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350 BC 
by Aristotle 

translated by W. D. Ross 

Book I 


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 differences between things. 

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 sense of hearing can be taught. 

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 when burning with fevers-this is a matter 
of art. 

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 anything-e . 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 sense-perception 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 (sense-perception 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, is one of the 
causes . 

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 
self-moving 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 much as if the 
diagonal turned out to be commensurable. 

We have stated, then, what is the nature of the science we are 
searching for, and what is the mark which our search and our whole 
investigation must reach. 


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 entity-either one or more than 
one-from 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 origin of the nature of moist things. 

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 of his 
thought . 

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 fourth-earth-to 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 one. 

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, and 
are not in any other sense generated or destroyed, but remain 
eternally . 

From these facts one might think that the only cause is the 

so-called 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 one-as though defeated by this search for the second 
cause-say 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 contrary way. 

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 
present-as in animals, so throughout nature-as 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 cause of beauty, and 
that sort of cause from which things acquire movement. 


One might suspect that Hesiod was the first to look for such a 
thing-or 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 universe, says:- 

Love first of all the Gods she planned. 

And Hesiod says:- 

First of all things was chaos made, and then 

Broad-breasted earth. . . 

And love, 'mid all the gods pre-eminent, 

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 
nature-not only order and the beautiful, but also disorder and the 
ugly, and bad things in greater number than good, and ignoble things 
than beautif ul-theref ore 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 cause of all 
goods is the good itself. 

These thinkers, as we say, evidently grasped, and to this 
extent, two of the causes which we distinguished in our work on 
nature-the matter and the source of the movement-vaguely, 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 parts must again be 
segregated out of each element. 

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 
opposite-earth, air, and water-as 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 non-being-the full and solid being 
being, the empty non-being (whence they say being no more is than 
non-being, 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 three-shape and order and position. 
For they say the real is differentiated only by 'rhythm and 
'inter-contact' and 'turning'; and of these rhythm is shape, 
inter-contact 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 
movement-whence or how it is to belong to things-these thinkers, 
like the others, lazily neglected. 

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


Contemporaneously with these philosophers and before them, the 
so-called 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 being-more than in fire and earth and water (such and such a 
modification of numbers being justice, another being soul and 

reason, another being opportunity-and 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 
tenth--the 'counter-earth'. We have discussed these matters more 
exactly elsewhere. 

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 cognates-limit 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 contrarieties 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 immanent parts they say substance is composed 
and moulded. 

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 inquiry-two 
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 non-existent 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 with the 
non-existent . 

From what has been said, then, and from the wise men who have 
now sat in council with us, we have got thus much-on 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 and from 
others as twofold. 

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 these-the source of movement-some 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 many-a consequence which they actually drew. From the 
earlier philosophers, then, and from their successors we can learn 
thus much. 


After the systems we have named came the philosophy of Plato, 
which in most respects followed these thinkers, but had 
peculiarities 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 kind-for 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 there are many alike, while the Form itself is in each 
case unique. 

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 small, by participation in the One, come the 
Numbers . 

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 
females; yet these are analogues of those first principles. 

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 Anaxagoras . 


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 who make friendship and 

strife, or reason, or love, a principle. 

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 as the essence of the Forms. 

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 a cause; for they do not call it a cause qua good but only 
incidentally . 

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 his situation relatively to 
the first principles. 

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 anothers-I 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 fine-grained 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 prior to air, and earth to water. 

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 denies. 

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 non-sensible 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 so-called '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 the bodies that move through the 
heavens can do what they do. 

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 peculiarly to perceptible things. 

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 
to-or not fewer than-the 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 the many are in this world or are eternal. 

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 the Ideas have come into conflict with the principles of the 

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 particulars-the 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 many insuperable objections to such a view. 

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 'two-footed' 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, will be so; therefore the same 
thing will be pattern and copy. 

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 way-that 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, this--the matter--is 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 
consistent with our thought on the matter. 

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 things-themselves? 

Further, the units in must each come from a prior but this is 
impossible . 

Further, why is a number, when taken all together, one? 

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 used in more than one sense; for otherwise the theory 
is impossible. 

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 line-and 
this he often posited-to 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 nothing. 

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 nature has been annihilated. 

And what is thought to be easy-to show that all things are 
one-is 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 
cases it cannot be. 

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 fourth class. 

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 strange that we are unaware of our possession of the greatest 
of sciences. 

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 elements proper to 
sound, are the same. 


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 if 

another had said this, he has not said it clearly. 

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 difficulties. 

Book II 

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 most evident of all. 

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, while the 
others have been responsible for the appearance of the former. 

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 truth. 


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 
there is no cause at all. 

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 ways-not 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 
morning-in 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 something came to be must be non-eternal . 

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 limit; for the end is a limit. 

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 exist; and if it could, at least the notion of infinity 
is not infinite. 

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 cannot be gone through in a finite time. 


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 not 
easy to get even one of the two. 

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) . 

Book III 

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-(l) 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 
discussed-whether 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 contrary? 

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 account of 
goods and evils. 

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 
investigate these causes severally. 

But (2), taking the starting-points 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 starting-points 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; for all demonstrative 
sciences use the axioms. 

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 about them? 

(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 sciences or by one 
compounded out of them. 

(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 self-dependent 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 man-himself and a horse-itself and 
health-itself , 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 making the 
Forms anything other than eternal sensible things. 

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 
lines-themselves 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 animals-themselves 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 medical-science-itself 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 healthy-itself . --And at 
the same time not even this is true, that mensuration deals with 
perceptible and perishable magnitudes; for then it would have perished 
when they perished. 

