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University of 
St. Michael s College, Toronto 









W. D. ROSS, M.A., HON. LL.D. (EDIN.) 









WITH the permission of Messrs. Teubner I have followed in 
this translation the text of W. Christ (Leipzig, 1895). All 
divergences from his readings have been mentioned in the 
notes, except that I have frequently left it to the rendering 
itself to show that I have not followed his punctuation or his 
excisions. The commentaries of Alexander and Bonitz have 
been my greatest help ; but I owe much also to Bullinger s 
notes, and to the translation of Book Z, chaps, i-xi, by 
the late Mr. Richard Shute. 

I wish to acknowledge my deep obligations to Mr. Bywater 
and Prof. Cook Wilson, whose opinions on several difficult pas 
sages have been most kindly placed at my disposal ; to the mem 
bers of the Oxford Aristotelian Society, for what I learnt from 
them during our reading of Books M and N ; to Mr. H. H. 
Joachim, Fellow of Merton College, for the loan of his valuable 
notes on Books Z, H, and ; to Mr. C. Cannan, Secretary to 
the Delegates of the University Press, and Mr. R. P. Hardie, of 
Edinburgh University, whose comments on various parts of 
the work have been of the greatest assistance to me ; to my 
co-editor Mr. J. A. Smith, and to Dr. G. R. T. Ross, who have 
read the whole book both in manuscript and in proof, and 
whose suggestions I have adopted in countless passages ; and 
to my wife, who has read the whole book in proof, and has 
aided me very greatly in points of style. 

W. D. R. 



THE present edition of this translation is based on the text 
published with my commentary on the Metaphysics (Oxford, 
1924). The translation has been carefully revised throughout, 
and brought into agreement with the commentary, except in 
a very few places where later reflection has led me to revive 
an old or to propose a new interpretation. 

My thanks are due to the officials and staff of the Clarendon 
Press for the care and skill shown in the production of the 

W. D. R. 



CH. A. 

1. The advance from sensation through memory, experience, and art, to 

theoretical knowledge. 

2. Characteristics of wisdom (philosophy). 

3. The successive recognition by earlier philosophers of the material, 

efficient, and final causes. 

4. Inadequacy of the treatment of these causes. 

5. The Pythagorean and Eleatic schools ; the former recognizes vaguely 

the formal cause. 

6. The Platonic philosophy ; it uses only the material and formal causes. 

7. The relation of the various systems to the four causes. 

8. Criticism of the pre-Platonic philosophers. 

9. Criticism of the doctrine of Ideas. 

10. The history of philosophy reveals no causes other than the four. 


1. General considerations about the study of philosophy. 

2. There cannot be an infinite series, nor an infinite variety of kinds, of 


3. Different methods are appropriate to different studies. 


1. Sketch of the main problems of philosophy. 

2. Fuller statement of the problems : 

(i) Can one science treat of all the four causes ? 
(ii) Are the primary axioms treated of by the science of substance, 

and if not, by what science ? 
(iii) Can one science treat of all substances? 
(iv) Does the science of substance treat also of its attributes? 
(v) Are there any non-sensible substances, and if so, of how many 
kinds ? 

3. (vi) Are the genera, or the constituent paits, of things their first 

principles ? 
(vii) If the genera, is it the highest genera or the lowest ? 

4. (viii) Is there anything apart from individual things? 

(ix) Is each of the first principles one in kind, or in number ? 

(x) Are the principles of perishable and of imperishable things the 

same ? 
(xi) Are being and unity substances or attributes? 

5. (xii) Are the objects of mathematics substances ? 




6. (xiii) Do Ideas exist, as well as sensible things and the objects of 

mathematics ? 

(xiv) Do the first principles exist potentially or actually ? 
(xv) Are the first principles universal or individual ? 


1. Our object is the study of being as such. 

2. We must therefore study primary being (viz. substance), unity and 

plurality, and the derivative contraries, and the attributes of being 
and of substance. 

3. We must study also the primary axioms, and especially the law of 


4. Fatal difficulties involved in the denial of this law. 

5. The connexion of such denial with Protagoras doctrine of relativity ; 

the doctrine refuted. 

6. Further refutation of Protagoras. 

7. The law of excluded middle defended. 

8. All judgements are not true, nor are all false ; all things are not at 

rest, nor are all in motion. 


Philosophical Lexicon. 

1. Beginning. 

2. Cause. 

3. Element. 

4. Nature. 

5. Necessary. 

6. One. Many. 

7. Being. 

8. Substance. 

9. The same. Other. Different. Like. Unlike. 

10. Opposite. Contrary. Other in species. The same in species. 

11. Prior. Posterior. 

12. Potency. Capable. Incapacity. Possible. Impossible. 

13. Quantum. 

14. Quality. 

15. Relative. 

16. Complete. 

17. Limit. 

18. That in virtue of which. In virtue of itself. 

19. Disposition. 

20. Having or habit (eis~). 

21. Affection. 

22. Privation. 

23. Have or hold (ex*")- Be in - 

24. From. 



25. Part. 

26. Whole. Total. All. 

27. Mutilated. 

28. Race or genus (yevos). Other in genus. 

29. False. 

30. Accident. 


1. Distinction of theology , the science of being as such, from the other 

theoretical sciences, mathematics and physics. 

2. Four senses of being . Of these (i) accidental being is the object 

of no science. 

3. The nature and origin of accident. 

4. (ii) Being as truth is not primary being. 


1. The study of being is primarily the study 01 substance. 

2. Various opinions on the question, what things are substances ? 

3. Four things are commonly held to be substantial the essence, the 

universal, the genus, the substratum. The last may be conceived 
as matter, form, or the concrete individual. Reasons why matter 
and the concrete individual cannot be primary substance. Form 
to be studied first in sensible things. 

4. What is essence and to what does it belong, i. e. what things can be 

defined ? Primarily substance. 

5. Combinations of a subject with one of its proper attributes have no 

definition nor essence. 

6. Is a thing the same as its essence ? Yes, if it is a substance. 
(7. Analysis of generation, whether by nature, art, or spontaneity. 

8. Form is not generated, but put into matter ; yet it did not previously 

exist apart the agent in generation is form embodied in another 
individual of the same species. 

9. Why spontaneous generation sometimes takes place. The conditions 

of generation in the categories other than substance.) 

10. When are definitions of the parts included in the definition of the 

whole ? When the parts are parts of the form. 

1 1. Which parts are parts of the form, which of the concrete individual ? 

12. Wherein consists the unity of an object of definition ? In the appro 

priateness of the differentia to the genus. 

13. A universal cannot be either the substance or an element in the sub 

stance of anything (yet how else can a thing be defined ?). 

14. Hence it is fatal to make Ideas substances and yet hold that they are 

composed of other Ideas. 

15. No individual can be defined, whether sensible or, like the Ideas, 





16. The parts of sensible things are only potencies. Unity and being 

are not the substance of things. 

17. Substance is the cause or form which puts matter into a determinate 

state ; it is that in a thing which is distinct from its material 


1. The discussion of sensible substances continued. Their matter is 

itself substance. 

2. The main types of form or actuality. Definitions of matter, of form, 

and of the concrete individual distinguished. 

3. Form distinguished from the material elements ; Antisthenes attack 

on definition ; definition analogous to number. 

4. Remote and proximate matter ; the substratum of attributes not matter 

but the concrete individual. 

5. The relation of matter to its contrary states. 

6. What gives unity to a definition ? The fact that the genus is simply the 

potency of the differentia, the differentia the actuality of the genus. 


1. Being as potency and actuality. Potency in the strict sense, as 

potency of motion, active or passive. 

2. Non- rational potencies are single, rational potencies twofold. 

3. Potency defended against the attack of the Megaric school. 

4. Potency as possibility. 

5. How potency is acquired, and the conditions of its actualization. 

6. Actuality distinguished from potency ; a special type of potency 

described ; actuality distinguished from movement. 

7. When one thing may be called the potency or matter of another ; 

how things are described by names derived from their matter 
or their accidents. 

8. Actuality prior to potency in definition, time, and substantiality ; 

nothing eternal or necessary is a mere potency. 

9. Good actuality better than potency, and bad actuality worse ; therefore 

no separate evil principle in the universe. Geometrical truths 
found by actualization of potencies. 
10. Being as truth, with regard to both composite and simple objects. 


1. Four kinds of unit ; theessenceof a unit is to be a measure of quantity 

or of quality ; various types of measure. 

2. Unity not a substance but a universal predicate ; its denotation the 

same as that of being. 

3. Unity and plurality ; identity ; likeness ; otherness ; difference. 

4. Contrariety is complete difference ; how related to privation and 





5. The opposition of Jhe equal to the great and the small. 

6. The opposition of the one to the many. 

7. Intermediates are homogeneous with each other and with the 

extremes, stand between contraries, and are compounded out of 
these contraries. 

8. Otherness in species is otherness 0/"the genus and is contrariety ; 

its nature further described. 

9. What contrarieties constitute otherness in species. 
lo. The perishable and the imperishable differ in kind. 


1. Shorter form of B. 2, 3, 

2. B. 4-6. 

3. r. i, 2. 

4, 5- r. 3j 4 . 

6. r. 5-8. 

7. E. i. 

8. E. 2-4. 

Extracts from Physics : 

8. II. 5, 6, on luck. 

9. III. 1-3, on potency, actuality, and movement, 

10. III. 4, 5, 7, on the infinite; there is no actual infinite, and 

especially no infinite body. 

11. V. i, on change and movement. 

12. V. 2, on the three kinds of movement. 

V. 3, definitions of together in place , apart *, touch , be 
tween , contrary in place , successive , * contiguous , 
continuous . 

1. Substance the primary subject of inquiry. Three kinds of substance 

perishable sensible, eternal sensible, and unmovable (non- 

2. Change implies not only form and privation but matter. 

3. Neither matter nor form comes into being. Whatever comes into 

being comes from a substance of the same kind. If form ever 
exists apart from the concrete individual, it is in the case of 
natural objects. 

4. Different things have elements numerically different but the same 

in kind ; they all have form, privation, and matter. They also 
have a proximate and an ultimate moving cause. 

5. Again actuality and potency are principles common to all things, 

though they apply differently in different cases. The principles of 
all things are only analogous, not identical, 


6. Since movement must be eternal, there must be an eternal mover, 

and one whose essence is actuality (actuality being prior to 
potency). To account for the uniform change in the universe, 
there must be one principle which acts always alike, and one 
whose action varies. 

7. The eternal mover originates motion by being the primary object of 

desire (as it is of thought) ; being thoroughly actual, it cannot 
change or move ; it is a living being, perfect, separate from 
sensible things, and without parts. 

8. Besides the first mover there must be as many unmoved movers 

as there are simple motions involved in the motions of the planets. 
The number is probably either 55 or 47. As there is but one 
prime mover, there must be but one heaven. 

9. The divine thought must be concerned with the most divine object, 

which is itself. Thought and the object of thought are never 
different when the ooject is immaterial. 

10. How the good is present in the universe both as the order of the parts 
and (more primarily) as their ruler. Difficulties which attend the 
views of other philosophers. 


1. We pass to immaterial substance. Two kinds of immaterial 

substances have been believed in, mathematical objects and 
Ideas. We shall discuss first the former, then the latter, then 
the view that numbers and Ideas are the substance of sensible 

2. (i) Mathematical objects cannot exist as distinct substances either in 

or apart from sensible things. 

3. They can be separated only in thought. Mathematics is not entirely 

divorced from consideration of the beautiful, as is sometimes 

4. (ii) Arguments which led to the belief in Ideas. Some prove too 

little, others too much. 

5. Even if there were Ideas, they would not explain the changes in the 

sensible world. 

6. (iii) Various ways in which numbers may be conceived as the substance 

of things. 

7. (a) If all units are associable, this gives only mathematical, not ideal 

number, (b) If all units are inassociable, this gives neither mathe 
matical nor ideal number, (c) If only the units in the same 
number are associable, this leads to equal difficulties ; units must 
have no difference of kind. 

8. The views of Platonists who disagree with Plato, and those of the 

Pythagoreans, lead to equal difficulties. Further objections to 
ideal numbers : (a) How are the units derived from the indefinite 



dyad ? (b] Is the series of numbers infinite or finite ; and if finite, 
what is its limit ? (c) What sort of principle is the One ? 
9. Discussion of the principles of geometrical objects. Criticism of the 
generation of numbers from unity and plurality, and of spatial 
magnitudes from similar principles. The criticism of ideal 
numbers summed up. The upholders of Ideas make them at once 
universal and individual. 

10. Are the first principles of substances individual or universal ? 


1. The principles cannot be contraries. The Platonists in making them 

contraries treated one of the contraries as matter. Various forms 
of this theory. The nature of unity and plurality expounded. 

2. Eternal substances cannot be compounded out of elements. The 

object of the Platonists is to explain the presence of plurality in 
the world, but in this they do not succeed. What justifies the 
belief in the separate existence of numbers ? 

3. Difficulties in the various theories of number. The Pythagoreans 

ascribe generation to numbers, which are eternal. 

4. The relation between the first principles and the good. 

5. How is number supposed to be derived from its elements ? How is it 

the cause of substances ? 

6. The causal agency ascribed to numbers is purely fanciful. 



I ALL men by nature desire to know. An indication of g8o a 
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 any- 25 
thing, 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 98 
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 

The animals other than man live by appearances and 25 
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 98i a 
pretty much like science and art, but really science and art 
come to men throiigh experience ; for experience made 
art , as Polus says, 1 but inexperience luck . Now art 5 
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 experi 
ence ; but to judge that it has done good to all persons of 10 

1 Cf. PI. Gorg. 448 c, 462 BC. 


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 fever, this is a matter of art. 

