', and also 'manhimself', will be Forms of man. Again,

the Forms are patterns not only of sensible things, but of Forms themselves also; i.e. the genus is the pattern

of the various formsofagenus; therefore the same thing will be pattern and copy.

Again, it would seem impossible that substance and that whose substance it is should exist apart; how,

In the Phaedo the case is stated in this waythat the Forms are causes both of being and of becoming. Yet

though the Forms exist, still things do not come into being, unless there is something to originate movement;

and many other things come into being (e.g. a house or a ring) of which they say there are no Forms. Clearly

therefore even the things of which they say there are Ideas can both be and come into being owing to such

causes as produce the things just mentioned, and not owing to the Forms. But regarding the Ideas it is

possible, both in this way and by more abstract and accurate arguments, to collect many objections like those

Since we have discussed these points, it is well to consider again the results regarding numbers which

confront those who say that numbers are separable substances and first causes of things. If number is an

entity and its substance is nothing other than just number, as some say, it follows that either (1) there is a first

in it and a second, each being different in species,and either (a) this is true of the units without exception,

and any unit is inassociable with any unit, or (b) they are all without exception successive, and any of them

are associable with any, as they say is the case with mathematical number; for in mathematical number no

one unit is in any way different from another. Or (c) some units must be associable and some not; e.g.

suppose that 2 is first after 1, and then comes 3 and then the rest of the number series, and the units in each

number are associable, e.g. those in the first 2 are associable with one another, and those in the first 3 with

one another, and so with the other numbers; but the units in the '2itself' are inassociable with those in the

'3itself'; and similarly in the case of the other successive numbers. And so while mathematical number is

counted thusafter 1, 2 (which consists of another 1 besides the former 1), and 3 which consists of another 1

besides these two), and the other numbers similarly, ideal number is counted thusafter 1, a distinct 2 which

does not include the first 1, and a 3 which does not include the 2 and the rest of the number series similarly.

Or (2) one kind of number must be like the first that was named, one like that which the mathematicians

Again, these kinds of numbers must either be separable from things, or not separable but in objects of

perception (not however in the way which we first considered, in the sense that objects of perception consists

of numbers which are present in them)either one kind and not another, or all of them.

These are of necessity the only ways in which the numbers can exist. And of those who say that the 1 is the

beginning and substance and element of all things, and that number is formed from the 1 and something else,

almost every one has described number in one of these ways; only no one has said all the units are

inassociable. And this has happened reasonably enough; for there can be no way besides those mentioned.

Some say both kinds of number exist, that which has a before and after being identical with the Ideas, and

mathematical number being different from the Ideas and from sensible things, and both being separable from

sensible things; and others say mathematical number alone exists, as the first of realities, separate from

sensible things. And the Pythagoreans, also, believe in one kind of numberthe mathematical; only they say it

is not separate but sensible substances are formed out of it. For they construct the whole universe out of

numbersonly not numbers consisting of abstract units; they suppose the units to have spatial magnitude. But

how the first 1 was constructed so as to have magnitude, they seem unable to say.

Another thinker says the first kind of number, that of the Forms, alone exists, and some say mathematical

The case of lines, planes, and solids is similar. For some think that those which are the objects of

mathematics are different from those which come after the Ideas; and of those who express themselves

otherwise some speak of the objects of mathematics and in a mathematical wayviz. those who do not make

the Ideas numbers nor say that Ideas exist; and others speak of the objects of mathematics, but not

mathematically; for they say that neither is every spatial magnitude divisible into magnitudes, nor do any two

units taken at random make 2. All who say the 1 is an element and principle of things suppose numbers to

consist of abstract units, except the Pythagoreans; but they suppose the numbers to have magnitude, as has

been said before. It is clear from this statement, then, in how many ways numbers may be described, and that

all the ways have been mentioned; and all these views are impossible, but some perhaps more than others.

First, then, let us inquire if the units are associable or inassociable, and if inassociable, in which of the two

ways we distinguished. For it is possible that any unity is inassociable with any, and it is possible that those

in the 'itself' are inassociable with those in the 'itself', and, generally, that those in each ideal number are

inassociable with those in other ideal numbers. Now (1) all units are associable and without difference, we

get mathematical numberonly one kind of number, and the Ideas cannot be the numbers. For what sort of

number will manhimself or animalitself or any other Form be? There is one Idea of each thing e.g. one of

manhimself and another one of animalitself; but the similar and undifferentiated numbers are infinitely

many, so that any particular 3 is no more manhimself than any other 3. But if the Ideas are not numbers,

neither can they exist at all. For from what principles will the Ideas come? It is number that comes from the 1

and the indefinite dyad, and the principles or elements are said to be principles and elements of number, and

But (2) if the units are inassociable, and inassociable in the sense that any is inassociable with any other,

number of this sort cannot be mathematical number; for mathematical number consists of undifferentiated

units, and the truths proved of it suit this character. Nor can it be ideal number. For 2 will not proceed

immediately from 1 and the indefinite dyad, and be followed by the successive numbers, as they say '2,3,4'

for the units in the ideal are generated at the same time, whether, as the first holder of the theory said, from

unequals (coming into being when these were equalized) or in some other waysince, if one unit is to be prior

to the other, it will be prior also to 2 the composed of these; for when there is one thing prior and another

posterior, the resultant of these will be prior to one and posterior to the other. Again, since the 1itself is first,

and then there is a particular 1 which is first among the others and next after the 1itself, and again a third

which is next after the second and next but one after the first 1,so the units must be prior to the numbers

after which they are named when we count them; e.g. there will be a third unit in 2 before 3 exists, and a

fourth and a fifth in 3 before the numbers 4 and 5 exist.Now none of these thinkers has said the units are

inassociable in this way, but according to their principles it is reasonable that they should be so even in this

way, though in truth it is impossible. For it is reasonable both that the units should have priority and

posteriority if there is a first unit or first 1, and also that the 2's should if there is a first 2; for after the first it

is reasonable and necessary that there should be a second, and if a second, a third, and so with the others

successively. (And to say both things at the same time, that a unit is first and another unit is second after the

ideal 1, and that a 2 is first after it, is impossible.) But they make a first unit or 1, but not also a second and a

third, and a first 2, but not also a second and a third. Clearly, also, it is not possible, if all the units are

inassociable, that there should be a 2itself and a 3itself; and so with the other numbers. For whether the

units are undifferentiated or different each from each, number must be counted by addition, e.g. 2 by adding

another 1 to the one, 3 by adding another 1 to the two, and similarly. This being so, numbers cannot be

generated as they generate them, from the 2 and the 1; for 2 becomes part of 3 and 3 of 4 and the same

happens in the case of the succeeding numbers, but they say 4 came from the first 2 and the indefinite which

makes it two 2's other than the 2itself; if not, the 2itself will be a part of 4 and one other 2 will be added.