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 so-called 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 
still more impossible. 


(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 genus-articulate 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 know its nature. 

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 starting-points 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 starting-points 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 genera. 

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 nature of principles; so that the highest 
genera would be the principles . 


(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 as some attribute belongs to 
them universally. 

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 just now that this is impossible. 

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 be something besides the concrete thing, viz. 
the shape or form. 

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 the concrete thing these two elements? 

(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 unity-itself and being-itself ; and how 
will knowing exist, if there is not to be something common to a 
whole set of individuals? 

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 individual-the 
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 predecessors-whether 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 cross-examine 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 consistently-Empedocles, 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 says:- 

From which all that was and is and will be hereafter- 
Trees, and men and women, took their growth, 
And beasts and birds and water-nourished fish, 
And long-aged gods. 

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, 

we see earth, by water water, 
By ether godlike ether, by fire wasting fire, 
Love by love, and strife by gloomy strife. 

But-and 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 cause of the change itself, except that things are so by 
nature . 

But when strife at last waxed great in the limbs of the 

And sprang to assert its rights as the time was fulfilled 
Which is fixed for them in turn by a mighty oath. 

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 and others are not, 
if they consist of the same principles. 

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 
first as if they took it to be something trifling. 

(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. Empedocles-as 
though reducing to something more intelligible-says 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 which they say are principles. 

(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 
being-itself , 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 the unit 
is precisely a certain kind of one. 

But (B) if there is a unity-itself 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 being-itself and a 
unity-itself, 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 are one and this is being. 

There are objections to both views. For whether unity is not a 
substance or there is a unity-itself, 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 unity-itself? 
It must be not-one; but all things are either one or many, and of 
the many each is one. 

Further, if unity-itself 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 
line is made out of points. 

But even if ore supposes the case to be such that, as some say, 
number proceeds from unity-itself 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 not-one 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 number and this principle. 


(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 other-when 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 sound-whose 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 not-besides perceptible 
and mathematical objects-others 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 none is by accident. 

But if we are to suppose both that the Forms exist and that the 
principles are one in number, not in kind, we have mentioned the 
impossible results that necessarily follow. 

(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 animals-himself and 'man' and 'animal', if each of these 
indicates a 'this' and a single thing. 

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 predicated of them. 

Book IV 

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 so-called 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 we also must grasp 
the first causes. 

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 starting-point; 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 non-being 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 
must grasp the principles and the causes . 

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 specific parts of the science. 

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 
that-in 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 one-I 
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 ones within the sphere of 
mathematics . 

Now since it is the work of one science to investigate 
opposites, and plurality is opposed to unity-and 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 
they possess it, others because they produce it, and others in other 
such ways . 

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 claims 
to know, and sophistic is what appears to be philosophy but is not. 

Again, in the list of contraries one of the two columns is 
privative, and all contraries are reducible to being and non-being, 
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 principles-some 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 starting-points 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 
starting-point . --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 inquiring into them while they are listening 
to lectures on it. 

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 non-hypothetical. 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 belief; for this is naturally the starting-point even 
for all the other axioms. 


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 
self-evident 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 
starting-point 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 so ' ) . 

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 
'two-footed 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. 'two-footed 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 this is possible, one name might be assigned to this thing.) 

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 same significance) . 

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 'not-man'; 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 'not-man' 
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 
this-being related as 'raiment' and 'dress' are, if their definition 
is one. And if 'being a man' and 'being a not-man' 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 two-footed 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 two-footed animal; for this is what 
'being necessary' means-that it is impossible for the thing not to be. 
It is, then, impossible that it should be at the same time true to say 
the same thing is a man and is not a man. 

The same account holds good with regard to 'not being a man', 
for 'being a man' and 'being a not-man' 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 opponent will only answer our question. 

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 not-man, he must not, 
in answering the question whether this is a man, add that it is also 
at the same time a not-man, 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 observing the rules of argument. 

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 not-man' 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 not-man 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 
cannot be predicated at the same time. 

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 non-being; 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; and, if this is predicable, the 
affirmative will be so too. 

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 
not-man, evidently also it will be neither a man nor a not-man. 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 former. 

Again, either the theory is true in all cases, and a thing is both 
white and not-white, and existent and non-existent, 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 non-being 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 not-white), 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 
non-existent 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 above-mentioned 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 the very question at issue. 

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 not-a-man, one thing to be sweet and another to be 
not-sweet. 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 not-a-man. 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 healthy state as far as the truth is concerned. 

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 determining 
anything in our thought. 


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 right in their beliefs. 

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 be cured only by refuting the 
argument as expressed in speech and in words. 

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 non-being. 
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 being-but 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 others. 

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; 

For wisdom increases in men according to what is before them. 

And elsewhere he says that : - 

So far as their nature changed, so far to them always 
Came changed thoughts into mind. 

And Parmenides also expresses himself in the same way: 

For as at each time the much-bent limbs are composed, 
So is the mind of men; for in each and all men 
"Tis one thing thinks-the substance of their limbs: 
For that of which there is more is thought. 

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 game. 

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 
indeterminate-of 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 thought one could not do it even 
once . 

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 is-so to speak-not 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 
sensation-at least of the object peculiar to the sense in 
question-is 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 so and not so' . 

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 starting-point, 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 
starting-point of demonstration is not demonstration. 