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

15 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 

20 happens to be a man. If, then, a man has the theory with 
out 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 

25 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 

3 o why, while the others know the 4 why and the cause. Hence 
we think also that the master-workers in each craft are 
more honourable and know in a truer sense and are wiser 
9 8i b 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, 
5 the labourers perform them through habit) ; 1 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 experi 
ence is ; for artists can teach, and men of mere experience 

10 Again, we do not regard any of the senses as Wisdom ; 
1 98i b 2 TOVS ... 5 etfoy may be a later addition. 

BOOK A. I 981* 

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 I5 
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, ao 
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. 1 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 2 what the difference is 25 
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 30 
the possessors of any sense-perception whatever, the artist 
wiser than the men of experience, the master-worker 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 982* 
and causes. 

2 Since we are seeking this knowledge, we must inquire of 5 
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 

1 Reading in 98 l b 23 ov Trpurov e 

2 Ii39 b i4-ii4i b 8. 

B 2 


10 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 

1 5 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 hint. 

20 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 w r ho 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 

25 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 instritctive, in 
a higher degree, for the people who instruct us are those 

30 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 
g82 b readily that \vhich 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 
5 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 

BOOK A. 2 g82 b 

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 i 
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 diffi 
culties about the greater matters, e.g. about the phenomena J 5 
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 
in order to escape from ignorance, evidently they were 20 
pursuing science in order to know, and not for any utili 
tarian 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 25 
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 l God alone 30 
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 983** 
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, 2 l bards 
tell many a lie ), nor should any other science be thought 
more honourable than one of this sort. For the most 5 
1 Fr. 3 Hiller. 2 Cf. Solon, fr. 26 Killer. 


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 (i) 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 

10 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 

15 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, 1 
the better state, as is the case in these instances too when 
men learn the cause ; for there is nothing which would 

ao 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 3 
25 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 defini 
tion, and the ultimate why is a cause and principle) ; in 
30 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, 2 but yet let us call to our aid those who 

1 Cf. Leutsch and Schneidewin, Paroemiographi Graeci, i. 62, 234, 
ii. 357- 

2 Phys. ii. 3, 7- 

BOOK A. 3 9 8a b 

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 5 
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 prin 
ciples 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 10 
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 he loses these characteristics, because 15 
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 20 
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, 25 
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 

Some l 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 3 
and Tethys the parents of creation, 2 and described the oath 

1 The reference is probably to Plato (Crat. 4026, Theaet. 152 E, 
162 D, i8oc). 

2 Horn. //. xiv. 201, 246. 


of the gods as being by water, 1 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 
984** 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. 
5 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 

T O 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 

i 5 way, only by aggregation and segregation, and are not 
in any other sense generated or destroyed, but remain 

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 

20 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 

25 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 

1 Ibid. ii. 755, xiv. 271, xv. 37. 

BOOK A. 3 g84 a 

of inquiry, and said the substratum was one, 1 were not at 
all dissatisfied with themselves ; but some at least of those 
who maintain it to be one 2 as though defeated by this 30 
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 3 it is more possible 5 
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 10 
itself, as we said, 4 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 5 said, then, that 15 
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 20 
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. 

4 One might suspect that Hesiod was the first to look for 

1 Thales, Anaximenes, and Heraclitus. 2 The Eleatics. 

3 The reference is probably to Empedocles 4 a i8. 

5 Anaxagoras ; cf. esp. fr. 12. 


such a thing or some one else who put love or desire 
among existing things as a principle, as Parmenides, too, 
25 does; for he, in constructing the genesis of the universe, 
says l : 

Love first of all the Gods she planned. 
And Hesiod says 2 : 

First of all things was chaos made, and then 

Broad-breasted earth, . . . 

And love, mid all the gods pre-eminent, 

30 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, 
985 and bad things in greater number than good, and ignoble 
things than beautiful therefore 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 
5 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 men 
tions, 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. 

10 These thinkers, as we say, evidently grasped, and to this 
extent, two of the causes which we distinguished in our 
work on nature 4 the matter and the source of the move 
ment vaguely, however, and with no clearness, but as 
untrained men behave in fights ; for they go round their 

15 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 

1 Fr. 13. 2 Theog. 116-120. 

3 The promise is not fulfilled. * Phys. ii. 3, 7. 

BOOK A. 4 985 

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 20 
reason in, but in all other cases ascribes events to any 
thing rather than to reason. 1 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 dis- 25 
solved 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 

Empedocles, then, in contrast with his predecessors, was 
the first to introduce the dividing of this cause, not positing 30 
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 opposites -earth, air, and water 
as one kind of thing. We may learn this by study of his 
verses. 2 

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 5 
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 10 
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 15 
say the real is differentiated only by rhythm and inter- 

1 Cf. PI. PhaedO) 98 BC, Laws, 967 B-D. 2 Cf. fr. 62. 


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, HJ from H in 
position. The question of movement whence or how it is 
to belong to things these thinkers, like the others, lazily 

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

Contemporaneously with these philosophers and before 5 
them, the so-called Pythagoreans, who were the first to take 
up mathematics, not only advanced this study, but also 

25 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 

30 justice, another being soul and reason, another being oppor 
tunity and similarly almost all other things being numeri 
cally expressible l ) ; 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 
g86 a 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 attri- 

5 butes 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 

ic of numbers, they say that the bodies which move through 
the heavens are ten, but as the visible bodies are only nine, 

1 Cf. Diels, Vorsokratiker, ed. 3, i. 303. 15-19. 

BOOK A. 5 g86 a 

to meet this they invent a tenth the * counter-earth . We 
have discussed these matters more exactly elsewhere. 1 

But the object of our review is that we may learn from 
these philosophers also what they suppose to be the prin 
ciples and how these fall under the causes we have named. 15 
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 20 
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 2 
limit and unlimited, odd and even, one and plurality, 
right and left, male and female, resting and moving, straight 25 

1 De Caelo, ii. 13; Fr. de Pythagoreis, ii. I5i3 a 4.o- b 20. Cf. Diels, 
ibid. 347. 3-11. 

2 arvo-Toi\in and o-to-roi^o? are used in a great variety of connexions by 
Aristotle, but the common notion is that of things which from some point 
of view may be treated as forming one line or column. The meanings 
in the Metaphysics may be summarized thus : 

In A. g86 a 23, N. ic93 b 12 the reference is to a Pythagorean classifica 
tion of important general notions. The first column is the line of good 
(f) (Tvoroi^ta TI TOV KaXoO, N. io93 b 12), the second the line of evil. To 
the line of good N. io93 b 13 adds the equal and the potencies of 
certain numbers . 

In r. ioo4 b 27, K. io66 a 15, A. io72 a 31 there is no explicit reference 
to the Pythagorean doctrine, but Aristotle speaks of two lines , one 
of which is knowable in itself, while the other is privative , and its 
* principles are indefinite because they are privative . 

In I. I054 b 35, 1058*13 we have a different sort of line. Terms 
which in the strict sense differ are said to be either different in genus 
or in the same line of predication, and therefore in the same genus ; 
and contraries which differ in species and not in genus are said to be 
in the same line of predication, o-uorot^ia rfjs Karr^yopias seems to 
correspond to V\THJM rr}? Karrjyopins (lo54 b 29), which is said in A. 
Ioi6 b 33 to be coextensive with a ycvos. It is at first sight surprising 
to find genus identified with category, and one is tempted to suggest 
that orvtTTotxia (or o-^/ua) TTJS KaTr)yopis means one of the main divisions 
of a category, within which the same sort of predicate is found. Thus 
number would be the genus within which the predicates odd and even, 
and various subordinate predicates, are found. Then the subordinate 
predicates might be thought of as forming a column under odd and 
even . But A. io24 b 12-16 shows that genus in one sense can be 
identified with category. The categories are the only genera proper, 
since they are the only genera which are not species. 


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 

30 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 Pytha 
goreans 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 con- 
g86 b trarieties, 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 
5 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 sub 
stance is composed and moulded. 

From these facts we may sufficiently perceive the mean 
ing of the ancients who said the elements of nature were 

10 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 philo 
sophers, assume being to be one and yet generate it out of 

15 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, 

a 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), 

1 Cf. Phys. 185* 32- b 3, 2o; a 15-17. 

BOOK A. 5 g86 b 

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 25 
these thinkers, as we said, must be neglected for the pur 
poses of the present inquiry two of them entirely, as being 
a little too nai ve, viz. Xenophanes and Melissus ; but Par- 
menides 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 30 
clearly in our work on nature), 1 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 987** 

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 supposes 
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, 10 
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 15 
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 

1 Phys. i. 3. 


substance of the things of which they are predicated. This 
is why number was the substance of all things. On this 

20 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 sub 
stance of the thing defined, as if one supposed that l double 
and 2 were the same, because 2 is the first thing of which 

25 double is predicable. But surely to be double and to be 
2 are not the same ; if they are, one thing will be many l 
a consequence which they actually drew. 2 From the earlier 
philosophers, then, and from their successors we can learn 
thus much. 

After the systems we have named came the philosophy 6 
30 of Plato, which in most respects followed these thinkers, 
but had peculiarities that distinguished it from the philo 
sophy 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 
5 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 
10 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 

1 i. e. 2 will be each of several things whose definition is predicable 
of it. 

2 e.g. 2 was identified both with opinion and with daring. 

BOOK A. 6 g87 b 

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 inter- 15 
mediate position, differing 1 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 20 
matter, the great and the small were principles ; as essen 
tial 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 25 
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 Num 
bers, and do not place the objects of mathematics between 
Forms and sensible things. His divergence from the 30 
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, 1 could be 
neatly produced out of the dyad as out of some plastic 

Yet what happens is the contrary ; the theory is not a 988* 
reasonable one. For they make many things out of the 
matter, and the form generates only once, but what we 

1 This is not quite accurate. Really it is only 2 and its powers that 
could be neatly produced out of the I and the indefinite dyad ; cf. 
N. 109^9-12. In Parmenides 143 C-I44A, 3 is derived from I and 2 
(the number 2, not, as Aristotle says, the indefinite 2) by addition, and 
the numbers higher than 3 are derived from 2 and 3 by multiplication. 
Primes are not there excepted ; Plato speaks as if all the higher 
numbers could be got by multiplication. Nothing in the works of 
Plato corresponds exactly to what Aristotle says here. 


observe is that one table is made from one matter, while the 
man who applies the form, though he is one, makes many 

5 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 ques 
tion ; it is evident from what has been said that he has used 
only two causes, that of the essence and the material cause 

10 (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 

15 of the two, as we say 1 some of his predecessors sought to 
do, e. g. Empedocles and Anaxagoras. 

Our review of those who have spoken about first prin- 7 
ciples and reality and of the way in which they have 

20 spoken, has been concise and summary ; but yet we have 
learnt this much from them, that of those \vho speak about 
4 principle and * cause no one has mentioned any principle 
except those which have been distinguished in our work 
on nature, 2 but all evidently have some inkling of them^ 
though only vaguely. For some speak of the first prin 
ciple as matter, whether they suppose one or more first 

25 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 com 
posed of similar parts. These, then, have all had a notion 
of this kind of cause, and so have all who speak of air or 

30 fire or water, or something denser than fire and rarer than 
air ; for some have said the prime element is of this kind. 3 

1 Cf. 984 b i5-i9, 32- b 10. 

2 Phys. ii. 3, 7. 

3 Cf. Diels, Vorsokratiker, ed. 3, i. 18. 8-21, 415. 32-416. 27. The 
reference is probably to some follower of \naximenes. 

BOOK A. 7 9 88 a 

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 ex 
pressed distinctly. It is hinted at chiefly by those who believe 35 
in the Forms ; for they do not suppose either that the Forms g88 b 
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. 5 

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 10 
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 15 
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 diffi- *o 
culties with regard to the way in which each of these 
thinkers has spoken, and with regard to his situation rela 
tively to the first principles. 

8 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 35 
things, though there are also incorporeal things. And in 

c 2, 


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 any 
thing, and besides this in lightly calling any of the simple 

30 bodies except earth the first principle, without inquiring 
how they are produced out of one another, 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 pos- 

35 teriority. For (i) in a way the property of being most 
elementary of all would seem to belong to the first thing 
g8g a 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 prin 
ciple would be most in agreement with this argument. 
But each of the other thinkers agrees that the element of 
5 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 

10 earth. And Hesiod says l earth was produced first of cor 
poreal 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 

15 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 

20 these, as Fmpedocles says the matter of things is four 
bodies. For he too is confronted by consequences some of 
1 Theog. 1 1 6. 

BOOK A. 8 989 

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 l ) ; and regarding the cause of 25 
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. 2 

As regards Anaxagoras, if one were to suppose that he 3 
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 5 
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 10 
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 par- 
1 De Caelo, iii. 7. 2 989* 26 oAo>? ... 30 (prjaiv is possibly a gloss. 


ticular form would necessarily have been already separated 

15 out, but he says all were mixed except reason, and this 
alone w r as unmixed and pure. 1 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 

20 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 argu 
ments 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 

25 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 

3 o 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 dis 
cussions and investigations are all about nature ; for they 
99 a 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 philo 
sophers, that the real is just all that which is perceptible 
5 and contained by the so-called heavens . But the causes 
and the principles which they mention are, as we said, 2 
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 

10 the only things assumed, or how without movement and 
1 Fr. 12. 8 99 b 3i-3. 