And similarly 2 will consist of the 1itself and another 1; but if this is so, the other element cannot be an

indefinite 2; for it generates one unit, not, as the indefinite 2 does, a definite 2.

Again, besides the 3itself and the 2itself how can there be other 3's and 2's? And how do they consist of

prior and posterior units? All this is absurd and fictitious, and there cannot be a first 2 and then a 3itself. Yet

there must, if the 1 and the indefinite dyad are to be the elements. But if the results are impossible, it is also

If the units, then, are differentiated, each from each, these results and others similar to these follow of

necessity. But (3) if those in different numbers are differentiated, but those in the same number are alone

undifferentiated from one another, even so the difficulties that follow are no less. E.g. in the 10itself their

are ten units, and the 10 is composed both of them and of two 5's. But since the 10itself is not any chance

number nor composed of any chance 5'sor, for that matter, unitsthe units in this 10 must differ. For if

they do not differ, neither will the 5's of which the 10 consists differ; but since these differ, the units also will

differ. But if they differ, will there be no other 5's in the 10 but only these two, or will there be others? If

there are not, this is paradoxical; and if there are, what sort of 10 will consist of them? For there is no other in

the 10 but the 10 itself. But it is actually necessary on their view that the 4 should not consist of any chance

2's; for the indefinite as they say, received the definite 2 and made two 2's; for its nature was to double what it

Again, as to the 2 being an entity apart from its two units, and the 3 an entity apart from its three units, how is

this possible? Either by one's sharing in the other, as 'pale man' is different from 'pale' and 'man' (for it shares

in these), or when one is a differentia of the other, as 'man' is different from 'animal' and 'twofooted'.

Again, some things are one by contact, some by intermixture, some by position; none of which can belong to

the units of which the 2 or the 3 consists; but as two men are not a unity apart from both, so must it be with

the units. And their being indivisible will make no difference to them; for points too are indivisible, but yet a

But this consequence also we must not forget, that it follows that there are prior and posterior 2 and similarly

with the other numbers. For let the 2's in the 4 be simultaneous; yet these are prior to those in the 8 and as the

2 generated them, they generated the 4's in the 8itself. Therefore if the first 2 is an Idea, these 2's also will

be Ideas of some kind. And the same account applies to the units; for the units in the first 2 generate the four

in 4, so that all the units come to be Ideas and an Idea will be composed of Ideas. Clearly therefore those

things also of which these happen to be the Ideas will be composite, e.g. one might say that animals are

In general, to differentiate the units in any way is an absurdity and a fiction; and by a fiction I mean a forced

statement made to suit a hypothesis. For neither in quantity nor in quality do we see unit differing from unit,

and number must be either equal or unequalall number but especially that which consists of abstract

unitsso that if one number is neither greater nor less than another, it is equal to it; but things that are equal

and in no wise differentiated we take to be the same when we are speaking of numbers. If not, not even the 2

in the 10itself will be undifferentiated, though they are equal; for what reason will the man who alleges that

Again, if every unit + another unit makes two, a unit from the 2itself and one from the 3itself will make a

2. Now (a) this will consist of differentiated units; and will it be prior to the 3 or posterior? It rather seems

that it must be prior; for one of the units is simultaneous with the 3 and the other is simultaneous with the 2.

And we, for our part, suppose that in general 1 and 1, whether the things are equal or unequal, is 2, e.g. the

good and the bad, or a man and a horse; but those who hold these views say that not even two units are 2.

If the number of the 3itself is not greater than that of the 2, this is surprising; and if it is greater, clearly there

is also a number in it equal to the 2, so that this is not different from the 2itself. But this is not possible, if

Nor will the Ideas be numbers. For in this particular point they are right who claim that the units must be

different, if there are to be Ideas; as has been said before. For the Form is unique; but if the units are not

different, the 2's and the 3's also will not be different. This is also the reason why they must say that when we

count thus'1,2'we do not proceed by adding to the given number; for if we do, neither will the numbers be

generated from the indefinite dyad, nor can a number be an Idea; for then one Idea will be in another, and all

Forms will be parts of one Form. And so with a view to their hypothesis their statements are right, but as a

whole they are wrong; for their view is very destructive, since they will admit that this question itself affords

some difficultywhether, when we count and say 1,2,3we count by addition or by separate portions. But

we do both; and so it is absurd to reason back from this problem to so great a difference of essence.

First of all it is well to determine what is the differentia of a numberand of a unit, if it has a differentia.

Units must differ either in quantity or in quality; and neither of these seems to be possible. But number qua

number differs in quantity. And if the units also did differ in quantity, number would differ from number,

though equal in number of units. Again, are the first units greater or smaller, and do the later ones increase or

diminish? All these are irrational suppositions. But neither can they differ in quality. For no attribute can

attach to them; for even to numbers quality is said to belong after quantity. Again, quality could not come to

them either from the 1 or the dyad; for the former has no quality, and the latter gives quantity; for this entity

is what makes things to be many. If the facts are really otherwise, they should state this quite at the beginning

and determine if possible, regarding the differentia of the unit, why it must exist, and, failing this, what

Evidently then, if the Ideas are numbers, the units cannot all be associable, nor can they be inassociable in

either of the two ways. But neither is the way in which some others speak about numbers correct. These are

those who do not think there are Ideas, either without qualification or as identified with certain numbers, but

think the objects of mathematics exist and the numbers are the first of existing things, and the 1itself is the

startingpoint of them. It is paradoxical that there should be a 1 which is first of 1's, as they say, but not a 2

which is first of 2's, nor a 3 of 3's; for the same reasoning applies to all. If, then, the facts with regard to

number are so, and one supposes mathematical number alone to exist, the 1 is not the startingpoint (for this

sort of 1 must differ from theother units; and if this is so, there must also be a 2 which is first of 2's, and

similarly with the other successive numbers). But if the 1 is the startingpoint, the truth about the numbers

must rather be what Plato used to say, and there must be a first 2 and 3 and numbers must not be associable

with one another. But if on the other hand one supposes this, many impossible results, as we have said,

follow. But either this or the other must be the case, so that if neither is, number cannot exist separately.

It is evident, also, from this that the third version is the worst,the view ideal and mathematical number is the

same. For two mistakes must then meet in the one opinion. (1) Mathematical number cannot be of this sort,

but the holder of this view has to spin it out by making suppositions peculiar to himself. And (2) he must also

admit all the consequences that confront those who speak of number in the sense of 'Forms'.