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 themselves-a claim which contradicts itself from the very 
first. -But if not all things are relative, but some are self-existent, 
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 relative-relative 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 relative to an infinity of specifically different 
things . 

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 contrary-and 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 relations, or one in 
a particular relation and one without qualification. 


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 not-good to 
good, or from good to not-good) , 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 not-white; but as it is, 
this is never seen. -Again, every object of understanding or reason the 
understanding either affirms or denies-this is obvious from the 
def inition-whenever 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 not-odd. But this is impossible, as is 
obvious from the def inition . -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 diff erent . -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 negation. 

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 
starting-point 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 
def inition . -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 not-good, so that one cannot say anything that is 
true . 

In view of these distinctions it is obvious that the one-sided 
theories which some people express about all things cannot be valid-on 

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 true-nor 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 infinity. 

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 unmoved. 

Book V 

'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 cause-for the good and the beautiful are the beginning 
both of the knowledge and of the movement of many things. 


'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 change-producing 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 both-the presence and the privation-are 
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 as the 
builder . 


'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 so-called 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 and proceed by means of one middle, 
are of this nature. 

(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 so-called 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 first component immanent in each. 


'Nature' means (1) the genesis of growing things-the 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:- 

Nothing that is has a nature, 
But only mixing and parting of the mixed, 
And nature is but a name given them by men. 

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 be called a 'nature', because the nature of a 
thing is one kind of essence. 

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, being present in them somehow, either 
potentially or in complete reality. 


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 persuaded-and 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 forces-which 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 that the propositions from which the 
syllogism proceeds cannot be otherwise. 

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, nothing 
compulsory or against their nature attaches to them. 


'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 has 
magnitude rests while another moves, as in the bent line. 

(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 dif f erentiae-these 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 . 

(c) Two things are called one, when the definition which states 
the essence of one is indivisible from another 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 is not one. 

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, because it is 
whole and complete. 

(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 quarter-tone, 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 

all--i.e. in three--dimensions . 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 
analogy are not all one in genus. 

Evidently 'many' will have meanings opposite to those of 'one'; 
some things are many because they are not continuous, others because 
their matter-either the proximate matter or the ultimate-is 
divisible in kind, others because the definitions which state their 
essence are more than one. 


Things are said to 'be' (1) in an accidental sense, (2) by their 
own nature. 

(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 not-pale 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 an attribute that of 
which it is itself predicated, itself is. 

(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'; and similarly in all other cases. 

(3) Again, 'being' and 'is' mean that a statement is true, 'not 
being' that it is not true but falses-and this alike in the case of 
affirmation and of negation; e.g. 'Socrates is musical' means that 
this is true, or 'Socrates is not-pale' means that this is true; but 
'the diagonal of the square is not commensurate with the side' means 
that it is false to say it is. 

(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 explained elsewhere. 

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 each thing. 


'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 'every Socrates' as we say 'every man' . 

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 thing is the same as itself; for 
we treat it as two. 

Things are called 'other' if either their kinds or their matters 
or the definitions of their essence are more than one; and in 
general 'other' has meanings opposite to those of 'the same'. 

'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 things that have their otherness in their 
essence . 

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 'like'. 


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 same thing; hence their 
constituents are opposed. 

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 correspond, so that they must be different for each 

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 
other-i.e. the posterior-must 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 case the 
leader and in the other the middle string is the beginning. 

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 attribute of a line 
as such, and the other of a surface. 

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 cases. 


'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' and because they 'can' do something and are in some positive 
state . 

'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 all, if it has not a good tone. 

Incapacity is privation of capacity-i . 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 
incapacity-both to that which only can produce movement and to that 
which can produce it well. 

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 
non-continuous 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 this is a quantum time is one. 


'Quality' means (1) the differentia of the essence, e.g. man is an 
animal of a certain quality because he is two-footed, and the horse is 
so because it is four-footed; 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 quality-the 
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 once; for 6 is 
once 6 . 

(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 in respect of virtue and vice, and in general, 
of evil and good. 

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 another--the 
contrary--way is vicious. Good and evil indicate quality especially in 
living things, and among these especially in those which have purpose. 


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 knowable to knowledge, and the 
perceptible to perception. 

(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 the same way. 

(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 said 
twice, -'the sight is of that of which it is. ' 

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 flute-player, 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 
scandal-monger and a complete thief; indeed we even call them good, 
i.e. a good thief and a good scandal-monger. 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 are-though 
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 cause — animal, two-f ooted--but 
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 by itself. 


'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 has-something 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' of the whole thing. 


'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 
these-the already accomplished alterations .- (3) Especially, 
injurious alterations and movements, and, above all painful 
in juries . - ( 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 is called privation. 

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. 'kernel-less'; 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 one-eyed 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 according to its own impulse. 

'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 ' two-footed ' 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, because after 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 consists-the 'whole' meaning either the form or that which has 
the form; e.g. of the bronze sphere or of the bronze cube both the 
bronze-i.e. the matter in which the form is-and 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 species is part of 
the genus . 


'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 senses-either 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 oneness. 

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 removed cannot grow again. Therefore baldness is not a 
mutilation . 


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 race-name 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 analysed either into one another or 
into some one thing. 


'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 non-existent, (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 non-existent objects, in 
so far as it is false. Hence every account is false when applied t 
something other than that of which it is true; e.g. the account of 
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 simple-minded 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 t 
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 definition of two. 

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 induction-f or a man who limps willingly is better than one 
who does so unwillingly-by 'limping' Plato means 'mimicking a limp', 
for if the man were lame willingly, he would presumably be worse in 
this case as in the corresponding case of moral character. 