BOOK A. 8 ggo a 

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 magni 
tude 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 15 
speaking no more of mathematical bodies than of percep 
tible ; 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 per 
ceptible things. 

Further, how are we to combine the beliefs that the 
attributes of number, and number itself, are causes of what 20 
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 mix 
ture, and allege, as proof, that, each of these is a number, 
and that there happens to be already in this place a plurality 25 
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 30 
and their causes are numbers, but that the intelligible num 
bers are causes, while the others are sensible. 

9 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 99O b 
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 practi 
cally equal to or not fewer than the things, in trying to 5 
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 

Further, of the ways in which we l prove that the Forms 

10 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 accord 
ing 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 argu 
ment that there is an object for thought even when the 
thing has perished, there will be Forms of perishable things ; 

15 for we have an image of these. Further, of the more accu 
rate arguments, some lead to Ideas of relations, of which 
we say there is no independent class, and others introduce 
the * third man . 2 

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 3 but 

20 number is first, i. e. that the relative is prior to the abso 
lute, 4 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 theory. 

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 

25 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 

1 Aristotle speaks as a Platonist. 

2 Cf. Z. I039 a 2, Soph. EL i;8 b 36-179* 10, and Plato Farm. 132 AB, 

3 Sc. the * indefinite 2 which Plato held to be one of the first prin 
ciples of number. 

4 i.e. number, which is relative, is prior to the indefinite 2, which 
Plato held to be an absolute first principle. 

BOOK A. 9 990 b 

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 30 
in its Form as in something 1 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 99 1 
something apart from the particulars the one over many P). 1 
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 5 
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 com 
munity between them. 2 

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 I0 
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 the) were, they might be thought 
to be causes, as white causes whiteness in a white object 15 
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 

1 This seems to be an enthymeme, the conclusion to be supplied 
being that the Forms, since they are substances, must be of sub 

2 With 99o b 2~99i a 8 cf. M. io;8 b 34-io79 b 3. 


20 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 

25 from it, 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 

30 of 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. 

ggi b 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 l 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 
5 do not come into being, unless there is something to origi 
nate 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. 2 

Again, if the Forms are numbers, how can they be 

10 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 

15 matter is some definite thing, 3 evidently the numbers 
themselves too will be ratios of something to something 

1 ioo c-E. 2 With 991* 8- b 9 cf. M. io79 b !2-io8o a 8. 

3 Reading in 991^ 14 &T) n TOVTO, 17 vA/;. 

BOOK A. 9 ggi b 

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 kind of number merely because it is a numerical 20 
ratio. 1 

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 25 
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 30 
this sensible world and the things-themselves ? 

Further, the units in 2 must each come from a prior 2 ; 
but this is impossible. 

Further, why is a number, when taken all together, one ? 992 a 

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 5 
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 sub 
stances. 2 Evidently, if there is a One-itself and this is a first 

1 i. e. the Idea is a numerical ratio in some underlying material. It 
may perhaps be called a sort of (rt?) number, but strictly it is a 
numerical ratio. The passage, however, is very difficult, and the 
contradiction in 11. 19, 20 almost intolerable. 

2 Sc. but ordinary mathematical numbers. Cf. M. 1081*5-12. 


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

ID 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 

15 class from the deep and shallow. Therefore, just as num 
ber 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. 1 Further, from what prin 
ciple will the presence of the points in the line be derived ? 

20 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 ofper- 

25 ceptible 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 sub 
stances of perceptible things is empty talk ; for * sharing f , 
as we said before, 2 means nothing. 

Nor have the Forms any connexion with what we see to 

30 be the cause in the case of the arts, that for whose sake both 
all mind and the whole of nature are operative, 3 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. 4 

1 With 992* 10-19 cf. M. 1085*9-19. 

2 991*20-22. 3 Sc. the final cause. 
4 Cf. Plato, Rep. vii. 531 D, 533 B-E. 

BOOK A. 9 992 b 

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, i. e. 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 5 
of the substratum ; for these are a kind of excess and defect. 
And regarding movement, if the great and the small are to 
be 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 10 
setting out instances 1 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 T5 
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. 2 

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 con- 30 
ducted in this manner. For it is surely impossible to dis 
cover 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 

And how could we learn the elements of all things ? 
Evidently we cannot start by knowing anything before. 25 
For as he who is learning geometry, though he may know 

1 For this Platonic method cf. Z. iO3i b 2i, M. io86 b 9, N. iogo a 17. 

2 Cf. M. ic8o b 23-30, 1085*7-9. 


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 
3 know nothing before. Yet all learning is by means of pre 
misses which are (either all or some of them) known before, 
whether the learning be by demonstration or by defini 
tions ; for the elements of the definition must be known 
before and be familiar ; and learning by induction proceeds 
993 a 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, 
5 as there is about certain syllables ; some say za is made out 
of s and d and <z, 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 
10 consist of the elements proper to sound, are the same. 

It is evident, then, even from what we have said before, 10 
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 

15 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 2 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 

20 not one of them should ; for it is on account of this that 
both flesh and bone and everything else wall exist, and not 
on account of the matter, which he names, fire and 

1 > 7- 

2 Diels, Vorsokratiker, ed. 3, fr. 96 and i. 214. 22-215. 6. 

BOOK A. 10 993 a 

earth and water and air. But while he would necessarily 
have agreed if another had said this, he has not said it 

On these questions our views have been expressed before ; 
but let us return to enumerate the difficulties that might be 25 
raised on these same points ; 1 for perhaps we may get from 
them some help towards our later difficulties. 

1 The reference is to Bk. B. 


30 THE investigation of the truth is in one way hard, in i 
another easy. An indication of this is found in the fact 
that no one is able to attain the truth adequately, while, on 
993 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. There 
fore, since the truth seems to be like the proverbial door, 1 

5 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 

10 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. 

15 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 know- 

20 ledge 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 2 and in the present). Now 

1 Cf. Leutsch and Schneidewin, Faroemiographi Craed, ii. 678. 

2 Reading in 993 b 22 dAX 6 rrpos . 

BOOK a. I 993 b 

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 25 
heat of all other things) ; so that that which causes deriva 
tive 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 3 
is it in respect of truth. 

But evidently there is a first principle, and the causes of 994 a 
things are neither an infinite series nor infinitely various in 
kind. For (i) 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 5 
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, 1 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 10 
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 15 
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 20 
proceed from fire, earth from water, and so always some 

1 The illustration is taken from the cosmology of Empedocles. 

646-28 ) 


other kind should be produced. For one thing comes 
from another in two ways not in the sense in which 
4 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 
35 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 
sofrom 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 
994 b 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, 1 must 
5 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. 2 

1 Cf. a 27 f. 

2 This paragraph is very obscure. Aristotle has in a ii-i9 given a 
general argument which applies to all the four causes, to show that 
there must always be a first cause. This, he assumes, must be 
eternal. He now applies this argument to the prime material cause, 
and shows that it must be indestructible. There are two difficulties in 
the paragraph : 

(i) It seems pointless to say that the first cause must be inde- 

BOOK a. 2 994 b 

Further, the final caiise 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 to 
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 15 
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. 1 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, 2 o 
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 ? 2 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 35 
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. 3 

But (2) if the kinds of causes had been infinite in number, 
then also knowledge would have been impossible ; for we 

structible because it is eternal. Ground and consequent appear to be 
identical. But probably the object is to show that the first cause must 
be to its effects not as water to air but as boy to man. It develops 
into them, and is not destroyed when they come into being. 

(2) The clause beginning with eW seems, as is often the case in 
Aristotle, to be elliptical. The meaning probably is : Since the pro 
cess of becoming is not infinite in the upward direction, (there must 
be an eternal first cause, but) that which is the first thing by whose 
destruction something came to be cannot be eternal. 

1 i. e. one can reduce the definition of man as * rational animal to 
rational sensitive living substance , but one cannot carry on this 
process ad infinituin, 

2 i. e. actually infinite. 

3 i. e. does not contain an infinite number of marks. 

D 2 


think we know, only when we have ascertained the causes, 
30 but that which is infinite by addition cannot be gone through 
in a finite time. 

The effect which lectures produce on a hearer depends 3 
on his habits ; for we demand the language we are accus- 
995 a to me d 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 intelli 
gible. The force of habit is shown by the laws, in which 

5 the legendary and childish elements prevail over our know 
ledge 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 

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

1 5 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 its 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 

20 principles of things]. 1 

1 This clause has probably been wrongly inserted from 995 b 5-6. 


I WE must, with a view to the science which we are seek 
ing, first recount the subjects that should be first discussed. 
These include both the other opinions that some have held 25 
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 30 
the difficulty of our thinking points to a 4 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 35 
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 995^ 
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 

The first problem concerns the subject 1 which we dis 
cussed in our prefatory remarks. It is this (i) whether 5 
the investigation of the causes belongs to one or to more 
sciences, 2 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 ; :i and (3) if the science 10 
in question deals with substance, whether one science deals 

1 Sc. the four causes. 2 Cf. 996** i8- b 26. 

3 Cf. 996 b 26-997 a i5. 


with all substances, or more than one, 1 and it more, whether 
all are akin, or some of them must be called forms of Wis 
dom 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 

15 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. 2 
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. 3 

20 Further, with regard to the same and other and like and un 
like 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 pre 
mises only, whose business is it to inquire into all these ? 

25 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. 4 
Again (6), are the principles and elements of things the 
genera, or the parts present in each thing, into which it is 
divided ; 5 and (7) if they are the genera, are they the genera 
that are predicated proximately of the individuals, or the 

30 highest genera, e. g. is animal or man the first principle and 
the more independent of the individual instance ? 6 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 

35 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. 7 

gg6 a Again (9) we ask whether the principles are limited in num- 

1 Cf. 997*15-25. 

2 Cf. 997 a 34-998* 19. The reference is to Plato. 

3 Cf. 997 ;1 25-34. 4 Cf. r. ioo3 b 22-ioc>5 a 18. 
5 Cf. 99S a 2o- b 14. 6 Cf. 998 b 14-999*23. 

7 Cf. 999* 24~ b 24. 

BOOK B. i 996 

her or in kind, both those in the definitions and those in the 
substratum j 1 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. 2 Further (n) there is the question 
which is hardest of all and most perplexing, whether unity 5 
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 some 
thing else, as Empedocles says, love ; as some one else 3 
says, fire; while another 4 says water or air. 5 Again 
(12) we ask whether the principles are universal or like 
individual things, 6 and (13) whether they exist potentially or 10 
actually 7 , and further, whether they are potential or actual 
in any other sense than in reference to movement; 8 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 ? 9 With 1 5 
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. 

2 (i) 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 20 
to recognize the principles if these are not contrary ? 

Further, there are many things to which not all the prin 
ciples 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 25 
things both come to be and are, and since an end or pur 
pose is the end of some action, and all actions imply change ? 
So in the case of unchangeable things this principle could not 

1 Cf. 999 b 24-iooo a 4. 2 Cf. icoo a s~iooi a 3. 

3 Hippasus and Heraclitus. 

4 Thales (water) ; Anaximenes and Diogenes of Apollonia (air). 

6 Cf. iooi a 4-^25. e Cf. ioo3 a 5-i;. 

7 Cf. ioo2 b 32-ioo3 a 5. 8 Cf. e. 6. 

9 Cf. IOOI b 26-I002 b II. 


exist, nor could there be a good-itself. This is why in 
mathematics nothing is proved by means of this kind ot 
30 cause, nor is there any demonstration of this kind 
because it is better, or worse ; indeed no one even men 
tions anything of the kind. And so for this reason some 
of the Sophists, e.g. Aristippus, used to ridicule mathe 
matics ; for in the arts (he maintained), even in the indus 
trial arts, e. g. in carpentry and cobbling, the reason always 
35 given is because it is better, or worse \ but the mathe 
matical sciences take no account of goods and evils. 
gg6 b 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 
5 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 func 
tion it fulfils, the matter is earth and stones, and the form 
is the definition. To judge from our previous discussion J 
of the question which of the sciences should be called Wis 
dom, there is reason for applying the name to each of them. 
10 For inasmuch as it is most architectonic and authoritative 
and the other sciences, like slave-women, 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 2 as dealing 
w r ith 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 
15 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 
w r ho 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 other cases also we 
think that the knowledge of each even of the things of which 

1 Cf. A. 982*8-19. 2 ib. 30- b 2. 

3 i. e. essence. 

BOOK B. 2 996 

demonstration is possible l is present only when we know 
what the thing is, e. g. what squaring a rectangle is, viz. that 20 
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 25 
these causes severally. 2 

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 3 
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 under 
stand these matters ? If then it belongs to every science 35 
alike, and cannot belong to all, it is not peculiar to the 997* 
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) ; 5 
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 

1 The meaning is that whether the essence is known directly (as in 
the case of substances) or by means of demonstration (as in the case of 
attributes or of events like thunder or eclipse), knowledge of the 
essence is the primary knowledge. 