The Pythagorean version in one way affords fewer difficulties than those before named, but in another way

has others peculiar to itself. For not thinking of number as capable of existing separately removes many of the

impossible consequences; but that bodies should be composed of numbers, and that this should be

mathematical number, is impossible. For it is not true to speak of indivisible spatial magnitudes; and however

much there might be magnitudes of this sort, units at least have not magnitude; and how can a magnitude be

composed of indivisibles? But arithmetical number, at least, consists of units, while these thinkers identify

number with real things; at any rate they apply their propositions to bodies as if they consisted of those

If, then, it is necessary, if number is a selfsubsistent real thing, that it should exist in one of these ways

which have been mentioned, and if it cannot exist in any of these, evidently number has no such nature as

Again, does each unit come from the great and the small, equalized, or one from the small, another from the

great? (a) If the latter, neither does each thing contain all the elements, nor are the units without difference;

for in one there is the great and in another the small, which is contrary in its nature to the great. Again, how is

it with the units in the 3itself? One of them is an odd unit. But perhaps it is for this reason that they give

1itself the middle place in odd numbers. (b) But if each of the two units consists of both the great and the

small, equalized, how will the 2 which is a single thing, consist of the great and the small? Or how will it

differ from the unit? Again, the unit is prior to the 2; for when it is destroyed the 2 is destroyed. It must, then,

be the Idea of an Idea since it is prior to an Idea, and it must have come into being before it. From what, then?

Again, number must be either infinite or finite; for these thinkers think of number as capable of existing

separately, so that it is not possible that neither of those alternatives should be true. Clearly it cannot be

infinite; for infinite number is neither odd nor even, but the generation of numbers is always the generation

either of an odd or of an even number; in one way, when 1 operates on an even number, an odd number is

produced; in another way, when 2 operates, the numbers got from 1 by doubling are produced; in another

way, when the odd numbers operate, the other even numbers are produced. Again, if every Idea is an Idea of

something, and the numbers are Ideas, infinite number itself will be an Idea of something, either of some

sensible thing or of something else. Yet this is not possible in view of their thesis any more than it is

But if number is finite, how far does it go? With regard to this not only the fact but the reason should be

stated. But if number goes only up to 10 as some say, firstly the Forms will soon run short; e.g. if 3 is

manhimself, what number will be the horseitself? The series of the numbers which are the several

thingsthemselves goes up to 10. It must, then, be one of the numbers within these limits; for it is these that

are substances and Ideas. Yet they will run short; for the various forms of animal will outnumber them. At the

same time it is clear that if in this way the 3 is manhimself, the other 3's are so also (for those in identical

numbers are similar), so that there will be an infinite number of men; if each 3 is an Idea, each of the numbers

will be manhimself, and if not, they will at least be men. And if the smaller number is part of the greater

(being number of such a sort that the units in the same number are associable), then if the 4itself is an Idea

of something, e.g. of 'horse' or of 'white', man will be a part of horse, if man is It is paradoxical also that there

should be an Idea of 10 but not of 11, nor of the succeeding numbers. Again, there both are and come to be

certain things of which there are no Forms; why, then, are there not Forms of them also? We infer that the

Forms are not causes. Again, it is paradoxicalif the number series up to 10 is more of a real thing and a

Form than 10 itself. There is no generation of the former as one thing, and there is of the latter. But they try to

work on the assumption that the series of numbers up to 10 is a complete series. At least they generate the

derivativese.g. the void, proportion, the odd, and the others of this kindwithin the decade. For some things,

e.g. movement and rest, good and bad, they assign to the originative principles, and the others to the numbers.

This is why they identify the odd with 1; for if the odd implied 3 how would 5 be odd? Again, spatial

magnitudes and all such things are explained without going beyond a definite number; e.g. the first, the

Again, if number can exist separately, one might ask which is prior 1, or 3 or 2? Inasmuch as the number is

composite, 1 is prior, but inasmuch as the universal and the form is prior, the number is prior; for each of the

units is part of the number as its matter, and the number acts as form. And in a sense the right angle is prior to

the acute, because it is determinate and in virtue of its definition; but in a sense the acute is prior, because it is

a part and the right angle is divided into acute angles. As matter, then, the acute angle and the element and the

unit are prior, but in respect of the form and of the substance as expressed in the definition, the right angle,

and the whole consisting of the matter and the form, are prior; for the concrete thing is nearer to the form and

to what is expressed in the definition, though in generation it is later. How then is 1 the startingpoint?

Because it is not divisiable, they say; but both the universal, and the particular or the element, are indivisible.

But they are startingpoints in different ways, one in definition and the other in time. In which way, then, is 1

the startingpoint? As has been said, the right angle is thought to be prior to the acute, and the acute to the

right, and each is one. Accordingly they make 1 the startingpoint in both ways. But this is impossible. For

the universal is one as form or substance, while the element is one as a part or as matter. For each of the two

is in a sense onein truth each of the two units exists potentially (at least if the number is a unity and not like

a heap, i.e. if different numbers consist of differentiated units, as they say), but not in complete reality; and

the cause of the error they fell into is that they were conducting their inquiry at the same time from the

standpoint of mathematics and from that of universal definitions, so that (1) from the former standpoint they

treated unity, their first principle, as a point; for the unit is a point without position. They put things together

out of the smallest parts, as some others also have done. Therefore the unit becomes the matter of numbers

and at the same time prior to 2; and again posterior, 2 being treated as a whole, a unity, and a form. But (2)

because they were seeking the universal they treated the unity which can be predicated of a number, as in this

sense also a part of the number. But these characteristics cannot belong at the same time to the same thing.

If the 1itself must be unitary (for it differs in nothing from other 1's except that it is the startingpoint), and

the 2 is divisible but the unit is not, the unit must be liker the 1itself than the 2 is. But if the unit is liker it, it

must be liker to the unit than to the 2; therefore each of the units in 2 must be prior to the 2. But they deny

this; at least they generate the 2 first. Again, if the 2itself is a unity and the 3itself is one also, both form a

Since there is not contact in numbers, but succession, viz. between the units between which there is nothing,

e.g. between those in 2 or in 3 one might ask whether these succeed the 1itself or not, and whether, of the

Similar difficulties occur with regard to the classes of things posterior to number,the line, the plane, and the

solid. For some construct these out of the species of the 'great and small'; e.g. lines from the 'long and short',

planes from the 'broad and narrow', masses from the 'deep and shallow'; which are species of the 'great and

small'. And the originative principle of such things which answers to the 1 different thinkers describe in

different ways, And in these also the impossibilities, the fictions, and the contradictions of all probability are

seen to be innumerable. For (i) geometrical classes are severed from one another, unless the principles of

these are implied in one another in such a way that the 'broad and narrow' is also 'long and short' (but if this is

so, the plane will be line and the solid a plane; again, how will angles and figures and such things be

explained?). And (ii) the same happens as in regard to number; for 'long and short', are attributes of

magnitude, but magnitude does not consist of these, any more than the line consists of 'straight and curved',