'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. This-the finding 
of treasure-is 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 place for which he was not sailing, and 
this was Aegina. 

'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 be eternal, but no accident of the other 
sort is. This is explained elsewhere. 

Book VI 

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 being-some 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 
essence-some making it plain to the senses, others assuming it as a 
hypothesis-they 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 thinking to show what it is and that it is. 

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 maker-it is either reason or art or some 
faculty, while in the case of things done it is in the doer-viz. 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 
substance-as-defined 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 
movement-they 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 as is not independent of matter. 

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 
being-both 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 
('non-being' 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 different-to 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 non-being. 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 it. 

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 dog-days 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 starting-point 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 honey-water 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 from what cause it arises, 
and that there is no science which deals with it. 


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 this-I mean the past condition-is 
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 starting-point, but this no longer points to something 
further. This then will be the starting-point for the fortuitous, 
and will have nothing else as cause of its coming to be. But to what 
sort of starting-point and what sort of cause we thus refer the 
f ortuitous-whether to matter or to the purpose or to the motive power, 
must be carefully considered. 


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 things-it 
is not as if the good were true, and the bad were in itself 
false-but in thought; while with regard to simple concepts and 'whats' 
falsity and truth do not exist even in thought--this 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 . ) 

Book VII 

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 self-subsistent 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 
substance . 

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 
substances, and more so than body or the solid. 

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 
substance-the Forms and objects of mathematics-as 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 
them-lines and planes-until we come to the substance of the material 
universe and to sensible bodies. 

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 substance. 


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 way-through 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 way of 
those very things which one does know. 


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 same. 

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 is not to be white. 

But is being-a-cloak 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 essence-only 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 meaning-viz. 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 that is which is not is-not is simply, but is non-existent; 
so too with quality. 

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 which there is a definition either of 
white or of a substance. 


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 
so-called '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, as we have said. 

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 concavity-in-a-nose) , either 
it is impossible to say 'snub nose' or the same thing will have been 
said twice, concave-nose nose; for snub nose will be concave-nose 
nose. And so it is absurd that such things should have an essence; 
if they have, there will be an infinite regress; for in snub-nose 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 the 
unqualified sense. 


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 is said to be the substance of each thing. 

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 not actually thought to be the case. 

But in the case of so-called self-subsistent 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 them-substances 
such as some assert the Ideas to be?-If the essence of good is to be 
different from good-itself, and the essence of animal from 
animal-itself , and the essence of being from being-itself , 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 good-itself 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 self-subsistent 
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 even by the exhibition of instances it becomes 
clear that both must be one. 

(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, 
so that to terms of the former kind the same argument will be 
applicable . 

Clearly, then, each primary and self-subsistent 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 what sense each thing is the 
same as its essence and in what sense it is not. 


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 some size or of some 
quality or somewhere. 

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 is-all 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 each-and, 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 produced--the so-called 'formal' nature, which is 
specifically the same (though this is in another individual); for 
man begets man. 

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 starting-point 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 starting-point 
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 limiting-point--and so too with 
a house (the stones are the limiting-point 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 pre-exist 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 starting-point 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 and the other form. 

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 comings-to-be and 
to substances; and the Forms need not, for this reason at least, be 
self-subsistent 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 themselves-and 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 from a part of the product. 

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 starting-point 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 animals 
themselves . 

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 pre-exist 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 existing apart from each other the wholes are 
prior to the parts . 

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 individual circle, 
because there is no name peculiar to the individuals. 

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 and others must not. 


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 matters we 
are unable to perform the abstraction. 

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 
line-itself, 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 the Form of two; but in the case of 'line' they say 
this is no longer so. 

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 
Form-itself of all, and to hold that the others are not Forms; but 
thus all things will be one. 

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 movement-nor , 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 it is not alive it is not a part. 

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 
another which is intelligible. 

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 analogous to the universal in its 
composition . 

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 thing one, although it 
has parts? ), -this must be considered later. 

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 substance-e . g . in the case of man the 
formula of the soul-, for the substance is the indwelling form, from 
which and the matter the so-called 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 only 
by accident. 


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, 'two-footed 
animal'; for let this be the formula of man. Why, then, is this one, 
and not many, viz. 'animal' and 'two-footed'? 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, 
two-footed, 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 thing; for substance means a 'one' and a 'this', 
as we maintain. 

We must first inquire about definitions reached by the method of 
divisions. There is nothing in the definition except the first-named 
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 two-footed', and again 
'animal which is two-footed 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 'two-footed animal' 
'animal' is genus, and the other is differentia. 

If then the genus absolutely does not exist apart from the 
species-of-a-genus, 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), clearly the definition is the formula which 
comprises the differentiae. 

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 cloven-footed and not cloven; 
for these are differentiae in the foot; cloven-f ootedness 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 two-footed' 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 once-as many 
times as there are differentiae. 

If then a differentia of a differentia be taken at each step, 
one dif f erentia-the last-will 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 two-footed 
and endowed with feet'; for 'endowed with feet' is superfluous when 
'two-footed' 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 this suffice as our first attempt at stating their 
nature . 


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 attributes-or 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 substance is one and whose 
essence is one are themselves also one. 

Further, substance means that which is not predicable of a 
subject, but the universal is predicable of some subject always. 

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 difficulties follow and especially the 
' third man ' . 

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 halves-potentially; 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 ' man-in-himself ' who is a 'this' and exists apart, the parts also 
of which he consists, e.g. 'animal' and 'two-footed', must indicate 
'thises', and be capable of separate existence, and substances; 
therefore 'animal', as well as 'man', must be of this sort. 