2 With 996* i8- b 26 cf. 995 b 4-6, K. 1059** 20-23 (with 996 a 2i- b I cf. 



certain attributes. Therefore it follows that all attributes 
10 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 ? l 
15 (3) In general, do all substances fall under one science 
or under more than one ? If the latter, to what sort of sub 
stance 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 every demonstrative science 
20 investigates with regard to some subject its essential attri 
butes, starting from the common beliefs. 2 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. 3 
25 (5) 4 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 differ- 
so ent 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 ot 
another, what will be the science that investigates the attri 
butes of substance ? This is a very difficult question. 5 

1 With 996 b 26-997* 15 cf. 995 b 6-10, 1059** 23-6. For the answer 
cf. r. 3 2 Cf. 996 b 28. 

8 With 997*15-25 cf. 995 b 10-13, io59 a 26~9. For the answer cf. r. 
1004*2-9, E. i. 

4 I number the problems as in ch. i. 

5 With 997*25-34 cf. 995 b 18-20, 1059*29-34. For the answer cf. 
r. I003 b 22-ioo5 a 18. 

BOOK B. 2 997 a 

(4) Further, must we say that sensible substances alone 
exist, or that there are others besides these ? And are sub- 35 
stances of one kind or are there in fact several kinds of 
substances, as those say who assert the existence both of the 997 
Forms and of the intermediates, with which they say the 
mathematical sciences deal ? The sense in which we l 
say the Forms are both causes and self-dependent sub 
stances has been explained in our first remarks about them ; 2 
while the theory presents difficulties in many ways, the 5 
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 TO 
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 15 
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 mathe- 20 
matical 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 perish 
able animals. We might also raise the question, with 25 
reference to which kind of existing things we must look for 
1 Cf. note on A. 99o b 9. 2 Cf. A. 6 and 9. 


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 

3 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 

35 us. For neither are perceptible lines such lines as the 
998 a geometer speaks of (for no perceptible thing is straight or 
round in the way in which he defines straight and 
1 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), 1 nor are the movements and spiral orbits 

5 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 inter 
mediates between the Forms and the perceptible things 
exist, not apart from the perceptible things, however, but 
in these ; 2 the impossible results of this view would take too 

10 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 

15 are in the moving perceptible things. And in general to 
what purpose would one suppose them to exist indeed, but 

1 Possibly in a work Hepi TWV Ma6r]piiTa>v, for which cf. Diog. 
Laert. ix. 55. 

2 The reference is to a school of semi-Pythagorean, semi-Platonic 

BOOK B. 2 998* 

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. 1 

3 (6) Apart from the great difficulty of stating the case 2 
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 2 5 
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 30 
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 99& b 
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 5 
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, 2 or the great and the small, 3 are elements of 10 
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 

1 With 997 a 34-998 a 19 cf. 995 b 13-18, I059 a 38- b 2i. For the 
answer cf. A. 6-lo, M, N. 

2 The reference is to the Pythagoreans and Plato (cf. 996*6). 

3 The reference is to Plato (cf. A. 98; b 20). 


definition by genera will be different from that which states 
the constituent parts of a thing. 1 

(7) Besides this, even if the genera are in the highest 

15 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, 

20 so that both being and unity will be principles and sub 
stances ; 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 

25 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 

3 others are not thought to be so. Besides this, the differ 
entiae 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 
999 a highest genus to be a principle. But again, if unity ? s 
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 
5 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 
1 With 998* 2o- b 14 cf. 995** 27-9. For the answer cf. Z. 10, 13. 

BOOK B. 3 999 a 

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 10 
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 J 5 
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 20 
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. 1 

4 (8) There is a difficulty connected with these, the hardest 
of all and the most necessary to examine, and of this the 25 
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 know 
ledge 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 30 
genera exist apart from the individuals, either the lowest 
or the highest genera ; but we found by discussion just now 
that this is impossible. 2 

Further, if we admit in the fullest sense that something 

1 With 998 b I4~999 a 23 cf. 995 b 29-31. For the answer cf. Z. 12. 
iO38 a 19, and 13. With this and the previous problem cf. loco 15 21- 
1060* i. 2 Ch. 3. 


exists apart from the concrete thing, whenever something- 
is predicated of the matter, must there, if there is some 
thing apart, be something apart from each set of individuals, 
999 b or from some and not from others, or from none ? l (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. 2 Further, nothing will be 
eternal or unmovable ; for all perceptible things perish and 

5 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 ; 

10 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 be as soon as it has come 
to be. 3 Further, since the matter exists, 4 because it is un- 
generated, 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, 

r5 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 

20 houses. Besides this, will the substance of all the indi 
viduals, e. g. of all men, be one ? This is paradoxical, for 

1 The question which individuals have something apart correspond 
ing to them suggests to Aristotle the further question whether any 
have. Thus the end of the sentence takes a form inconsistent with the 

2 The reference is to Protagoras (cf. PI. Theaet. 152 -153 A). 

3 Sc. and thus there is a limit to its coming to be. 

4 Sc. before the concrete thing. 

BOOK B. 4 999 b 

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 ? l 

(9) Again, one might ask the following question also 
about the first principles. If they are one in kind only, 35 
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 of it are also 
the same in kind ; only in kind, for these also, like the 30 
syllable, are numerically different in different contexts), if 
it is not like this but the principles of things are numeri 
cally 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). There- iooo a 
fore 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. 2 

(10) One difficulty which is as great as any has been 5 
neglected both by modern philosophers and by their pre 
decessors 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 10 

1 With 999 a 24- b 24 cf. 995 b 31-6, io6o a 3-27, b 23-8. For the 
answer cf. Z. 8, 13, 14, A. 6-10, M. 10. 

2 With 999 b 24-iooo a 4 cf. 996*1-2, 1060 b 28-30. For the answer 
cf. Z. 14, A. 4, 5, M. 10. 

645-28 E 


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 comprehen- 
15 sion. For if the gods taste of nectar and ambrosia for their 
pleasure, these are in no w T ise 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 
20 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 sup- 
25 pose 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 prodtice 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 
30 Trees, and men and women, took their growth, 
And beasts and birds and water- nourished fish, 
And long-aged gods. 1 

The implication is evident even apart from these words ; 

iooo b 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. 2 Hence it also 

follows on his theory that God most blessed is less wise 

5 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. 3 

1 Fr. 21. 2 Fr. 36. 3 Fr. 109. 

BOOK B. 4 iooo b 

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 l 
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. 1 15 

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. 2 The difficulty we are speaking of 20 
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, 25 
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 perish 
able, while those composed of the others are imperishable ? 30 
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 3 as if they iooi a 
took it to be something trifling. 4 

1 Fr. 30. 2 Cf. Diels, Vorsokratiker, ed. 3, i. 209. 11-21. 

3 iooo a 5~ b 21. 

4 With iooo a 5-icoi a 3 cf. 996 a 2-4, 1060*27-36. For the answer 
cf. Z. 7-10. 

E 2 


(n) The inquiry that is both the hardest of all and the 

5 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 respec 
tively, 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 

10 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. Empe- 
docles as though reducing it to something more intel 
ligible 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 

15 one. Others say this unity and being, of which things 
consist and have been made, is fire, 1 and others say it is air. 2 
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 sub- 

20 stances, 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 indi- 

25 viduals. 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 

30 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 

1 Hippasus and Heraclitus. 

3 Anaximenes and Diogenes of Apollonia. 

BOOK B. 4 iooi a 

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 iooi b 
is not a substance or there is a unity-itself, number cannot 
be a substance. We have already l said why this result 
follows if unity is not a substance ; and if it is, the same 
difficulty arises as arose 2 with regard to being. For whence 
is there to be another one besides unity-itself? It must be 5 
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 3 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 10 
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, 4 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 indi- 15 
visible 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 one supposes the case to be such that, as 20 
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 some 
times a magnitude, if the not-one was inequality 5 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. 6 25 

1 a 24-27. 2 a 3i- b i. 

5 Cf. Diels, Vorsokratiker,t&. 3, i. 170. 16-38. 

4 e. g. a line added to another at the end makes it longer, but one 
which lies beside another makes it no broader. 

5 The reference is to Plato s theory (cf. M. io8l a 24). 

6 With iooi a 4- b 25 cf. 996*4 9. For the answer cf. Z. io4o b 
16-24, I. 2. 


(14) A question connected with these is whether numbers 5 
and bodies and planes and points are substances of a kind, 
or not. If they are not, it baffles us to say what being 1 is 
and what the substances of things are. For modifications 

30 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 
ioo2 a 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 
5 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 with 
out 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 iden 
tical with body, and that all other things were modifications 

10 of this, so that the first principles of bodies were the first 
principles of being, the more recent and those who were 
held to be wiser l 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. 

15 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 

20 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 

25 too. And the same account applies to the line and to the 
1 The Pythagoreans and Plato are probably meant. 

^BOOK B. 5 ioo2 a 

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, 1 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 destruction con 
front us with further paradoxes. For if substance, not 30 
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 iooa b 
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 5 
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 2 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 10 
either limits or divisions. 3 

6 In general one might raise the question why after all, 
besides perceptible things and the intermediates, 4 we have 
to look for another class of things, i. e. the Forms which 
we 5 posit. If it is for this reason, because the objects 
of mathematics, while they differ from the things in this 

1 Sc. not to speak of their being the most real substances. 

2 Reading in Ioo2 b 7-8 eu/m, s owe (<os OVK. A b ). 

3 For the answer cf. M. 1-3 (esp. io9o b 5-13), 6-9, N. 1-3, 5, 6. 
With problems (li), (14) cf. io6o a 36- b 19. 

* For these cf. A. 987^14-18. 
5 Sc. Platonists. 


i 5 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 

ao 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, 

25 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 

30 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 1 the impossible results that necessarily follow. 2 

(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 
ioo3 a 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 w r hich 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. 3 
5 (12) We must not only raise these questions about the 
first principles, but also ask whether they are universal or 
w r hat we call individuals. If they are universal, they will 
not be substances ; for everything that is common indicates 

1 999 b 27-iooo a 4. 

2 (15) is a question not raised in ch. I but akin to problems (4), (8), 

3 With ioo2 b 32-1003* 5 cf. 996*10-11. For the answer cf. e. 8, 
A. 6, 7. 

BOOK B. 6 ioo3 a 

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 predi 
cate is a this and a single thing, Socrates will be several 10 
animals himself and man and animal , if each of these 
indicates a this and a single thing. 

If, then, the principles are universals, these results follow ; 
if they are not universals but of the nature of individuals, 
they will not be knowable ; for the knowledge of anything 
is universal. Therefore if there is to be knowledge of the 15 
principles there must be other principles prior to them, 
namely those that are universally predicated of them. 1 

1 With 1003*5-17 cf. 996*9-10, io6o b 19-23. For the answer 
cf. Z. 13, 15, M. 10. 


THERE is a science which investigates being- as being i 
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 investi- 

25 gate 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 

3 o that the elements must be elements of being not by accident 
but just because it zs 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 2 
4 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 
35 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 
ioo3 b 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 
5 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 
10 of these things or of substance itself. It is for this reason 
that we say even of non-being that it is non-being. As, 

BOOK T. 2 1003 

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 15 
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 percep 
tion, so there is one science, as for instance grammar, being 20 
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 prin 
ciple and cause are, not in the sense that they are explained 
by the same definition (though it makes no difference even 25 
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 ceas 
ing to be) ; and similarly one existent man adds nothing 3 
to 4 existent man , so that it is obvious that the addition in 
these cases means the same thing, and unity is nothing 
apart from being l ; 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 

1 The argument is obscured by doubts as to the reading, but seems 
to be that being and unity are not severed from the particular thing 
which is and is one, and .*. are not severed from one another. 


35 science which is generically one I mean, for instance, the 
discussion of the same and the similar and the other con 
cepts of this sort ; and nearly all contraries may be referred 
ioo4 a 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 
5 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. 2 

Now since it is the work of one science to investigate 

10 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 particu 
lar class ; in the latter case difference is present over and 
above what is implied in negation ; for negation means just 

15 the absence of the thing in question, while in privation there 
is also employed an underlying nature of which the priva 
tion is asserted 3 ) : in view of all these facts, the contraries 
of the concepts we named above, the other and the dis 
similar 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. 

20 And contrariety is one of these concepts ; for contrariety 
is a kind of difference, and difference is a kind of other 
ness. Therefore, since there are many senses in which 
a thing is said to be one, these terms also will have 

1 Cf. Fr. I478 b 35-I479 a 5, I497 a 32-149^43- 

2 With ioo4 a 2-9 cf. B. 995 b 10-13, 997 a 15-25, E. i. 

8 i. e. negation is simply the negation of an attribute ; in privation 
some member of a definite class is said not to have the attribute in the 
form appropriate to that class. I conjecture that TO> f.vl or TO> iv\ r] 
should be omitted in 1004* 13-14. 

BOOK T. 2 ioo4 a 

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 25 
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 30 
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), 1 
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 ioo4 b 
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 ques 
tions. Since, then, these are essential modifications of unity 5 
qua unity and of being qua being, not qua numbers or lines 
or fire, it is clear that it belongs to this science to investi 
gate both the essence of these concepts and their properties. 
And those who study these properties err not by leaving 
the sphere of philosophy, 2 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, I0 
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 pro- 15 

1 i. e. B. 995 b 18-27, 997 a 25-34. 