(All these views share a difficulty which occurs with regard to speciesofagenus, when one posits the

universals, viz. whether it is animalitself or something other than animalitself that is in the particular

animal. True, if the universal is not separable from sensible things, this will present no difficulty; but if the 1

and the numbers are separable, as those who express these views say, it is not easy to solve the difficulty, if

one may apply the words 'not easy' to the impossible. For when we apprehend the unity in 2, or in general in a

Some, then, generate spatial magnitudes from matter of this sort, others from the point and the point is

thought by them to be not 1 but something like 1and from other matter like plurality, but not identical with

it; about which principles none the less the same difficulties occur. For if the matter is one, line and

planeand soli will be the same; for from the same elements will come one and the same thing. But if the

matters are more than one, and there is one for the line and a second for the plane and another for the solid,

they either are implied in one another or not, so that the same results will follow even so; for either the plane

Again, how number can consist of the one and plurality, they make no attempt to explain; but however they

express themselves, the same objections arise as confront those who construct number out of the one and the

indefinite dyad. For the one view generates number from the universally predicated plurality, and not from a

particular plurality; and the other generates it from a particular plurality, but the first; for 2 is said to be a 'first

plurality'. Therefore there is practically no difference, but the same difficulties will follow,is it intermixture

or position or blending or generation? and so on. Above all one might press the question 'if each unit is one,

what does it come from?' Certainly each is not the oneitself. It must, then, come from the one itself and

plurality, or a part of plurality. To say that the unit is a plurality is impossible, for it is indivisible; and to

generate it from a part of plurality involves many other objections; for (a) each of the parts must be

indivisible (or it will be a plurality and the unit will be divisible) and the elements will not be the one and

plurality; for the single units do not come from plurality and the one. Again, (,the holder of this view does

nothing but presuppose another number; for his plurality of indivisibles is a number. Again, we must inquire,

in view of this theory also, whether the number is infinite or finite. For there was at first, as it seems, a

plurality that was itself finite, from which and from the one comes the finite number of units. And there is

another plurality that is pluralityitself and infinite plurality; which sort of plurality, then, is the element

which cooperates with the one? One might inquire similarly about the point, i.e. the element out of which

they make spatial magnitudes. For surely this is not the one and only point; at any rate, then, let them say out

of what each of the points is formed. Certainly not of some distance + the pointitself. Nor again can there be

indivisible parts of a distance, as the elements out of which the units are said to be made are indivisible parts

of plurality; for number consists of indivisibles, but spatial magnitudes do not.

All these objections, then, and others of the sort make it evident that number and spatial magnitudes cannot

exist apart from things. Again, the discord about numbers between the various versions is a sign that it is the

incorrectness of the alleged facts themselves that brings confusion into the theories. For those who make the

objects of mathematics alone exist apart from sensible things, seeing the difficulty about the Forms and their

fictitiousness, abandoned ideal number and posited mathematical. But those who wished to make the Forms

at the same time also numbers, but did not see, if one assumed these principles, how mathematical number

was to exist apart from ideal, made ideal and mathematical number the samein words, since in fact

mathematical number has been destroyed; for they state hypotheses peculiar to themselves and not those of

mathematics. And he who first supposed that the Forms exist and that the Forms are numbers and that the

objects of mathematics exist, naturally separated the two. Therefore it turns out that all of them are right in

some respect, but on the whole not right. And they themselves confirm this, for their statements do not agree

but conflict. The cause is that their hypotheses and their principles are false. And it is hard to make a good

case out of bad materials, according to Epicharmus: 'as soon as 'tis said, 'tis seen to be wrong.'

But regarding numbers the questions we have raised and the conclusions we have reached are sufficient (for

while he who is already convinced might be further convinced by a longer discussion, one not yet convinced

would not come any nearer to conviction); regarding the first principles and the first causes and elements, the

views expressed by those who discuss only sensible substance have been partly stated in our works on nature,

and partly do not belong to the present inquiry; but the views of those who assert that there are other

substances besides the sensible must be considered next after those we have been mentioning. Since, then,

some say that the Ideas and the numbers are such substances, and that the elements of these are elements and

principles of real things, we must inquire regarding these what they say and in what sense they say it.

Those who posit numbers only, and these mathematical, must be considered later; but as regards those who

believe in the Ideas one might survey at the same time their way of thinking and the difficulty into which they

fall. For they at the same time make the Ideas universal and again treat them as separable and as individuals.

That this is not possible has been argued before. The reason why those who described their substances as

universal combined these two characteristics in one thing, is that they did not make substances identical with

sensible things. They thought that the particulars in the sensible world were a state of flux and none of them

remained, but that the universal was apart from these and something different. And Socrates gave the impulse

to this theory, as we said in our earlier discussion, by reason of his definitions, but he did not separate

universals from individuals; and in this he thought rightly, in not separating them. This is plain from the

results; for without the universal it is not possible to get knowledge, but the separation is the cause of the

objections that arise with regard to the Ideas. His successors, however, treating it as necessary, if there are to

be any substances besides the sensible and transient substances, that they must be separable, had no others,

but gave separate existence to these universally predicated substances, so that it followed that universals and

individuals were almost the same sort of thing. This in itself, then, would be one difficulty in the view we

Let us now mention a point which presents a certain difficulty both to those who believe in the Ideas and to

those who do not, and which was stated before, at the beginning, among the problems. If we do not suppose

substances to be separate, and in the way in which individual things are said to be separate, we shall destroy

substance in the sense in which we understand 'substance'; but if we conceive substances to be separable, how

If they are individual and not universal, (a) real things will be just of the same number as the elements, and

(b) the elements will not be knowable. For (a) let the syllables in speech be substances, and their elements

elements of substances; then there must be only one 'ba' and one of each of the syllables, since they are not

universal and the same in form but each is one in number and a 'this' and not a kind possessed of a common

name (and again they suppose that the 'just what a thing is' is in each case one). And if the syllables are

unique, so too are the parts of which they consist; there will not, then, be more a's than one, nor more than

one of any of the other elements, on the same principle on which an identical syllable cannot exist in the

plural number. But if this is so, there will not be other things existing besides the elements, but only the

(b) Again, the elements will not be even knowable; for they are not universal, and knowledge is of universals.

This is clear from demonstrations and from definitions; for we do not conclude that this triangle has its angles

equal to two right angles, unless every triangle has its angles equal to two right angles, nor that this man is an

But if the principles are universal, either the substances composed of them are also universal, or

nonsubstance will be prior to substance; for the universal is not a substance, but the element or principle is

universal, and the element or principle is prior to the things of which it is the principle or element.