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 'two-footed' and 
'many-footed', 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 two-footed 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 ' animal-itself ' . 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 animal-itself. Further, 
from what is this 'animal' in each species derived, and how will it be 
derived from animal-itself? Or how can this 'animal', whose essence is 
simply animality, exist apart from animal-itself? 

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 maintain their existence. 


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 
definition-mongers defines any individual, he must recognize that 
his definition may always be overthrown; for it is not possible to 
define such things. 

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. 'two-footed animal' belongs 
to animal and to the two-footed. (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 'two-footed' are prior in being to 'two-footed animal'; 
and things which are prior to others are not destroyed when the others 
are . 

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 
'two-footed', 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 possible-every Idea is thought to be capable of being shared. 

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 'night-hidden' (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 now been said is true. 


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 apart from its individuals. 

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) -- 'man-himself ' and ' horse-itself ' , 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 non-sensible 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 starting-point; 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 starting-point. 
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 inquire--as 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 evident-e.g. that the moon is 
eclipsed-but 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 being also. 

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 
border-line 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 things is other than that of inquiry. 

Since that which is compounded out of something so that the 
whole is one, not like a heap but like a syllable-now 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 
something-not 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 is present in it as matter; 
e.g. a and b are the elements of the syllable. 

Book VIII 

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, &c, 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 species, 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 not. 

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 have matter for 
generation and destruction. 

The difference between becoming in the full sense and becoming 
in a qualified sense has been stated in our physical works. 


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 inter-contact, 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 honey-water; 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 cases . 

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 exists-one kind of it as matter, another as 
form or actuality, while the third kind is that which is composed of 
these two. 


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, they will not 
be stating the substance itself. 

(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 cases-in 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 natural objects is the only substance 
to be found in destructible things . ) 

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 
play the part of matter and the other that of form. 

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 so-called substances in what sense it is 
possible and in what sense impossible--and of the reduction of 
things to number. 


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 starting-point 
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 the matter and the moving 
cause were different, the product would be so too. 

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 name not fire or earth, but the matter 
peculiar to the thing. 

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 af f ection-that 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 


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 becomes wine. 

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 animal-itself and a biped-itself ? Why are not those Forms 
themselves the man, so that men would exist by participation not in 
man, nor in-one Form, but in two, animal and biped, and in general man 
would be not one but more than one thing, animal and biped? 

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 this-that which was potentially to be 
actually-except, 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 
being-individual 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 being-and 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 
apart from particulars. 

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 
all things which have no matter are without qualification 
essentially unities. 

Book IX 

WE have treated of that which is primarily and to which all the 
other categories of being are ref erred-i . e . of substance. For it is in 
virtue of the concept of substance that the others also are said to 
be-quantity 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' explain the other kinds of potency as well. 

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 so-called 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 the 
prior kinds of potency are somehow implied. 

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 
non-rational and some will be non-rational 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 himself considered 
as other. 

And each of those which are accompanied by a rational formula is 
alike capable of contrary effects, but one non-rational 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 non-rational; for the products of the former are included 
under one originative source, the rational formula. 

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 also do it, but he who does it merely need 
not also do it well. 


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 f orgetf ulness 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 
day-and deaf too. 

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 non-existent things, 
though they do assign some other predicates. E.g. they say that 
non-existent 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 non-existent things some exist potentially; but they 
do not exist, because they do not exist in complete reality. 


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 man-one who did not take account of that which is 
incapable of being-were 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 
non-rational, 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 actuality-what, 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 
half-line 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 analogy-as A is in B or to B, C 
is in D or to D; for some are as movement to potency, and the others 
as substance to some sort of matter. 

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 
potentially, but not that the infinite exists separately. 

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 fat-removal, 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 incomplete-making 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? No-but 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 side-viz. in that which is 
healed-is 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 on-i.e. in the matter-prevents 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 to become brass.) 

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 reference both to the matter and to the accidents; for 
both are indeterminates . 

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 movement-not, 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 in one sense, and in another 
not . 

(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 time, prior to potency. 

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 being built, and comes to 
be, and is, at the same time as the house. 

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 well-being also; for it is a certain kind of 
life) . 

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 in time right back to the 
actuality of the eternal prime mover. 

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 this. 

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 non-rational potencies will produce 
opposite results by their presence or absence. 

If, then, there are any entities or substances such as the 
dialecticians say the Ideas are, there must be something much more 
scientific than science-itself and something more mobile than 
movement-itself ; for these will be more of the nature of 
actualities, while science-itself and movement-itself are potencies 
for these. 

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 something bad) . 

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 centre-the 
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 corresponding potency) . 
(See diagram. ) 


The terms 'being' and 'non-being' are employed firstly with 
reference to the categories, and secondly with reference to the 
potency or actuality of these or their non-potency 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 another false, but the same 
opinions are always true or always false. 

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 
f ollows--contact and assertion are truth (assertion not being the same 
as affirmation), and ignorance is non-contact. 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 
non-composite 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 are of such and such a nature 
or not. 

(b) As regards the 'being' that answers to truth and the 

'non-being' 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 ignorance-and 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 is implied that the fact is eternal. 

Book X 

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 meanings-the 
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 starting-point 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 unit-in 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 starting-point 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 starting-point 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 
quarter-tone (because it is the least interval), and in speech the 
letter. And all these are ones in this sense--not that 'one' is 
something predicable in the same sense of all of these, but in the 
sense we have mentioned. 