2 Sc. which they do not do. 


parties 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 

20 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 

35 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 1 
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 

30 all thinkers agree that being and substance are composed 
of contraries ; at least all name contraries as their first prin 
ciples some name odd and even, 2 some hot and cold, 3 
some limit and the unlimited, 4 some love and strife. 5 And 
all the others as well are evidently reducible to unity and 
ioos a plurality (this reduction we must take for granted 6 ), and the 
principles stated by other thinkers fall entirely under these 
as their genera. It is obvious then from these considera 
tions too that it belongs to one science to examine being 
qua being. For all things are either contraries or com 
posed of contraries, and unity and plurality are the starting- 
5 points of all contraries. And these belong to one science, 
whether they have or have not one single meaning. Prob 
ably 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 con 
traries), even if being or unity is not a universal and the 

1 Cf. note on A. 986 a 23. 2 The Pythagoreans. 

3 Parmenides in the k Way of Opinion . 

4 The Platonists. 6 Empedocles. 
fi Cf. Fr. 1 4;8 b 36-i479 a 5- 

BOOK P. 2 ioos a 

same in every instance or is not separable from the particu 
lar instances (as in fact it probably is not ; the unity is in 10 
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 complete 
ness 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 15 
named l and the concepts prior and posterior , * genus 
and species , whole and part , and the others of this 
sort. 2 

3 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 20 
into these also belongs to one science, and that the science 
of the philosopher ; for these truths hold good for every 
thing that is, and not for some special genus apart from 
others. And all men use them, because they are true of 
being qtia being and each genus has being. But men use 25 
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 q^ia 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 30 
falsity, neither the geometer nor the arithmetician. Some 
natural philosophers indeed have done so, and their pro 
cedure 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 particu 
lar genus of being), the discussion of these truths also will 35 

1 1. 12. 

2 With ioo3 b 22-ioo5 a 18 cf. B. 995 b 18-27, 997*25-34. With the 
whole ch. cf. K. 3. 


belong to him whose inquiry is universal and deals with 
I0 5 b primary substance. Physics also is a kind of Wisdom, but 
it is not the first kind. 1 And the attempts of some of those 
who discuss the terms on which truth should be accepted, 2 
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. 

5 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 

10 principles of his subject, so that he whose subject is exist 
ing things qtta 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-hypothe- 

T 5 tical. For a principle which every one must have who 
understands any thing 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 

20 the same subject and in the same respect ; we must pre 
suppose, 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 defini- 
^c, tion given above. For it is impossible for any one to be 
lieve the same thing to be and not to be, as some think 

25 Heraclitus says. For what a man says, he does not neces 
sarily believe ; and if it is impossible that contrary attri 
butes should belong at the same time to the same subject 
(the usual qualifications must be presupposed in this pre 
miss too), and if an opinion which contradicts another is 

1 With ioo5 a iQ- b 2 cf. K. 4. 

2 The reference may be to Antisthenes. 

BOOK T. 3 ioos b 

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 3 
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. 1 

4 There are some who, as we said, 2 both themselves assert 35 
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. 3 And ioo6 
among others many writers about nature use this language. 
But w r e have now posited that it is impossible for anything v 
at the same time to be and not to be, and by this means 
have shown that this is the most indisputable of all prin 
ciples. 4 Some indeed demand that even this shall be 5 
demonstrated, 5 but this they do through want of education, 
for not to know of what things one should demand demon 
stration, and of what one should not, argues want of educa 
tion. 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 10 
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 6 is impossible ) if our opponent will only say some 
thing ; 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 15 
negative demonstration I distinguish from demonstra 
tion proper, because in a demonstration one might be 

1 With ch. 3 cf. B. 995 b 6-10, 996 b 26-997 a 15. With ioc>5 b 8-34 cf. 
K. io6i b 34-io62 a 2(with ioo5 b 23~6 cf. io62 a 31-5). 

2 Apparently a loose reference to ioo5 b 23-5. 

3 The Megaric school may be referred to. 

4 i.e. we have shown that since A cannot be both B and not-jB, no 
one can think A is both B and not-j5 (icos b 22-32). 

6 The reference may be to Antisthenes. 
6 That the same thing can be and not be. 


thought to be begging the question, but if another person 
is responsible for the assumption we shall have negative 
proof, not demonstration. 1 The starting-point for all such 
arguments is not the demand that our opponent shall say 

20 that something either is or is not (for this one might per 
haps 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 any 
thing. 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 ; 

2 5 for we shall already have something definite. The person 
responsible for the proof, however, is not he who demon 
strates 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 

3 4 be or not be has a definite meaning, so that not every 
thing will be so and not so \ 2 Again, if man has one 
meaning, let this be two-footed animal ; by having one 
meaning I understand this : if man means c 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 ; 
ioo6 b 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 defini 
tion, 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 

5 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 

10 ourselves, has been annihilated ; for it is impossible to think 

1 With 11. s-i 8 cf. K. 1062*2-5. 

2 For so and not so cf. PI. Theaet. 183 A. 

BOOK F. 4 ioo6 b 

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, 1 
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 15 
not identify having one significance with 4 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 w r ere to call not-man ; but the point 20 
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 dif 
ferent, 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 25 
means this being related as raiment and 4 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 2 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 3 ) ; and if this is necessary, it is impossible that the 30 
same thing should not at that time be a two-footed animal ; 
for this is what being necessary meansthat it is im 
possible 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 ioo7 a 
different things, since even being white and being a man 
are different ; for the former terms are much more opposed, 
so that they must a fortiori mean different things. And 
1 a 2i, 31. 2 11. 11-15. 3 in a 3if- 

F 2 


if any one says that white means one and the same thing 
5 as man , again we shall say the same as what was said 
before, 1 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 

10 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 attri- 

15 butes, 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. 2 

20 And in general those who say this do away with sub 
stance 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 

25 negations of it 3 ) ; 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 

1 ioo6 b i7. 

2 With ioo6 a i8-ioo; a 20 cf. K. 1062* 5-20 (with ioo6 b 28-34 cf. 
1062* 20-3). 

3 Sc. and hence (on the view attacked) should be compatible with it. 

BOOK T. 4 ioo 7 a 

such a definition of anything, but that all attributes are 30 
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 35 
about a subject. The predication, then, must go on ad in- ioo7 b 
finitum. But this is impossible ; for not even more than two 
terms can be combined in accidental predication. For (i) 
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 5 
is musical, not in this sense, that both terms are accidental 
to something else. Since then some predicates are acci 
dental 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 direc 
tion ; 1 e. g. Socrates the white has not yet another acci 
dent ; for no unity can be got out of such a sum. Nor 10 
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 acci 
dental to Socrates ; and the accident is an accident of an 
accident not in cases of the latter kind, but only in cases of T 5 
the other kind, so that not all terms will be accidental. 2 
There must, then, even so be something which denotes sub 
stance. And if this is so, it has been shown that contra 
dictories 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 20 
man, if of every thing it is possible either to affirm or to deny 

1 i. e. in the direction of predicates, which are naturally wider or 
higher than the subject. 

2 Sense (i) reduces to sense (2), and in this an infinite number of 
accidents combined together is impossible ; there must be substance 


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 

25 statements are both true. And we thus get the doctrine of 
Anaxagoras, 1 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 attri- 

3 bute. 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 2 can be 

35 predicated, the negative must be predicable too ; and if the 
affirmative is not predicable, the negative, at least, will be 
ioo8 a 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. 3 

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 
5 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 4 is treated as 
a single proposition compounded out of two, the latter also 
is a single proposition opposite to the former. 5 

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 com- 

1 Fr. i. 2 Sc. trireme . 

8 With ico7 b i8-ioo8 a 2 cf. K. io62 a 23-30. 

4 Sc. that the thing is a man and a not-man. 

5 With 11. 6-7 cf. K. io62 a 36- b ;. 

BOOK T. 4 ioo8 a 

patible, or the theory is true of some statements and not of 10 
others. And if not of all, the exceptions will be contradic 
tories of which admittedly only one is true ; but if of all, 
again either the negation will be true wherever the asser 
tion 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) 15 
in the latter case there will be something which fixedly 
z s not, and this will be an indisputable belief ; and if non- 
being is something indisputable and knowable, the oppo 
site assertion will be more knowable. But (6) 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 pre 
dicates (and says, for instance, that a thing is white, arid 
again that it is not-white), or not. And if (i) it is not true 2 
to apply the predicates separately, our opponent is not say 
ing 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, 1 and man and God and trireme and their 
contradictories will be the same. For if contradictories can 25 
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 30 
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 

Again, it when the assertion is true, the negation is false, 
and when this is true, the affirmation is false, it will not be 35 
possible to assert and deny the same thing truly at the same 

1 ioc6 b 17, ioo7 a 6. 


ioo8 b time. But perhaps they might say this was the very ques 
tion 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 
5 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 

10 he says at the same time both yes and no . And if he 
makes no judgement but * thinks and 4 does not think , in 
differently, 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 

J 5 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 

20 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 

2 5 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. 1 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 

30 his health than one who is healthy ; for he who has opinions 

1 With 11. 12-27 cf. K. io63 a 28-35. 

BOOK T. 4 ioo8 fc 

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 35 
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 1009* 
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. 5 

5 From the same opinion proceeds the doctrine of Prota 
goras, 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 10 
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 15 
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 argu 
ment but their thought that one has to meet. But those 20 
who argue for the sake of argument can be cured only by 
refuting the argument as expressed in speech and in words. 1 
Those who really feel the difficulties have been led to 
this opinion by observation of the sensible world, (i) They 

1 With 11. 16-22 cf. K. io6s b 7-i6. 


think that contradictories or contraries are true at the same 
time, because they see contraries coming into existence out 

25 of the same thing 1 . 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 Demo- 
critus too ; for he says the void and the full exist alike in 
every part, and yet one of these is being, and the other 

30 non-being. 1 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 

35 potentially at the same time two contraries, but it cannot 
actually. 2 And again we shall ask them to believe that 
among existing things there is also another kind of sub 
stance to which neither movement nor destruction nor 
generation at all belongs. 

ioo9 b 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, 
5 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 

10 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 altera- 

1 With 11. 6-1 6, 22-30 cf. K. io62 b 12-24. 

2 With 11. 30-6 cf. K. 1062*24-33. 

BOOK T. 5 ioo9 b 

tion, that they say that what appears to our senses must be 
true ; for it is for these reasons that both Empedocles and 1 5 
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. 1 

And elsewhere he says that 

So far as their nature changed, so far to them always 20 
Came changed thoughts into mind. 2 

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. :i 

A saying of Anaxagoras to some of his friends is also 25 
related, that things would be for them such as they sup 
posed 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 , 4 
which implies that even those who are bereft of thought 30 
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 V 5 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 35 
have such opinions and express these views about the truth, 
is it not natural that beginners in philosophy should lose 
heart ? For to seek the truth would be to follow flying 

But the reason why these thinkers held this opinion is ioio a 
that while they were inquiring into the truth of that which 
is, they thought that which is was identical with the 

1 Fr. 106. 2 Fr. 108. 3 Fr. 16. 

* Cf. //. xxiii. 698, which does not, however, refer to Hector. 

6 With a 38- b 33 cf. K. 1063* 35~ b 7. 


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 ; 1 and therefore, 
while they speak plausibly, they do not say what is true 
5 (for it is fitting to put the matter so rather than as Epichar- 
musput it against Xenophanes 2 ;. 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. 

10 It was this belief that blossomed into the most extreme of 
the views above mentioned, that of the professed Hera- 
cliteans, 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 ; 3 for he thought one could 
not do it even once. 

J 5 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 some 
thing 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, there will be present something that 

20 exists ; and if a thing is coming to be, there must be some 
thing 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 

25 respect of its form that we know each thing. 4 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 

1 Cf. ioo9 a 32. 

2 Fr. 252 Kaibel. Epicharmus may have said that Xenophanes 
views were neither plausible nor true , or that they were true but 
not plausible . 

3 Fr. 91. 4 With 11. 22-5 cf - K . io63 a 22-8. 

BOOK r. 5 ioio a 

us is always in process of destruction and generation ; but 3 
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. 1 And again, obviously we shall make to 
them also the same reply that we made long ago ; 2 we 
must show them and persuade them that there is something 
whose nature is changeless. Indeed, those who say that 35 
things at the same time are and are not, should in conse 
quence 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 ioio b 
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 5 
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 
sleeping or to the waking. For obviously they do not 
think these to be open questions ; no one, at least, if when 10 
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, 3 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 sensa- 15 
tion 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, 4 are not equally authoritative, but in the 

1 With 11. 25-32 cf. K. 1063* 10-17. 

2 Cf. 1009*36-8. 3 Cf. Theaetetus 178 6-179 A. 

4 E.g. the awareness which smell gives us of savour and of odour 


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 

20 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, 

25 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. 1 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 . 

3 o 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 sub 
strata which cause the sensation should not exist even apart 

35 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 

ion a 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 6 
and among those who merely profess these views, some who 
5 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 ; 2 for they seek a starting-point, and they seek 

1 With 11. 1-26 cf. K. io62 b 33-io63 a io. 

2 The reference may be to Antisthenes. 

BOOK T. 6 ion* 

to get this by demonstration, while it is obvious from their 10 
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 15 
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. 1 But if not all 
things are relative, but some are self-existent, not every 
thing 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, 20 
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, andw/ien, 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 25 
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 2 say that what appears is true, and 30 
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), 3 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 35 
the same time , so that what appears will be with these 
qualifications true. But perhaps for this reason those who ion b 
argue thus not because they feel a difficulty but for the sake 

1 With 11. 3-16 cf. K. 1063*7-16. a Cf. ioo9 a 38-ioio a 15. 

3 With 11. 31-4 cf. K. io62 b 33-io63 a 10. 



of argument, should say that this is not true, but true for 
this man. And as has been said x before, they must make 

5 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, 2 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 corre 
lative. 3 If, then, in relation to that which thinks, man and 

10 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 

Let this, then, suffice to show (i) that the most indis 
putable 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 

15 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. 