All these difficulties follow naturally, when they make the Ideas out of elements and at the same time claim

that apart from the substances which have the same form there are Ideas, a single separate entity. But if, e.g.

in the case of the elements of speech, the a's and the b's may quite well be many and there need be no aitself

and bitself besides the many, there may be, so far as this goes, an infinite number of similar syllables. The

statement that an knowledge is universal, so that the principles of things must also be universal and not

separate substances, presents indeed, of all the points we have mentioned, the greatest difficulty, but yet the

statement is in a sense true, although in a sense it is not. For knowledge, like the verb 'to know', means two

things, of which one is potential and one actual. The potency, being, as matter, universal and indefinite, deals

with the universal and indefinite; but the actuality, being definite, deals with a definite object, being a 'this', it

deals with a 'this'. But per accidens sight sees universal colour, because this individual colour which it sees is

colour; and this individual a which the grammarian investigates is an a. For if the principles must be

universal, what is derived from them must also be universal, as in demonstrations; and if this is so, there will

be nothing capable of separate existencei.e. no substance. But evidently in a sense knowledge is universal,

REGARDING this kind of substance, what we have said must be taken as sufficient. All philosophers make

the first principles contraries: as in natural things, so also in the case of unchangeable substances. But since

there cannot be anything prior to the first principle of all things, the principle cannot be the principle and yet

be an attribute of something else. To suggest this is like saying that the white is a first principle, not qua

anything else but qua white, but yet that it is predicable of a subject, i.e. that its being white presupposes its

being something else; this is absurd, for then that subject will be prior. But all things which are generated

from their contraries involve an underlying subject; a subject, then, must be present in the case of contraries,

if anywhere. All contraries, then, are always predicable of a subject, and none can exist apart, but just as

appearances suggest that there is nothing contrary to substance, argument confirms this. No contrary, then, is

the first principle of all things in the full sense; the first principle is something different.

But these thinkers make one of the contraries matter, some making the unequal which they take to be the

essence of pluralitymatter for the One, and others making plurality matter for the One. (The former generate

numbers out of the dyad of the unequal, i.e. of the great and small, and the other thinker we have referred to

generates them out of plurality, while according to both it is generated by the essence of the One.) For even

the philosopher who says the unequal and the One are the elements, and the unequal is a dyad composed of

the great and small, treats the unequal, or the great and the small, as being one, and does not draw the

distinction that they are one in definition, but not in number. But they do not describe rightly even the

principles which they call elements, for some name the great and the small with the One and treat these three

as elements of numbers, two being matter, one the form; while others name the many and few, because the

great and the small are more appropriate in their nature to magnitude than to number; and others name rather

the universal character common to these'that which exceeds and that which is exceeded'. None of these

varieties of opinion makes any difference to speak of, in view of some of the consequences; they affect only

the abstract objections, which these thinkers take care to avoid because the demonstrations they themselves

offer are abstract,with this exception, that if the exceeding and the exceeded are the principles, and not the

great and the small, consistency requires that number should come from the elements before does; for number

is more universal than as the exceeding and the exceeded are more universal than the great and the small. But

as it is, they say one of these things but do not say the other. Others oppose the different and the other to the

One, and others oppose plurality to the One. But if, as they claim, things consist of contraries, and to the One

either there is nothing contrary, or if there is to be anything it is plurality, and the unequal is contrary to the

equal, and the different to the same, and the other to the thing itself, those who oppose the One to plurality

have most claim to plausibility, but even their view is inadequate, for the One would on their view be a few;

'The one' evidently means a measure. And in every case there is some underlying thing with a distinct nature

of its own, e.g. in the scale a quartertone, in spatial magnitude a finger or a foot or something of the sort, in

rhythms a beat or a syllable; and similarly in gravity it is a definite weight; and in the same way in all cases,

in qualities a quality, in quantities a quantity (and the measure is indivisible, in the former case in kind, and in

the latter to the sense); which implies that the one is not in itself the substance of anything. And this is

reasonable; for 'the one' means the measure of some plurality, and 'number' means a measured plurality and a

plurality of measures. (Thus it is natural that one is not a number; for the measure is not measures, but both

the measure and the one are startingpoints.) The measure must always be some identical thing predicable of

all the things it measures, e.g. if the things are horses, the measure is 'horse', and if they are men, 'man'. If

they are a man, a horse, and a god, the measure is perhaps 'living being', and the number of them will be a

number of living beings. If the things are 'man' and 'pale' and 'walking', these will scarcely have a number,

because all belong to a subject which is one and the same in number, yet the number of these will be a

Those who treat the unequal as one thing, and the dyad as an indefinite compound of great and small, say

what is very far from being probable or possible. For (a) these are modifications and accidents, rather than

substrata, of numbers and magnitudesthe many and few of number, and the great and small of

magnitudelike even and odd, smooth and rough, straight and curved. Again, (b) apart from this mistake, the

great and the small, and so on, must be relative to something; but what is relative is least of all things a kind

of entity or substance, and is posterior to quality and quantity; and the relative is an accident of quantity, as

was said, not its matter, since something with a distinct nature of its own must serve as matter both to the

relative in general and to its parts and kinds. For there is nothing either great or small, many or few, or, in

general, relative to something else, which without having a nature of its own is many or few, great or small,

or relative to something else. A sign that the relative is least of all a substance and a real thing is the fact that

it alone has no proper generation or destruction or movement, as in respect of quantity there is increase and

diminution, in respect of quality alteration, in respect of place locomotion, in respect of substance simple

generation and destruction. In respect of relation there is no proper change; for, without changing, a thing will

be now greater and now less or equal, if that with which it is compared has changed in quantity. And (c) the

matter of each thing, and therefore of substance, must be that which is potentially of the nature in question;

but the relative is neither potentially nor actually substance. It is strange, then, or rather impossible, to make

notsubstance an element in, and prior to, substance; for all the categories are posterior to substance. Again,

(d) elements are not predicated of the things of which they are elements, but many and few are predicated

both apart and together of number, and long and short of the line, and both broad and narrow apply to the

plane. If there is a plurality, then, of which the one term, viz. few, is always predicated, e.g. 2 (which cannot

be many, for if it were many, 1 would be few), there must be also one which is absolutely many, e.g. 10 is

many (if there is no number which is greater than 10), or 10,000. How then, in view of this, can number

consist of few and many? Either both ought to be predicated of it, or neither; but in fact only the one or the