But the measure is not always one in number--sometimes there are 
several; e.g. the quarter-tones (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 
already-only to perception, for doubtless every continuous thing is 
divisible . 

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 correspond-it is as if one claimed that the measure of units is 
units and not a unit; number is a plurality of units.) 

Knowledge, also, and perception, we call the measure of things for 
the same reason, because we come to know something by them-while 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 cubit-measure 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, while they appear to be saying 
something remarkable. 

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 or qua one. 


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, and another the indefinite. 

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 cannot be genera. 

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 definite-some particular kind 
of thing-and 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 quarter-tones, 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 quarter-tone. 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 one-itself which we must seek is one colour, so too in 
substance the one-itself 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 be a particular thing. 


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 indivisible, because of the conditions of perception. 

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 equal-angled 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 
same-e.g. whiteness-in 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 differ-either the qualities in general or the prominent 
qualities; e.g. tin is like silver, qua white, and gold is like 
fire, qua yellow and red. 

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 else-but 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 non-existent 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 very 

nature either one or not one with anything else. 

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 essentially predicated of both 
the different things) . 

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 extremes-and 
therefore that between the contraries-is the greatest. 

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 answer to the various 
modes of contrariety which attach to the contraries. 

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 difference, must be between two things. 

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 complete difference is the greatest) . 

The primary contrariety is that between positive state and 
privation-not 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 
comings-to-be 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 first-i.e. 
the generic-contraries, e.g. the one and the many; for the others 
can be reduced to these. 


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 
something intermediate between its own terms . 

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 attributes. 

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 bad-as 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 combined, belong to different classes, so that the 
substratum is not one. 


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 easily-bounded 
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 many-not, 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 is not one, as 
some say, but two, that make a few. 

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 the one is a 
measure . 


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 and as the things they stand between. 

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 is-an 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 knowable? But between great and small there is one. 

(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 species-of-a-genus 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 
diff erentiae- ' 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 
compounded out of the contraries. 

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 itself other. 

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 degree-for 
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 species-of-a-genus 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 opposite, so that the 
things must be different in kind. 

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. 

Book XI 

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 with which it is to be 

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 said to 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 
subject-matters . 

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 as 
dealing with what is primary, the science of substances claims the 
tide . 

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 mover-for that is the nature of the end-but 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 deal with perceptible 
substances; for they are perishable. 

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 philosophy which we 
have set before ourselves that treats of those subjects. 

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 are the subjects that 
involve difficulties. 


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 permanent? 

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 divisions-the 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, the question arises, how are we to suppose 
the first principle to be substance? 

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 same. 


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 which is being is one. 

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 just-in 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 respect the privation 
will attach to him; and similarly in all other cases. 

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 things--geometry) --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,-! mean the question how there can be a single 

science of things which are many and different in genus. 


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 quantity-not, 
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 
'not-man' . 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 animal. 

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 true-viz. 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 way-the combined and complex statement being like a single 
af f irmation-the 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 false-the 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 pleasant to some and the contrary of pleasant 
to others . 

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 not-white 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 not-white. 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 sense-organ 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 eye the one object 
appears one) . 

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 no change. 

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 not true at the same time, as these thinkers assert they are. 

And if the things of this earth continuously flow and move in 
respect of quantity-if one were to suppose this, although it is not 
true-why 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 indeterminate. 

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 and flowed for ever. 

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 
afore-said change takes place.) But if we do not change but remain the 
same, there will be something that endures. 

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 from what has been said. 

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 evident if we reduce the definitions of 
contraries to their principle. 

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, and this is the contradictory of white. 

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 even this, and 
if all are true it will not be false to say all are false. 


Every science seeks certain principles and causes for each of 
its objects-e.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 demonstration, 
of the substance or 'what' . 

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 essence-whether 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 matter. 

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 sciences-physics, 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 better or worse in 
virtue of its proper object. 

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 must be different and prior to 
physics and universal because it is prior. 

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 non-being. 

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 part, but the accidental is in 
neither of these classes. 

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 to-morrow'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 to-morrow we shall come 
sometime to the already existing condition. Therefore since this 
exists, everything after this will occur of necessity, so that all 
things occur of necessity. 

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 large. 

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. ' this-ness ' -f or 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 same-for if they were, being 
well and being ill would have been the same-it 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 this-the act of building-or 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 to all other 
movements . 

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 said-both actuality and the actuality we have 
described-which is hard to detect but capable of existing. 

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 moved is 

similar . 


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 themselvess-since 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, but that of which it 
is an accident-the air or the even number. 

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 
simple-neither , 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 contrary to contrary, e.g. 
from hot to cold. 

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 it-cannot 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 is called infinite because of the movement which occupies 


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 by induction. 

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 generation-absolute change absolute 
generation, and partial change partial generation; and the change from 

positive to negative is destruction-absolute 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 not-white or not-good can be moved incidentally, for the 
not-white 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 'not-being' 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 'toothless' or 
'black' . 


If the categories are classified as substance, quality, place, 
acting or being acted on, relation, quantity, there must be three 
kinds of movement-of 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 ignorance. 

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 privation in that which is receptive of movement. 

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. 

Book XII 

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 not-white 
and the not-straight would be being; at least we say even these are, 
e.g. 'there is a not-white' . 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 what is common to both, body. 

There are three kinds of substance-one 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, if there is no principle 
common to it and to the other kinds . 