20 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 par 
ticular relations, or one in a particular relation and one 
without qualification. 4 

But on the other hand there cannot be an intermediate 7 

between contradictories, but of one subject we must either 

25 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, 

2 Sc. without some one s first thinking so. 

3 Sc. but the equal to the equal, the half to the double. 

4 With 11. 17-22 cf. K. io63 b 17-19- 

BOOK r. 7 ion b 

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. 1 Again, the intermediate between the contradictories 
will be so either in the way in which grey is between black 3o 
and white, 2 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 3 and to their intermediates. (<5) But if it 35 
is really intermediate, 4 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 ioi2 a 
or reason the understanding either affirms or denies this is 
obvious from the definition whenever it says what is true 
or false. When it connects in one way by assertion or nega 
tion, it says what is true, and when it does so in another way, 
what is false. Again, there must be an intermediate between 5 
#// 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 genera 
tion and destruction. Again, in all classes in which the 
negation of an attribute involves the assertion of its con 
trary, even in these there will be an intermediate ; for 10 
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 definition. Again, the process will 
go on ad infinitum, and the number of realities will be 

1 Sc. by those who say there is an intermediate between contradic 
tories. Hence such a statement is neither true nor false, which is 

2 Though of course it differs from this case in being between con 
tradictories, not contraries. 

3 Sc. contrary, not contradictory opposites. 

4 Sc. as grey is between black and white. 


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, 1 and this new term 
will be some definite thing; for its essence is something 

15 different. Again, when a man, on being asked whether 
a thing is white, says 4 no , he has denied nothing except 
that it is ; and its not being is a negation. 

Some people have acquired this opinion as other para 
doxical opinions have been acquired ; when men cannot 
refute eristical arguments, they give in to the argument and 

20 agree that the conclusion is true. This, then, is why some 
express this view ; others do so because they demand 
a reason for everything. 2 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 definition. 3 
While the doctrine of Heraclitus, that all things are and are 

25 not, seems to make everything true, that of Anaxagoras, 
that there is an intermediate between the terms of a contra 
diction, 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- 8 
30 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 practi 
cally the same as that of Heraclitus ; for he who says that 
35 l all things are true and all are false also makes each of 
1012 these statements separately, so that since they are impos 
sible, the double statement must be impossible too. Again, 
there are obviously contradictories which cannot be at the 
same time truenor on the other hand can all statements 

1 i. e. if there is a term B which is neither A nor not- A, there will 
be a new term C which is neither B nor not-jS*. 

2 The reference may be to Antisthenes. 

5 With ion b 23-loi2 a 24 cf. K. io63 b 19-24. 

BOOK P. 8 ioi2 b 

be false ; yet this would seem more possible in the light of 
what has been said. But against all such views we must 5 
postulate, as we said above, 1 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 con- 10 
tradiction 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 I 5 
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. 2 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 20 
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 move 
ment. 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 25 
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 30 
which always moves the things that are in motion, and the 
first mover is itself unmoved. 

1 Cf. ioo6 a 18-22. 

2 With a 24- b 18 cf. K. io63 b 24-35 (with b 13-18 cf. io62 b 7-9). 

G 2 


4 BEGINNING means (i) that part of a thing from which i 

35 one would start first, e. g. a line or a road has a beginning 
ioi3 a in either of the contrary directions. (2) That from which 
each thing w r ould 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. (3) That from which, as an 
immanent part, a thing first comes to be, e. g. as the keel 
5 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 

10 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 apx af V an d so are tne arts > an d of 
these especially the architectonic arts. (6) That from which 

15 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. 

20 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 (i) that from which, as immanent 2 

1 The double meaning of apxn beginning and government - 
cannot be reproduced in English. 

BOOK A. 2 ioi3 a 

material, a thing comes into being, e. g. the bronze is the 25 
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 in 
clude this (e. g. the ratio 2 : i 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 3 
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 35 
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 5 
thing, and in no accidental sense (e. g. both the art of sculp 
ture 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 10 
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 5 
and both the presence and the privation are causes as 15 
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 hypo- 

20 theses 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 siib stratum (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, 

25 are all soiirces 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 \ve call it good or apparent good. 

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. 

30 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 

35 the classes which include these ; e. g. while in one sense 
the sculptor causes the statue, in another sense * Poly- 
clitus causes it, because the sculptor happens to be 
ioi4 a 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 

5 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 

10 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 

BOOK A. 2 ioi4 a 

image, and of this bronze 1 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 15 
of in two ways ; for (A) they are causes either as the indi 
vidual, or as the genus, or as the accidental, or as the genus 
that includes the accidental, and these either as combined, 2 
or as taken simply ; and (B) all may be taken as acting or 
as having a capacity. But they differ inasmuch as the act- 20 
ing causes, i. e. the individuals, exist, or do not exist, simul 
taneously 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. 3 25 

3 Element means (i) 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 con 
sists 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 30 
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 35 
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 demonstra- ioi4 b 

1 For this way of speaking cf. Phys. II. I94 a 33. 

2 Sc. the particular proper cause with the particular accidental, or 
the general proper with the general accidental. 

J With this chapter cf. Phys. I94 b 23-I95 b 21. 


tions ; 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, 
5 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), 

10 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 

15 thing is the first component immanent in each. 

* Nature means (i) the genesis of growing things the 4 
meaning which would be suggested if one were to pro 
nounce the v in fyva-is long. 2 (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 

20 object is present in it in virtue of its own essence. Those 
things are said to grow which derive increase from some 
thing 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 

3 5 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 

1 TJ on 7r\i(TTois shows that A. is not thinking of the strict universals 
of science but of the rough generalizations of dialectic. Cf. the use of 
o-TOLXfiov in the Topics , and Diels, Elementum, p. 29. 

2 This (i. e. growth ) is the etymological sense of (frvo-is. 
to grow , has v long in most of its forms. 

BOOK A. 4 ioi4 b 

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 3 
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 35 
natural objects, as with those who say the nature is the 
primary mode of composition, or as Empedocles 1 says : 

Nothing that is has a nature, ioi5 a 

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 5 
comprises both of these 2 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 10 
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 15 
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 

1 Fr. 8. 2 Matter and form. 


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

20 We call necessary (i) (a) that without which, as a con- 5 
dition, a thing 1 cannot live ; e. g. breathing and food are 
necessary for an animal ; for it is incapable of existing with 
out these ; (6) 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 

25 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 im 
pedes and tends to hinder, contrary to impulse and pur 
pose. For the compulsory is called necessary (whence the 
necessary is painful, as Evenus l says : For every necessary 

30 thing is ever irksome ), and compulsion is a form of neces 
sity, as Sophocles 2 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 

35 is. And from this sense of necessary all the others are 
somehow derived ; for a thing is said to do or suffer what 
ioi5 b is necessary in the sense of compulsory, only when it can 
not act according to its impulse because of the compelling 
force, 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 
5 good, in the other life and being, are not possible without cer 
tain conditions, these are necessary, and this kind of cause 
is a sort of necessity. Again, demonstration is a neces 
sary 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 

10 than themselves ; others do not, but are themselves the 

1 Fr. 8 Killer. 2 Electra 256. 

BOOK A. 5 iois b 

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 15 
nature attaches to them. 

6 One means (i) that which is one by accident, (2) that 
which is one by its own nature, (i) Instances of the acci 
dentally one are Coriscus and what is musical , and musical 
Coriscus (for it is the same thing to say 4 Coriscus and what 
is musical , and 4 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 20 
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 4 Coriscus because one of the 
parts of the phrase is an accident of the other, i. e. musical 25 
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 3 
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, 35 
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, ioi6 a 
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 


5 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 

10 are 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 

15 either simultaneous or not simultaneous ; but that of the 
straight line is always simultaneous, and no part of it which 
has magnitude 1 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 

20 farthest from, the final state. For, on 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 

25 though distinguished by opposite differentiae 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. 2 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 

30 genus) the genus above the proximate genera ; e. g. the 

1 Any point may remain fixed while the line rotates round it ; but 
a point has no magnitude. 

2 Cf. (b) (i) above. 

BOOK A. 6 ioi6 a 

isosceles and the equilateral are one and the same figure 
because both are triangles ; but they are not the same 
triangles. 1 

(c) Two things are called one, when the definition which 
states the essence of one is indivisible from another defini 
tion which shows us the other (though in itself every 
definition is divisible). Thus even that which has increased 35 
or is diminishing is one, because its definition is one, as, in 
the case of plane figures, is the definition of their form. In ioi6 b 
general those things the thought of whose essence is indi 
visible, 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 5 
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 10 
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 15 
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 begin 
ning of number ; for the first measure is the beginning, since 
that by which w r e first know each class is the first measure 

1 Horse, man, and dog are one, because all are animals. But if we 
are to call them one something^ we cannot call them one (kind of) 
animal, but must go to the higher genus and call them one (kind of) 
living thing. 


20 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 

25 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 it 
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 

30 in no way divisible in quantity is a point or a unit, that 
which has not position a unit, that which has position a 

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, 1 
by analogy those which are related as a third thing is to 

35 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 
ioi7 a 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 l one ; some things are many because they are not con- 

5 tinuous, 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 (i) in an accidental sense, (2) by 7 
their own nature. 

(i) In an accidental sense, e.g., we say * the righteous 
doer is musical , and the man is musical , and the musician 

1 Sc. the same category. Cf. note on A. 986 a 23. 

BOOK A. 7 ioi7 a 

is a man , just as we say the musician builds , because the 10 
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 15 
last two mean that both attributes are accidents of the same 
thing ; the first that the attribute is an accident of that 
which t s ; 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 t s.) Thus 
when one thing is said in an accidental sense to be another, 
this is either because both belong to the same thing, and 20 
this w, or because that to which the attribute belongs z>, 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 ; l for the senses 
of being are just as many as these figures. Since, then, 
some predicates indicate what the subject is, others its 25 
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 30 

(3) Again, being and is mean that a statement is 
true, not being that it is not true but false, 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 35 
of the things we have mentioned are potentially, others ioi7 b 
in complete reality. 2 For we say both of that which sees 

1 i. e. the categories. Cf. note on A. 986* 23. 

2 Omitting prjTov in 1017^ I. 


potentially and of that which sees actually, that it is seeing , 
and both of that which can actualize its knowledge and ot 
5 that which is actualizing it, that it knows, and both of that to 
w r hich 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 w T hich is not yet ripe that it is corn. 
When a thing is potential and when it is not yet potential 
must be explained elsewhere. 1 

I0 We call substance (i) the simple bodies, i. e. earth and 8 
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, 

15 being present in such things as are not predicated of a sub 
ject, 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 2 say, and the plane 

20 by the destruction of the line ; and in general number is 
thought by some 2 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) the 
ultimate substratum, which is no longer predicated of any 
thing else, and (B) that which, being a this , is also 

25 separable 3 and of this nature is the shape or form of each 

The same means (i) that which is the same in an acci- 9 
dental 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 ot 
30 the man. (The complex entity is the same as either of the 
1 e. 7. 2 The Pythagoreans and Plato. 3 Cf. H. 1042* 29. 

BOOK A. 9 ioi7 b 

simple ones and each of these is the same as it ; for both 
1 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 35 
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 ioi8 a 
are made without qualification. For 4 Socrates and musi 
cal 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 5 
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, i. e. 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 10 
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 (i) 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 all things 
that have their otherness in their essence. 

Those things are called like which have the same attri- 15 
butes 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. 1 The senses of unlike 
are opposite to those of like . 

1 Such attributes are hot and cold, wet and dry, rough and smooth, 

645-28 ]-[ 


20 The term opposite is applied to contradictories, and to 10 
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 
or their constituents. Grey and white colour do not belong 
at the same time to the same thing ; hence their constituents 
are opposed. 1 

2 5 The term contrary is applied (i) 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 

30 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 pro 
ducing or suffering them, or are losses or acquisitions, or 

35 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 category. 
The term other in species is applied to things which 
being of the same genus are not subordinate the one to the 
ioi8 b other, or which being in the same genus have a difference, 2 
or which have a contrariety in their substance ; and con 
traries are other than one another in species (either all 
contraries or those which are so called in the primary 
sense :5 ), and so are those things whose definitions differ in 
5 tiie infima species of the genus (e. g. man and horse are 

hard and soft, white and black, sweet and bitter. The more important 
pairs of contraries, in Aristotle s view, are the first two. 

1 We cannot say grey and white are opposites, but we say the consti 
tuents of grey (black and white) are opposites. 

2 This definition is wider than the previous one, since it includes 
species subordinate one to the other. 

3 Cf. a 25-31 in distinction from 31-35. 

BOOK A. 10 

indivisible in genus, but their definitions are different), and 
those which being- in the same substance have a difference. 1 
The same in species has the various meanings opposite to 

II The words prior and posterior are applied (i) to 
some things (on the assumption that there is a first, i. e. 
a beginning, in each class) because they are nearer some 10 
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 1 5 
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 w r hich is nearer the first mover is prior (e. g. the 20 
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 25 
are prior in arrangement ; these are the things that are 
placed at intervals in reference to some one definite thing 

1 No satisfactory explanation of this clause has been proposed. 
Alexander suggests that Aristotle may mean that individuals with the 
same specific essence differ in individual essence; but in ordinary 
language (which alone Aristotle is examining in A) these would not be 
called erep f idd. He also suggests that the reference may be to bodies 
such as earth and water which are eYepa e idfi without being contrary 
like fire and water; but these could hardly be said to be ev 177 avrf/ 
ovo-iq. Asclepius suggests more plausibly that the reference may be to 
different elements in the essence of complex substances, e.g. to heat 
and cold in the essence of man. Cf. vovs and amOr^is in the human 
soul. But probably the reference is to attributes present at different 
times in the same substance. 