We must inquire generally, whether eternal things can consist of elements. If they do, they will have matter;

for everything that consists of elements is composite. Since, then, even if a thing exists for ever, out of that of

which it consists it would necessarily also, if it had come into being, have come into being, and since

everything comes to be what it comes to be out of that which is it potentially (for it could not have come to be

out of that which had not this capacity, nor could it consist of such elements), and since the potential can be

either actual or not,this being so, however everlasting number or anything else that has matter is, it must be

capable of not existing, just as that which is any number of years old is as capable of not existing as that

which is a day old; if this is capable of not existing, so is that which has lasted for a time so long that it has no

limit. They cannot, then, be eternal, since that which is capable of not existing is not eternal, as we had

occasion to show in another context. If that which we are now saying is true universallythat no substance is

eternal unless it is actualityand if the elements are matter that underlies substance, no eternal substance can

There are some who describe the element which acts with the One as an indefinite dyad, and object to 'the

unequal', reasonably enough, because of the ensuing difficulties; but they have got rid only of those

objections which inevitably arise from the treatment of the unequal, i.e. the relative, as an element; those

which arise apart from this opinion must confront even these thinkers, whether it is ideal number, or

There are many causes which led them off into these explanations, and especially the fact that they framed

the difficulty in an obsolete form. For they thought that all things that are would be one (viz. Being itself), if

They thought it necessary to prove that that which is not is; for only thusof that which is and something

But, first, if 'being' has many senses (for it means sometimes substance, sometimes that it is of a certain

quality, sometimes that it is of a certain quantity, and at other times the other categories), what sort of 'one',

then, are all the things that are, if nonbeing is to be supposed not to be? Is it the substances that are one, or

the affections and similarly the other categories as well, or all togetherso that the 'this' and the 'such' and the

'so much' and the other categories that indicate each some one class of being will all be one? But it is strange,

or rather impossible, that the coming into play of a single thing should bring it about that part of that which is

Secondly, of what sort of nonbeing and being do the things that are consist? For 'nonbeing' also has many

senses, since 'being' has; and 'not being a man' means not being a certain substance, 'not being straight' not

being of a certain quality, 'not being three cubits long' not being of a certain quantity. What sort of being and

nonbeing, then, by their union pluralize the things that are? This thinker means by the nonbeing the union

of which with being pluralizes the things that are, the false and the character of falsity. This is also why it

used to be said that we must assume something that is false, as geometers assume the line which is not a foot

long to be a foot long. But this cannot be so. For neither do geometers assume anything false (for the

enunciation is extraneous to the inference), nor is it nonbeing in this sense that the things that are are

generated from or resolved into. But since 'nonbeing' taken in its various cases has as many senses as there

are categories, and besides this the false is said not to be, and so is the potential, it is from this that generation

proceeds, man from that which is not man but potentially man, and white from that which is not white but

potentially white, and this whether it is some one thing that is generated or many.

The question evidently is, how being, in the sense of 'the substances', is many; for the things that are

generated are numbers and lines and bodies. Now it is strange to inquire how being in the sense of the 'what'

is many, and not how either qualities or quantities are many. For surely the indefinite dyad or 'the great and

the small' is not a reason why there should be two kinds of white or many colours or flavours or shapes; for

then these also would be numbers and units. But if they had attacked these other categories, they would have

seen the cause of the plurality in substances also; for the same thing or something analogous is the cause.

This aberration is the reason also why in seeking the opposite of being and the one, from which with being

and the one the things that are proceed, they posited the relative term (i.e. the unequal), which is neither the

contrary nor the contradictory of these, and is one kind of being as 'what' and quality also are.

They should have asked this question also, how relative terms are many and not one. But as it is, they inquire

how there are many units besides the first 1, but do not go on to inquire how there are many unequals besides

the unequal. Yet they use them and speak of great and small, many and few (from which proceed numbers),

long and short (from which proceeds the line), broad and narrow (from which proceeds the plane), deep and

shallow (from which proceed solids); and they speak of yet more kinds of relative term. What is the reason,

It is necessary, then, as we say, to presuppose for each thing that which is it potentially; and the holder of

these views further declared what that is which is potentially a 'this' and a substance but is not in itself

beingviz. that it is the relative (as if he had said 'the qualitative'), which is neither potentially the one or

being, nor the negation of the one nor of being, but one among beings. And it was much more necessary, as

we said, if he was inquiring how beings are many, not to inquire about those in the same categoryhow there

are many substances or many qualitiesbut how beings as a whole are many; for some are substances, some

modifications, some relations. In the categories other than substance there is yet another problem involved in

the existence of plurality. Since they are not separable from substances, qualities and quantities are many just

because their substratum becomes and is many; yet there ought to be a matter for each category; only it

cannot be separable from substances. But in the case of 'thises', it is possible to explain how the 'this' is many

things, unless a thing is to be treated as both a 'this' and a general character. The difficulty arising from the

facts about substances is rather this, how there are actually many substances and not one.

But further, if the 'this' and the quantitative are not the same, we are not told how and why the things that are

are many, but how quantities are many. For all 'number' means a quantity, and so does the 'unit', unless it

means a measure or the quantitatively indivisible. If, then, the quantitative and the 'what' are different, we are

not told whence or how the 'what' is many; but if any one says they are the same, he has to face many

One might fix one's attention also on the question, regarding the numbers, what justifies the belief that they

exist. To the believer in Ideas they provide some sort of cause for existing things, since each number is an

Idea, and the Idea is to other things somehow or other the cause of their being; for let this supposition be

granted them. But as for him who does not hold this view because he sees the inherent objections to the Ideas

(so that it is not for this reason that he posits numbers), but who posits mathematical number, why must we

believe his statement that such number exists, and of what use is such number to other things? Neither does

he who says it exists maintain that it is the cause of anything (he rather says it is a thing existing by itself),

nor is it observed to be the cause of anything; for the theorems of arithmeticians will all be found true even of

As for those, then, who suppose the Ideas to exist and to be numbers, by their assumption in virtue of the

method of setting out each term apart from its instancesof the unity of each general term they try at least to

explain somehow why number must exist. Since their reasons, however, are neither conclusive nor in

themselves possible, one must not, for these reasons at least, assert the existence of number. Again, the

Pythagoreans, because they saw many attributes of numbers belonging te sensible bodies, supposed real

things to be numbersnot separable numbers, however, but numbers of which real things consist. But why?

Because the attributes of numbers are present in a musical scale and in the heavens and in many other things.

Those, however, who say that mathematical number alone exists cannot according to their hypotheses say

anything of this sort, but it used to be urged that these sensible things could not be the subject of the sciences.