Sensible substance is changeable. Now if change proceeds from 
opposites or from intermediates, and not from all opposites (for the 
voice is not-white, (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 kinds-either 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 Democritus-it 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 matter-not matter for generation, however, but for motion 
from one place to another. 

One might raise the question from what sort of non-being 
generation proceeds; for 'non-being' has three senses. If, then, one 
form of non-being 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 be-and 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 bronze comes to be; therefore there must be a 
stop . 

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 substance-the 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 sort-not 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 similarly in the arts; for the medical art 
is the formal cause of health. 


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 principles-the 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 is-for 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 causes will probably be soul and body, or 
reason and desire and body. 

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 above-named 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 same species with him, 

but moving causes. 

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 
qualification . 

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 qualities-whether they are 
the same or dif f erent-clearly 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 continuous. 

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 

actuality . 

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 things to be capable of 
existing but not yet to exist. 

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 itself-the 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 the menstrual blood. 

This is why some suppose eternal actuality-e . 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 
movement-that 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 
else-either 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 need then is 
there to seek for other principles? 


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 non-being, 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 starting-point. 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 column; and the first in any class is always 
best, or analogous to the best. 

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 senses-that 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 way. 

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 self-dependent 
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 God. 

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 
movements-those of the planets-which 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 philosophy-viz . 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 now-to give some notion of the subject-quote 
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 accurate. 

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 are--eight for 
Saturn and Jupiter and twenty-five for the others, and of these only 
those involved in the movement of the lowest-situated 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 spheres--both those which move the planets and 
those which counteract these--will be fifty-five. And if one were 
not to add to the moon and to the sun the movements we mentioned, 
the whole set of spheres will be forty-seven in number. 

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 move through the heaven. 

(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 alone-that 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 thinking is a thinking on thinking. 

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 object of its 
thought . 

A further question is left-whether 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 indivisible-as 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 whole. 

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 
say-whether 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 of his 'evil' is just strife. 

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 necessity of 
this make all things one. 

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 one-of 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; but the world refuses to be governed badly. 

'The rule of many is not good; one ruler let there be. ' 

Book XIII 


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 predecessors, and others no 
worse . 

Two opinions are held on this subject; it is said that the objects 
of mathematics-i . e . numbers and lines and the like-are substances, and 
again that the Ideas are substances. And (1) since some recognize 
these as two different classes-the 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 characteristic-not 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 discussion of the 
Ideas this remans as a third inquiry. 

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 exist but how they exist. 

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 planes-those 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 
parts-or anything else which has movement-should 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 together? 

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 man. 

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 'exist' has many 

senses . 


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 subject-not 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 science-with 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 sensibles-nor, 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 way-by 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 forms-it 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 def initeness, which the mathematical sciences demonstrate in a 
special degree. And since these (e.g. order and def initeness) 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 
these matters . 


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 
def initions-e . g . those of opportunity, justice, or marriage-they 
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 starting-point 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 Socrates-inductive arguments and universal 
definition, both of which are concerned with the starting-point 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 
groups there is a one over many, whether these be of this world or 
eternal . 

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 absolute-besides all the other points on which certain 
people, by following out the opinions held about the Forms, came 
into conflict with the principles of the theory. 

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 non-substances, 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 particulars-the 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', 
without observing any community between them. 

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 'two-footed'. Further, 
there must be some Ideal answering to 'plane' above, some nature which 
will be present in all the Forms as their genus. 


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; for it is easy to collect 
many and insuperable objections to such a view. 

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 
'two-footed', and also 'man-himself ' , 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 
f orms-of-a-genus ; 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, therefore, could the Ideas, 
being the substances of things, exist apart? 

In the Phaedo the case is stated in this way-that 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 we have considered. 


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 '2-itself' are inassociable with 
those in the '3-itself'; and similarly in the case of the other 
successive numbers. And so while mathematical number is counted 
thus-after 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 thus-after 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 speak of, and that which we have named last must be 
a third kind. 

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 number-the mathematical; only they say it is not 
separate but sensible substances are formed out of it. For they 
construct the whole universe out of numbers-only 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 number is identical 
with this . 

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 way-viz. 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 number-only one kind of number, and the Ideas 
cannot be the numbers. For what sort of number will man-himself or 
animal-itself or any other Form be? There is one Idea of each thing 
e.g. one of man-himself and another one of animal-itself; but the 
similar and undifferentiated numbers are infinitely many, so that 
any particular 3 is no more man-himself 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 the Ideas cannot be ranked as 
either prior or posterior to the numbers . 

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 way-since, 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 1-itself is 
first, and then there is a particular 1 which is first among the 
others and next after the 1-itself, 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 2-itself and a 
3-itself; 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 2-itself; if not, the 
2-itself will be a part of 4 and one other 2 will be added. And 
similarly 2 will consist of the 1-itself 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 3-itself and the 2-itself 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 3-itself. Yet there must, if the 1 and the 
indefinite dyad are to be the elements. But if the results are 
impossible, it is also impossible that these are the generating 
principles . 

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 10-itself their 
are ten units, and the 10 is composed both of them and of two 5's. But 
since the 10-itself is not any chance number nor composed of any 
chance 5's — or, for that matter, units--the 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 
received . 

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 
' two-footed' . 

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 pair 
of them is nothing apart from the two. 

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 8-itself. 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 

composed of animals, if there are Ideas of them. 

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 
unequal-all number but especially that which consists of abstract 
units-so 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 10-itself will be undifferentiated, 
though they are equal; for what reason will the man who alleges that 
they are not differentiated be able to give? 