H 2 


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. 

30 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 rela 
tion 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 musi- 

35 cal 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. 

1019 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 with 
out them, a distinction which Plato used. 1 (If we consider 
5 the various senses of being , 2 firstly the subject is prior, so 
that substance is prior; secondly, according as potency or com 
plete reality is taken into account, different things are prior, 
for some things are prior in respect of potency, others in re 
spect of complete reality, e. g. in potency the halfline 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 pos- 

10 terior ; 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 dissolu 
tion, e.g. the part without the whole. And the same is 
true in all other cases. 

1 The reference is to an oral utterance of Plato, or perhaps to the 
Platonic AicupeVay. Cf. Divisiones Aristoteleae, ed. Mutschmann, 
pp. xvii, xviii. 2 Cf. ch. 7. 

BOOK A. 12 1019* 

12 Potency means (i) a source of movement or change, 15 
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 20 
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 35 
(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 30 
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 35 
that over which something else has such a potency ; and in ioi9 b 
one sense that which has a potency of changing into some 
thing, whether for the worse or for the better (for even that 
which perishes is thought to be 4 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 5 
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 f 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 , 

10 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. 

15 Incapacity is privation of capacity i.e. of such a prin 
ciple 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 

20 both to that which only can produce movement and to that 
which can produce it well. 

vSome things, then, are called dSvvara in virtue of this 
kind of incapacity, while others are so in another sense ; 
i. e. both SVVCLTOV and aSvvarov a 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 

25 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 

30 seated is not of necessity false. The possible, then, in one 
sense, as has been said, means that which is not of necessity 

1 Aristotle passes now to Swarov and dbuvarov in the sense of possible 
and impossible . 

BOOK A. 12 1019 

false ; in one, that which is true ; in one, that which may be 
true. A potency or power 1 in geometry is so called 
by a change of meaning. These senses of capable or 
possible involve no reference to potency. But the senses 35 
which involve a reference to potency all refer to the primary 
kind of potency ; and this is a source of change in another iO2o a 
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 5 
another thing or in the same thing q2ia other . 

13 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 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 sur 
face, depth a solid. 

Again, some things are called quanta in virtue of their 
own nature, others incidentally ; e. g. the line is a quantum 15 
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 20 
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 2 5 
things that are quanta incidentally, some are so called in 

1 The reference is to squares and cubes. 


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 
30 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 (i) the differentia of the essence, e. g. 14 
man is an animal of a certain quality because he is tvvo- 

35 footed, and the horse is so because it is four-footed ; and a 
circle is a figure of particular quality because it is without 
iO2O b angles, which shows that the essential differentia is a 
quality. This, then, is one meaning of quality the differ 
entia 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, 
5 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 6 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. 

10 heat and cold, whiteness and blackness, heaviness and light 
ness, 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 

15 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,<?ua moving, and the 
differentiae of movements. Virtue and vice fall among these 
modifications ; for they indicate differentiae of the move- 

BOOK A. 14 io2o b 

ment or activity, according to which the things in motion 20 
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. 2 5 

Things are relative ( i ) 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 some 
thing 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 30 
measure, and the knowable to knowlege, and the per 
ceptible to perception. 

(i) Relative terms of the first kind are numerically 
related either indefinitely or definitely, to numbers them 
selves or to i. E.g. the double is in a definite numerical 
relation to i, and that which is many times as great is in 
a numerical, but not a definite, relation to i, i. e. not in this 35 
or in that numerical relation to it ; the relation of that io2i a 
which is half as big again as something else to that some 
thing is a definite numerical relation to a number ; that 

H ~\~ I 

which is - - times something else is in an indefinite rela 
tion to that something, as that which is many times as 
great is in an indefinite relation to i ; the relation of that 
which exceeds to that which is exceeded is numerically 
quite indefinite ; for number is always commensurate, and 5 
4 number is not predicated of that which is not commen 
surate, but that which exceeds is, in relation to that which 
is exceeded, so much and something more ; and this some 
thing 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 10 
the same whose substance is one ; those are like whose 


quality is one ; those are equal whose quantity is one ; and 
i is the beginning and measure of number, so that all these 
relations imply number, though not in the same way. 

15 (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 mimerical relations are 
not actualized except in the sense which has been else- 

20 where * 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 

25 way. 2 Further, some relative terms imply privation of 
potency, i. e. * incapable and terms of this sort, e.g. * in 
visible . 

Relative terms which imply number or potency, there 
fore, are all relative because their very essence includes in 
its nature a reference to something else, not because some 
thing else involves a reference to it ; but (3) that which is 

30 measurable or knowable or thinkable is called relative 
because something else involves a reference to it. For 
4 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 
4 of that of which it is the sight (though of course it is true 
io2i b to say this) ; in fact it is relative to colour or to something 
else of the sort. But according to the other way of speak 
ing the same thing would be said twice, the sight is of 
that of which it is. 

1 The reference may be to the H(p\ (Sewi/ and the Ile/ji rfys- ru>v 

2 i.e. there need not be any present relation to justify the use of the 
relative form of words in this case ; there is always the past relation. 

BOOK A. 15 io2i b 

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 rela- 5 
tive 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 10 
relative, if the same thing happens to be double and white. 

16 What is called complete is (i) 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 15 
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 20 
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 25 
end is something ultimate, we transfer the word to bad 
things and say a thing has been completely spoilt, and com 
pletely destroyed, when it in no wise falls short of destruc 
tion 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 3 
their own nature are so called in all these senses, some 
because in respect of goodness they lack nothing and can 
not be excelled and no part proper to them can be found out- 


side them, others in general because they cannot be exceeded 
in their several classes and no part proper to them is out- 
io22 a side them ; the others presuppose these first two kinds, and 
are called complete because they either make or have some 
thing of the sort or are adapted to it or in some way or 
other involve a reference to the things that are called com 
plete in the primary sense. 

Limit means (i) the last point of each thing, i.e. the 17 
first point beyond which it is not possible to find any part, 

5 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 ; 

10 and if of knowledge, of the object also. Evidently, there 
fore, 4 limit has as many senses as beginning , and yet 
more ; for the beginning is a limit, but not every limit is a 

That in virtue of which has several meanings : 18 
J 5 (i) 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 be found 
20 in the same number of senses as ; cause ; for we say in 
differently (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) KaO o l 
is used in reference to position, e. g. at which he stands 

1 Aristotle here mentions the original local sense of KCI& o. No 
English word or phrase has quite the same ambiguity. 

BOOK A. 18 io22 a 

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 25 
itself: (i) 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 3 
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 -footed but yet man is man in virtue of himself. 
(5) Whatever attributes belong to a thing alone, and in so 35 
far as they belong to it merely by virtue of itself considered 
apart by itself. 

19 Disposition means the arrangement of that which has 1022 
parts, in respect either of place or of potency or of kind ; 

for there must be a certain position, as even the word dis 
position shows. 

20 4 Having 1 means (i) 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 5 
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 l habit means 10 
a disposition according to which that which is disposed is 
either well or ill disposed, and either in itself or with refer 
ence 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. 

1 The word e|ts does duty for having , habit , and permanent 
state . 


15 Affection * means ( i) a quality in respect of which a thing 21 
can be altered, e. g. white and black, sweet and bitter, heavi 
ness and lightness, and all others of the kind. (2) The 
actualization of these the already accomplished altera 
tions. (3) Especially, injurious alterations and movements, 

20 and, above all, painful injuries. (4) Misfortunes and pain 
ful experiences when on a large scale are called affections. 

We speak of privation (i) if something has not one of 22 
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 attri- 

25 bute, 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, 1 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 blind 
ness 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 

30 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 natur 
ally have it, and invisible either because it has no colour at 

35 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 
J023 a 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 

1 i.e.* animal . 

BOOK A. 22 1023 

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 5 
bad , just or unjust , but there is also an intermediate state. 

23 To have or hold means many things : (i) 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 10 
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 hold the things con 
tained ; 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 15 
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, 1 implying that 20 
otherwise they would collapse on the earth, as some of 
the natural philosophers also say. 2 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 . 35 

24 To come from something means (i) 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 30 
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 

1 Cf. Hes. Theog. 517. >J Cf. De Caelo 284* 20-26. 


shape,) for the shape is the end, and only that which attains 
35 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 
ic23 b 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 some 
thing 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 
5 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 
10 equinox, and the festival of the Thargelia comes from the 
Dionysia, because after the Dionysia. 

Part means (i) (a) that into which a quantum can in 25 
any way be divided ; for that which is taken from a quan 
tum qua quantum is always called a part of it, e. g. two is 

I5 called in a sense a part of three. It means (), 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 

20 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 

3 5 part of the genus. 

BOOK A. 26 i023 b 

|a6 A whole means (i) 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 sever 
ally 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 
of whole) is true of a whole in the sense that it contains 3 
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, 1 
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 35 
said 2 in the case of unity also, wholeness being in fact a sort 
of oneness. 

Again (3), of quanta that have a beginning and a io24 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 5 
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, ex 
cept 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 10 
these units. 

27 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 

1 i. e. if they are only distinguishable, not distinct. 

2 Cf. ioi6 a 4. 

845-28 J 


equal to the remainder), but in general no number is thus 
mutilated ; for it is also necessary that the essence remain ; 

15 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. 

20 Again, they must be continuous ; for a musical scale con 
sists 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 

25 handle or a projecting part is removed, and a man is muti 
lated 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 c race or genus is used (i) if generation of 28 

30 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 lonians, 

because the former proceed from Hellen and the latter frorr 

Ion as their first begetter. And the word is used in refer- 

35 ence to the begetter more than to the matter, though people 

also get a race-name from the female, e. g. the descendants 

of Pyrrha > . 1 (3) There is genus in the sense in which 

iO24 b 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 

1 Aristotle thinks that the male supplies the efficient and the formal, 
the female the material cause of generation. 

BOOK A. 28 io24 b 

(4), in definitions the first constituent element, which is in 
cluded in the what , is the genus, whose differentiae the 5 
qualities are said to be. Genus then is used in all these 
ways, (i) 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 10 
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 l ) ; these also are not analysed either into one 1 5 
another or into some one thing. 

29 The false means (i) 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 commen 
surate with the side or * that you are sitting ; for one of 20 
these is false always, and the other sometimes ; it is in these 
two senses that they are non-existent. (6) 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 25 
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 to something other than that of which it is true ; 
e. g. the account of a circle is false when applied to a 
triangle. In a sense there is one account of each thing, i. e. 
the account of its essence, but in a sense there are many, 
since the thing itself and the thing itself with an attribute 30 

1 ioi7 a 24-27. 

I 2 


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 to be drawn that 
there could be no contradiction, and almost that there could 
be no error. But it is possible to describe each thing not 
35 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. 

io25 a 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 
5 people, just as we say things are false, 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 J (i. e. the man who knows 
and is wise) ; and further that he who is willingly bad is 
10 better. 2 This is a false result of induction for 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 

4 Accident means (i) that which attaches to something 30 
and can be truly asserted, but neither of necessity nor 

15 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 

20 might be pale ; but since this does not happen of necessity 
nor usually, we call it an accident. Therefore since there 

1 Hippias Minor 365-9. 2 Ib. 371-6. 

BOOK A. 30 1025 

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 25 
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. 

4 Accident has also (2) another meaning, i. e. all that 30 
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. 1 

1 An. Post. i. 75 a 18-22, 39-41, ;6 b 11-16. 


i025 b WE are seeking the principles and the causes of the I 
things that are, and obviously of them qzta being. For, 
while there is a cause of health and of good condition, and 
the objects of mathematics have first principles and 
5 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 

io this, but not into being simply nor qiia 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 

15 substance or of the essence, but some other way of exhibit 
ing 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 

30 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 

25 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 sub- 
stance-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, 

BOOK E. i i025 b 

inquiry is but idle. Of things defined, i. e. of whats , 3 
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 analogous 
to the snub in their nature e. g. nose, eye, face, flesh, bone, ic26 a 
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 5 
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 theo 
retical ; but whether its objects are immovable and separ 
able 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 I0 
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 separ 
ately 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 r 5 
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. 1 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 20 
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 
1 i. e. produce the movements of the heavenly bodies. 


might raise the question whether first philosophy is univer 
sal, or deals with one genus, i. e. some one kind of being ; 

25 for not even the mathematical sciences are all alike in this 
respect, geometry and astronomy deal with a certain par 
ticular 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, 

3 the science of this must be prior and must be first philo 
sophy, 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. 1 

But since the unqualified term being has several mean- 2 
ings, of which one was seen 2 to be the accidental, and another 

35 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 
iO26 b m ay have), and again besides all these there is that which 
4 is potentially or actually : since 4 being has many mean 
ings, we must first say regarding the accidental, that there 
can be no scientific treatment of it. This is confirmed by 
5 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 in 
numerable ; the house that has been made may quite well 
be pleasant for some people, hurtful to some, and useful to 
others, and different to put it shortly from all things 
that are ; j and the science of building does not aim at pro- 

10 ducing 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 

1 With ch. i cf. B. 955 b 10-13, 997** 15-25, K. 7. 

2 Cf. A. 7. 

3 For the point of the last clause cf. 11. 12, 17, below. The question 
as to the identity or difference of various things was popular with the 

BOOK E. 2 I026 1 

a mere name. And so Plato l was in a sense not wrong in 
ranking sophistic as dealing with that which is not. For the 15- 
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 every 
thing 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 20 
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 25 
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 3 
this the cause of the existence of the accidental ; for that 
which is neither always nor for the most part, we call acci 
dental. 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 35 
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 iO27 a 
the nature not of the builder but of the doctor to do this, 
but the builder happened to be a doctor. Again, a con 
fectioner, 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 
1 Cf. Sophistes 237 A, 254 A. 