But we maintain that they are, as we said before. And it is evident that the objects of mathematics do not exist

apart; for if they existed apart their attributes would not have been present in bodies. Now the Pythagoreans

in this point are open to no objection; but in that they construct natural bodies out of numbers, things that

have lightness and weight out of things that have not weight or lightness, they seem to speak of another

heaven and other bodies, not of the sensible. But those who make number separable assume that it both exists

and is separable because the axioms would not be true of sensible things, while the statements of mathematics

are true and 'greet the soul'; and similarly with the spatial magnitudes of mathematics. It is evident, then, both

that the rival theory will say the contrary of this, and that the difficulty we raised just now, why if numbers

are in no way present in sensible things their attributes are present in sensible things, has to be solved by

There are some who, because the point is the limit and extreme of the line, the line of the plane, and the plane

of the solid, think there must be real things of this sort. We must therefore examine this argument too, and see

whether it is not remarkably weak. For (i) extremes are not substances, but rather all these things are limits.

For even walking, and movement in general, has a limit, so that on their theory this will be a 'this' and a

substance. But that is absurd. Not but what (ii) even if they are substances, they will all be the substances of

the sensible things in this world; for it is to these that the argument applied. Why then should they be capable

Again, if we are not too easily satisfied, we may, regarding all number and the objects of mathematics, press

this difficulty, that they contribute nothing to one another, the prior to the posterior; for if number did not

exist, none the less spatial magnitudes would exist for those who maintain the existence of the objects of

mathematics only, and if spatial magnitudes did not exist, soul and sensible bodies would exist. But the

observed facts show that nature is not a series of episodes, like a bad tragedy. As for the believers in the

Ideas, this difficulty misses them; for they construct spatial magnitudes out of matter and number, lines out of

the number planes doubtless out of solids out of or they use other numbers, which makes no difference. But

will these magnitudes be Ideas, or what is their manner of existence, and what do they contribute to things?

These contribute nothing, as the objects of mathematics contribute nothing. But not even is any theorem true

of them, unless we want to change the objects of mathematics and invent doctrines of our own. But it is not

hard to assume any random hypotheses and spin out a long string of conclusions. These thinkers, then, are

wrong in this way, in wanting to unite the objects of mathematics with the Ideas. And those who first posited

two kinds of number, that of the Forms and that which is mathematical, neither have said nor can say how

mathematical number is to exist and of what it is to consist. For they place it between ideal and sensible

number. If (i) it consists of the great and small, it will be the same as the otheridealnumber (he makes

spatial magnitudes out of some other small and great). And if (ii) he names some other element, he will be

making his elements rather many. And if the principle of each of the two kinds of number is a 1, unity will be

something common to these, and we must inquire how the one is these many things, while at the same time

number, according to him, cannot be generated except from one and an indefinite dyad.

All this is absurd, and conflicts both with itself and with the probabilities, and we seem to see in it Simonides

'long rigmarole' for the long rigmarole comes into play, like those of slaves, when men have nothing sound to

say. And the very elementsthe great and the smallseem to cry out against the violence that is done to them;

for they cannot in any way generate numbers other than those got from 1 by doubling.

It is strange also to attribute generation to things that are eternal, or rather this is one of the things that are

impossible. There need be no doubt whether the Pythagoreans attribute generation to them or not; for they

say plainly that when the one had been constructed, whether out of planes or of surface or of seed or of

elements which they cannot express, immediately the nearest part of the unlimited began to be constrained

and limited by the limit. But since they are constructing a world and wish to speak the language of natural

science, it is fair to make some examination of their physical theorics, but to let them off from the present

inquiry; for we are investigating the principles at work in unchangeable things, so that it is numbers of this

These thinkers say there is no generation of the odd number, which evidently implies that there is generation

of the even; and some present the even as produced first from unequalsthe great and the smallwhen these

are equalized. The inequality, then, must belong to them before they are equalized. If they had always been

equalized, they would not have been unequal before; for there is nothing before that which is always.

Therefore evidently they are not giving their account of the generation of numbers merely to assist

A difficulty, and a reproach to any one who finds it no difficulty, are contained in the question how the

elements and the principles are related to the good and the beautiful; the difficulty is this, whether any of the

elements is such a thing as we mean by the good itself and the best, or this is not so, but these are later in

origin than the elements. The theologians seem to agree with some thinkers of the present day, who answer

the question in the negative, and say that both the good and the beautiful appear in the nature of things only

when that nature has made some progress. (This they do to avoid a real objection which confronts those who

say, as some do, that the one is a first principle. The objection arises not from their ascribing goodness to the

first principle as an attribute, but from their making the one a principleand a principle in the sense of an

elementand generating number from the one.) The old poets agree with this inasmuch as they say that not

those who are first in time, e.g. Night and Heaven or Chaos or Ocean, reign and rule, but Zeus. These poets,

however, are led to speak thus only because they think of the rulers of the world as changing; for those of

them who combine the two characters in that they do not use mythical language throughout, e.g. Pherecydes

and some others, make the original generating agent the Best, and so do the Magi, and some of the later sages

also, e.g. both Empedocles and Anaxagoras, of whom one made love an element, and the other made reason a

principle. Of those who maintain the existence of the unchangeable substances some say the One itself is the

This, then, is the problem,which of the two ways of speaking is right. It would be strange if to that which is

primary and eternal and most selfsufficient this very qualityselfsufficiency and

selfmaintenancebelongs primarily in some other way than as a good. But indeed it can be for no other

reason indestructible or selfsufficient than because its nature is good. Therefore to say that the first principle

is good is probably correct; but that this principle should be the One or, if not that, at least an element, and an

element of numbers, is impossible. Powerful objections arise, to avoid which some have given up the theory

(viz. those who agree that the One is a first principle and element, but only of mathematical number). For on

this view all the units become identical with species of good, and there is a great profusion of goods. Again, if

the Forms are numbers, all the Forms are identical with species of good. But let a man assume Ideas of

anything he pleases. If these are Ideas only of goods, the Ideas will not be substances; but if the Ideas are also

Ideas of substances, all animals and plants and all individuals that share in Ideas will be good.

These absurdities follow, and it also follows that the contrary element, whether it is plurality or the unequal,

i.e. the great and small, is the baditself. (Hence one thinker avoided attaching the good to the One, because

it would necessarily follow, since generation is from contraries, that badness is the fundamental nature of

plurality; while others say inequality is the nature of the bad.) It follows, then, that all things partake of the

bad except onethe One itself, and that numbers partake of it in a more undiluted form than spatial

magnitudes, and that the bad is the space in which the good is realized, and that it partakes in and desires that

which tends to destroy it; for contrary tends to destroy contrary. And if, as we were saying, the matter is that

which is potentially each thing, e.g. that of actual fire is that which is potentially fire, the bad will be just the

All these objections, then, follow, partly because they make every principle an element, partly because they

make contraries principles, partly because they make the One a principle, partly because they treat the

numbers as the first substances, and as capable of existing apart, and as Forms.