Again, if every unit + another unit makes two, a unit from the 
2-itself and one from the 3-itself 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 3-itself 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 
2-itself. But this is not possible, if there is a first and a second 
number . 

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 
dif f iculty-whether , when we count and say -1,2,3-we 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 number-and 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 
differentia they mean. 

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 1-itself is the starting-point of them. It is 
paradoxical that there should be a 1 which is first of l'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 starting-point (for this sort of 1 must differ from 
the-other 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 starting-point, 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 numbers . 

If, then, it is necessary, if number is a self-subsistent 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 those who make it separable set up for it. 

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 3-itself? One of them is an odd 
unit. But perhaps it is for this reason that they give 1-itself 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? Not from the indefinite dyad, for its 
function was to double. 

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 
reasonable in itself, at least if they arrange the Ideas as they do. 

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 man-himself, what number will be the horse-itself ? The 
series of the numbers which are the several things-themselves 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 man-himself, 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 man-himself, 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 4-itself 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 paradoxical-if 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 derivatives-e . g . the void, 
proportion, the odd, and the others of this kind-within 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 indivisible, line, then the 2 &c.; these entities also extend only 
up to 10 . 

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 starting-point? Because it is not divisiable, they 
say; but both the universal, and the particular or the element, are 
indivisible. But they are starting-points in different ways, one in 
definition and the other in time. In which way, then, is 1 the 
starting-point? 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 starting-point 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 one-in 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 1-itself must be unitary (for it differs in nothing from 
other l's except that it is the starting-point), and the 2 is 
divisible but the unit is not, the unit must be liker the 1-itself 
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 2-itself is a unity and the 3-itself is one also, both 
form a 2. From what, then, is this 2 produced? 


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 1-itself or 
not, and whether, of the terms that succeed it, 2 or either of the 
units in 2 is prior. 

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', &c., are attributes of magnitude, but 
magnitude does not consist of these, any more than the line consists 
of 'straight and curved', or solids of 'smooth and rough' . 

(All these views share a difficulty which occurs with regard to 
species-of-a-genus, when one posits the universals, viz. whether it is 
animal-itself or something other than animal-itself 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 number, do we apprehend a thing-itself or something else?) . 

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 1-and 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 plane-and 
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 will not contain a 
line or it will he a line. 

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 one-itself. 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 plurality-itself and infinite 
plurality; which sort of plurality, then, is the element which 
co-operates 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 point-itself . 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 f ictitiousness, 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 same-in 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 have mentioned. 


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 are we to conceive their 
elements and their principles? 

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 elements . 

(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 animal, unless every man is an animal. 

But if the principles are universal, either the substances 
composed of them are also universal, or non-substance 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 a-itself and 

b-itself 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 existence-i . e . no 
substance. But evidently in a sense knowledge is universal, and in a 
sense it is not. 

Book XIV 

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 
plurality-matter 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; for plurality is opposed to fewness, and the 
many to the 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 quarter-tone, 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 starting-points . ) 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 number of 
'kinds' or of some such term. 

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 magnitudes-the many 
and few of number, and the great and small of magnitude-like 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 not-substance 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 other is predicated. 


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 
universally-that no substance is eternal unless it is actuality-and if 
the elements are matter that underlies substance, no eternal substance 
can have elements present in it, of which it consists. 

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 mathematical, that they construct out of those 
elements . 

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 one did not join issue 
with and refute the saying of Parmenides: 

'For never will this he proved, that things that are not are.' 

They thought it necessary to prove that that which is not is; 
for only thus-of that which is and something else-could the things 
that are be composed, if they are many. 

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 non-being 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 
together-so 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 is a 'this', part a 'such', part a 'so much', part a 'here'. 

Secondly, of what sort of non-being 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 
non-being, then, by their union pluralize the things that are? This 
thinker means by the non-being 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 non-being in this sense that the things 
that are are generated from or resolved into. But since 'non-being' 
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, 
then, why there is a plurality of these? 

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 being-viz. 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 category-how 
there are many substances or many qualities-but 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 inconsistencies. 

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 sensible things, as was said before. 


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 instances-of 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 numbers-not 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 those who hold these views . 

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 
of existing apart? 

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 other-ideal-number (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 elements-the great and the 
small-seem 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 theories, 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 kind whose genesis we must study. 


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 unequals-the great and the 
small-when 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 contemplation of 
their nature. 

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 principle-and a principle 
in the sense of an element-and 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 good itself; but they 
thought its substance lay mainly in its unity. 

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 self-sufficient this very quality--self-suf f iciency and 
self-maintenance--belongs primarily in some other way than as a 
good. But indeed it can be for no other reason indestructible or 
self-sufficient 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 bad-itself. (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 one--the 
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 potentially good. 

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 incomplete-which 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 complete; for it is a man that produces a man, and 

the seed is not first. 

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 that they must be somewhere, but not say what 
kind of thing their place is. 

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 sense number comes from its first principles. 

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 want it to be so. 

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 this-a 
unit and plurality, or the one and the unequal. 

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 that 
that is contrary) . 

Once more, it has not been determined at all in which way 
numbers are the causes of substances and of being-whether (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 attributes-white and sweet 
and hot-numbers? 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 honey-water 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 at the same time 
that of water 2X3. 

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 double consonants there cannot be more. 

These people are like the old-fashioned 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 perishable things. 

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 found-as the straight is in length, so is the 
level in surface, perhaps the odd in number, and the white in colour. 

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 reason at least. 

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 not the first 
principles .