If, then, it is equally impossible not to put the good among the first principles and to put it among them in this

way, evidently the principles are not being correctly described, nor are the first substances. Nor does any one

conceive the matter correctly if he compares the principles of the universe to that of animals and plants, on

the ground that the more complete always comes from the indefinite and incompletewhich is what leads this

thinker to say that this is also true of the first principles of reality, so that the One itself is not even an existing

thing. This is incorrect, for even in this world of animals and plants the principles from which these come are

It is out of place, also, to generate place simultaneously with the mathematical solids (for place is peculiar to

the individual things, and hence they are separate in place; but mathematical objects are nowhere), and to say

Those who say that existing things come from elements and that the first of existing things are the numbers,

should have first distinguished the senses in which one thing comes from another, and then said in which

By intermixture? But (1) not everything is capable of intermixture, and (2) that which is produced by it is

different from its elements, and on this view the one will not remain separate or a distinct entity; but they

By juxtaposition, like a syllable? But then (1) the elements must have position; and (2) he who thinks of

number will be able to think of the unity and the plurality apart; number then will be thisa unit and plurality,

Again, coming from certain things means in one sense that these are still to be found in the product, and in

another that they are not; which sense does number come from these elements? Only things that are generated

can come from elements which are present in them. Does number come, then, from its elements as from

seed? But nothing can be excreted from that which is indivisible. Does it come from its contrary, its contrary

not persisting? But all things that come in this way come also from something else which does persist. Since,

then, one thinker places the 1 as contrary to plurality, and another places it as contrary to the unequal, treating

the 1 as equal, number must be being treated as coming from contraries. There is, then, something else that

persists, from which and from one contrary the compound is or has come to be. Again, why in the world do

the other things that come from contraries, or that have contraries, perish (even when all of the contrary is

used to produce them), while number does not? Nothing is said about this. Yet whether present or not present

in the compound the contrary destroys it, e.g. 'strife' destroys the 'mixture' (yet it should not; for it is not to

Once more, it has not been determined at all in which way numbers are the causes of substances and of

beingwhether (1) as boundaries (as points are of spatial magnitudes). This is how Eurytus decided what was

the number of what (e.g. one of man and another of horse), viz. by imitating the figures of living things with

pebbles, as some people bring numbers into the forms of triangle and square. Or (2) is it because harmony is

a ratio of numbers, and so is man and everything else? But how are the attributeswhite and sweet and

hotnumbers? Evidently it is not the numbers that are the essence or the causes of the form; for the ratio is

the essence, while the number the causes of the form; for the ratio is the essence, while the number is the

matter. E.g. the essence of flesh or bone is number only in this way, 'three parts of fire and two of earth'. And

a number, whatever number it is, is always a number of certain things, either of parts of fire or earth or of

units; but the essence is that there is so much of one thing to so much of another in the mixture; and this is no

longer a number but a ratio of mixture of numbers, whether these are corporeal or of any other kind.

Number, then, whether it be number in general or the number which consists of abstract units, is neither the

cause as agent, nor the matter, nor the ratio and form of things. Nor, of course, is it the final cause.

One might also raise the question what the good is that things get from numbers because their composition is

expressible by a number, either by one which is easily calculable or by an odd number. For in fact

honeywater is no more wholesome if it is mixed in the proportion of three times three, but it would do more

good if it were in no particular ratio but well diluted than if it were numerically expressible but strong. Again,

the ratios of mixtures are expressed by the adding of numbers, not by mere numbers; e.g. it is 'three parts to

two', not 'three times two'. For in any multiplication the genus of the things multiplied must be the same;

therefore the product 1X2X3 must be measurable by 1, and 4X5X6 by 4 and therefore all products into which

the same factor enters must be measurable by that factor. The number of fire, then, cannot be 2X5X3X6 and

If all things must share in number, it must follow that many things are the same, and the same number must

belong to one thing and to another. Is number the cause, then, and does the thing exist because of its number,

or is this not certain? E.g. the motions of the sun have a number, and again those of the moon,yes, and the

life and prime of each animal. Why, then, should not some of these numbers be squares, some cubes, and

some equal, others double? There is no reason why they should not, and indeed they must move within these

limits, since all things were assumed to share in number. And it was assumed that things that differed might

fall under the same number. Therefore if the same number had belonged to certain things, these would have

been the same as one another, since they would have had the same form of number; e.g. sun and moon would

have been the same. But why need these numbers be causes? There are seven vowels, the scale consists of

seven strings, the Pleiades are seven, at seven animals lose their teeth (at least some do, though some do not),

and the champions who fought against Thebes were seven. Is it then because the number is the kind of

number it is, that the champions were seven or the Pleiad consists of seven stars? Surely the champions were

seven because there were seven gates or for some other reason, and the Pleiad we count as seven, as we count

the Bear as twelve, while other peoples count more stars in both. Nay they even say that X, Ps and Z are

concords and that because there are three concords, the double consonants also are three. They quite neglect

the fact that there might be a thousand such letters; for one symbol might be assigned to GP. But if they say

that each of these three is equal to two of the other letters, and no other is so, and if the cause is that there are

three parts of the mouth and one letter is in each applied to sigma, it is for this reason that there are only

three, not because the concords are three; since as a matter of fact the concords are more than three, but of

These people are like the oldfashioned Homeric scholars, who see small resemblances but neglect great

ones. Some say that there are many such cases, e.g. that the middle strings are represented by nine and eight,

and that the epic verse has seventeen syllables, which is equal in number to the two strings, and that the

scansion is, in the right half of the line nine syllables, and in the left eight. And they say that the distance in

the letters from alpha to omega is equal to that from the lowest note of the flute to the highest, and that the

number of this note is equal to that of the whole choir of heaven. It may be suspected that no one could find

difficulty either in stating such analogies or in finding them in eternal things, since they can be found even in

But the lauded characteristics of numbers, and the contraries of these, and generally the mathematical

relations, as some describe them, making them causes of nature, seem, when we inspect them in this way, to

vanish; for none of them is a cause in any of the senses that have been distinguished in reference to the first

principles. In a sense, however, they make it plain that goodness belongs to numbers, and that the odd, the

straight, the square, the potencies of certain numbers, are in the column of the beautiful. For the seasons and a

particular kind of number go together; and the other agreements that they collect from the theorems of

mathematics all have this meaning. Hence they are like coincidences. For they are accidents, but the things

that agree are all appropriate to one another, and one by analogy. For in each category of being an analogous

term is foundas the straight is in length, so is the level in surface, perhaps the odd in number, and the white

Again, it is not the ideal numbers that are the causes of musical phenomena and the like (for equal ideal

numbers differ from one another in form; for even the units do); so that we need not assume Ideas for this

These, then, are the results of the theory, and yet more might be brought together. The fact that our opponnts

have much trouble with the generation of numbers and can in no way make a system of them, seems to

indicate that the objects of mathematics are not separable from sensible things, as some say, and that they are