5 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. There 
fore, since not all things either are or come to be of neces 
sity and always, but the majority of things areyftr the most 

\vpart, 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, every 
thing will be of necessity). The matter, therefore, which 
is capable of being otherwise than as it usually is, must be 

15 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 im 
possible. 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, 1 but that there is no science 

20 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 r 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. 4 on the day of new moon ; 

25 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 the re js no science which deals with it. 

That there are principles and causes which are generable 3 
and destructible without ever being in course of being 
30 generated or destroyed, is obvious. For otherwise all 
things will be of necessity, since that which is being gene 
rated or destroyed must have a cause which is not acci 
dentally its cause. Will A exist or not ? It will if B 

1 Cf. A. 6-8. 

BOOK E. 3 io27 a 

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, //"he goes out; and 1027 
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. 5 
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 10 
violence is not yet determined, but depends on the happen 
ing 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 fortuitous whether to 15 
matter or to the purpose or to the motive power, must be 
carefully considered. 1 

4 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 

1 The doctrine of the chapter seems to be as follows. Events in 
general occur as the necessary result of a series of causes. E. g. death 
is the necessary result of the presence of contrary elements in every 
living body. But there are certain events which, while beginning 
a causal nexus, are not the result of a causal nexus. We can never 
say of them, their conditions are being fulfilled, and they are coming 
to be. At one time they are not, and at another time they are. 
Therefore they come to be. But they never are coming to be. The 
events A. seems to be thinking of are those which he would ascribe to 
free will, e.g. a man s eating pungent food. Once he does this, his 
death in some determinate way is certain ; till he does it, only his 
death is certain. 


on combination and separation, and truth and falsity to 
gether depend on the allocation of a pair of contradictory 

20 judgements (for the true judgement affirms where the sub 
ject and predicate really are combined, and denies where 
they are separated, while the false judgement has the oppo 
site of this allocation ; it is another question, how it happens 
that we think things together or apart ; by together and 
4 apart I mean thinking them so that there is no succession 

2 5 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 l whats falsity and truth do 
not exist even in thought : this being so, we must consider 
later l what has to be discussed with regard to that which is 
or is not in this sense. But since the combination and the 

3 separation are in thought and not in the things, and that 
which is in this sense is a different sort of l being from the 
things that are in the full sense (for the thought attaches 
or removes 2 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 
iO28 a 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 
5 meanings of terms, that being has several meanings.] 3 

1 Cf. . 10. 2 Reading in 1. 33 

8 With chs. 2-4 cf. K. io64 b I5~io65 a 26. 


J THERE are several senses in which a thing may be said 10 

to be , as we pointed out previously in our book on the 

various senses of words ; l for in one sense the being 

meant is 4 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 T 5 

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 20 

the question whether the words to walk , to be healthy , 

4 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 35 

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. 3 o 

Now there are several senses in which a thing is said to 
be first; yet substance is first in every sense (i) in defini 
tion. (2) in order of knowledge, (3) in time. For (3) of the 
other categories none can exist independently, but only 

1 Cf. A. 7. 


35 substance. And (i) 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 
io28 b quantity, or its place ; since we know each of these pre 
dicates 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 l assert to be one, others more than 
5 one, and that some 2 assert to be limited in number, others ;>) 
unlimited. And so we also must consider chiefly and pri 
marily and almost exclusively what that is which t s in this 

Substance is thought to belong most obviously to bodies; 2 
and so we say that not only animals and plants and their 

10 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 

J 5 of these, or others as well, or none of these but only some 
other things, are substances, must be considered. Some 4 
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 the 

20 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 

1 The schools of Miletus and Elea. 

2 The Pythagoreans and Empedocles. 

3 Anaxagoras and the Atomists. 4 The Pythagoreans. 

BOOK Z. 2 io28 b 

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 l say Forms and numbers 25 
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 3 
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. 

3 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 sub- 35 
stratum 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 1029* 
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.) There- 5 
fore 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 10 
what, else is. When all else is stripped off evidently nothing but 
matter remains. For while the rest are affections, products, 

1 The school of Xenocrates. 


and potencies of bodies, length, breadth, and depth are 
quantities and not substances (for a quantity is not a sub- 

15 stance), 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. 

20 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 w r hich 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 sub 
stance, 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 charao 

25 terized ; 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 

30 be thought to be substance, rather than matter. The sub 
stance 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 

Some of the sensible substances are generally admitted 
to be substances, so that we must look first among these. 
iO2g b 3 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 
5 which is more knowable ; and just as in conduct our task is 
to start from what is good for each and make what is with 
out 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 

BOOK Z. 3 i029 b 

is often knowable to a very small extent, and has little or 
nothing of reality. But yet one must start from that which 10 
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. 

4 Since at the start x we distinguished the various marks i 
by which we determine substance, and one of these was 
thought to be the essence, we must investigate this. And 13 

. first let us make some linguistic remarks about it. The 
essence of each thing is what it is said to \>tpropter se. 2 
For being you is not being musical, since you are not by 
your very nature musical. What, then, you are by your T 5 
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 20 
of the essence of each thing. Therefore if to be a white 
surface is to be a smooth surface, 3 to be white and to be 
smooth are one and the same. 4 

But since there are also compounds answering to the 
other categories 5 (for there is a substratum for each category, 
e. g. for quality, quantity, time, place, and motion), we must 35 
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. to white man . 6 Let the compound be 

1 I028 b 33-6. 

2 It seems convenient here to translate thus the phrase translated in 
A. 18 as ; in virtue of itself. 

3 Cf. De Sensu 442 b 1 1 (on Democritus, whose doctrine, this is). 

4 i. e. this identification does not give the essence of surface (for 
surface is repeated) but it gives the essence of white , since this is 
not repeated but replaced by an equivalent. 

5 i. e. compounds of substance with the other categories. 

G XfvKos (iv0pu*7ros means a pale as opposed to a dark man, not a white 
man as opposed to a negro (cf. H. io44 b 25, I. ic-58 b 34, K. io68 a 17). 
But as Aristotle has already in this chapter used Xeu/coi/ in the general 
significance of white , I have thought it best to preserve this trans 
lation here and in chs. 5 and 6. 



denoted by cloak . What is the essence of cloak ? But, 
it may be said, this also is not & propter se expression. We 
reply that there are just two way sin which a predicate may 

3 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 ; 
iO3O a white man is white indeed, but its essence is not to be 

But is being-a-cloak an essence at all ? Probably not. For 
the essence is precisely what something is ; but when an attri 
bute is asserted of a subject other than itself, the complex is 
not precisely what some * this is, e. g. white man is not 
5 precisely what some 4 this is, since thisness belongs only to 
substances. 1 Therefore there is an essence only of those 
things whose formula is a definition. But we have a defini 
tion 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 2 ), but where there is a formula of something 

10 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, 3 or has it by 
accident ; but for everything else as well, if it has a name, 

15 there will be a formula of its meaning viz. that this 

1 The point is that \(v<6v is one thing, avdpu-rros another, while faov 
and SITTOVI/ are not distinct things but diirow is only a form of G>OV. 
Thus avQpnnos XCVKOS is not an individual type and cannot be defined, 
while (MOV SLTTOW is an individual type and can be defined. 

2 Sc. of the word Iliad . 

3 Cf. I037 b 14-21 for the interpretation of this. 

BOOK Z. 4 iQ30 a 

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 4 what a thing is , several mean 
ings ? * What a thing is in one sense means substance and 
the this , in another one or other of the predicates, quan- 2 o 
tity, 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 25 
just as, in the case of that which is not, some say, 1 empha 
sizing the linguistic form, that that which is not is not ts 
simply, but ts non-existent ; so too with quality. 

We must no doubt inquire how we should express our 
selves 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 30 
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 2 ), 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 35 
a reference to one and the same thing, not meaning one 
and the same thing, nor yet speaking ambiguously ; for iO3O b 
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 5 
primary and simple sense belong to substances. Still they 
belong to other things as well, only not in the primary 

1 Cf. PI. Soph. 237, 256 ff. 2 i. e. it is known to be unknown. 

K 2 


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 
10 the things that are one by being bound together, but in one 
of the main senses of * one , which answer to the senses of 
4 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 5 

15 an added determinant x 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 

20 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 
4 equal to quantity, and as all so-called 4 attributes propter 
se attach to their subjects. 2 And such attributes are those 
in which is involved either \hzformula or the name of the 
subject of the particular attribute, and which cannot be ex- 

25 plained 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. 3 
But there is also a second difficulty about them. For if 
snub nose and concave nose are the same thing, snub and 

30 concave will be the same thing ; but if snub and concave 
are not the same (because it is impossible to speak of snub- 

1 Cf. io29 b 30. 

2 In the sense of <a& avro explained in An. Post. i. 73* 37- b 3- 

3 a ^ 

BOOK Z. 5 io 3 o b 

ness apart from the thing of which it is an attribute propter 
se, for snubness is concavity -in-a- nose), either it is im 
possible 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 35 
infinite regress ; for in snub-nose nose yet another * nose 
will be involved. 

Clearly, then, only substance is definable. For if the iO3i a 
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 , 5 
will not be definable (but this escapes our notice because 
our formulae are not accurate). But if these also are de 
finable, either it is in some other way or, as we said, 1 
definition and essence must be said to have more than one 
sense. Therefore in one sense nothing will have a defini- 10 
tion 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. 

6 We must inquire whether each thing and its essence are 15 
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 20 
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 

1 1030 a i;- b i3. 


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 

25 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. 1 

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 

3 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 
iO3i b 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, 2 and (/?) the 
5 latter 3 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 know- 

1 The argument used in 11. 21-4 is : 

If essence of white man = white man, 

then since white man = man, 

and man = essence of man, 

. . essence of white man = essence of man. 

This is absurd, and Aristotle infers that essence of white man does 
not = white man. 

He next (11. 24-5) hints that this reductio ad absurdum fails because, 
while white man is (on the hypothesis under discussion) absolutely 
identical with the essence of white man, as well as man with the essence 
of man, white man is identical with man only per accidens. But, he 
urges (11. 25-8), it might at least seem to follow from the identification 
of an accidental unity with its essence that the accidental extremes, 
essence of white and essence of musical, are identical : - 

Musical man = essence of musical man. 

Man = musical man. 

White man = man. 

Essence of white man = white man. 

. .essence of white man = essence of musical man. 

. . essence of white = essence of musical. 
Which is absurd. 

2 The Ideas or things-themselves. 3 The essences. 

BOOK Z. 6 io 3 i b 

ledge of each thing only when we know its essence. And 
(/3) 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 10 
the essence of reality is not real, neither is any of the others. 
Again, that to which the essence of good does not belong l 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 15 
there are Ideas such as some people say there are, it will 
not be substratum that is substance ; for these must be sub 
stances, but not predicable of a substratum ; for if they were 
they would exist only by being participated in. 2 ) 

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 20 
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 2 5 
the same, and in a sense they are not ; for the essence of 
white is not the same as the man 3 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 3 
the essence of horse there will belong a second essence. 4 

1 i.e. the Idea of good (1. 5). 

2 i. e. as immanent in particulars. s Sc. who is white. 

4 Sc. and so ad infinitum. As an infinite process is absurd, why 
take the first step that commits you to it why say that the essence of 
horse is separate from the horse ? 


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 
iO32 a 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 (i) the essence of one. 
and (2) the one, so that to terms of the former kind the 
same argument will be applicable. 1 

5 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 
10 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, 7 
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. 

15 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 

20 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 

1 i. e. if the essence of one is different from the one, the essence of 
the essence of one is different from the essence Qf one. 

BOOK Z. 7 io 3 2 a 

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 pro 
duced 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 25 
productions are called makings . And all makings pro 
ceed either from art or from a faculty or from thought. 1 
Some of them happen also spontaneously or by luck 2 just 
as natural products sometimes do ; for there also the same 30 
things sometimes are produced without seed as well as from 
seed. Concerning these cases, then, we must inquire later, 3 
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 iO32 b 
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 5 
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 10 
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 think- I5 
ing and the other making, that which proceeds from the 
starting-point and the form is thinking, and that which pro 
ceeds from the final step of the thinking is making. And 

* Cf. E. I025 b 22. 

For the theory of these cf. Phys. ii. 5, 6. 
3 Cf. b 23-30, a b 


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 

20 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, 1 for the man who makes by 

25 art, as in healing the starting-point is perhaps the produc 
tion 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, 2 and so too with a house (the stones are 
the limiting-point here) and in all other cases. 

30 Therefore, as the saying goes, it is impossible that any 
thing 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 some- 
i033 a thing. But is the matter an element even in \hzformula ? 
We certainly describe in both ways 3 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. 
5 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 

1 Sc. not the thinking, cf. 11. 15-17. 

2 i. e. the minimum necessary basis. 

3 From the proportion established, warmth : health :: stones : house, 
and from the next paragraph, it would appear that warmth is treated 
as the matter which when specialized in a particular way becomes 

BOOK Z. 7 i033 a 

golden. 1 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 10 
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 be 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 par 
ticular shape or in bricks and timber the privation of 
arrangement as a house, the thing is thought to be pro- 15 
duced front 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 2 , not brass but brazen, not gold but 
golden J , and the house is said to be not bricks but bricken 
(though we should not say without qualification, if we 20 
looked at the matter carefully, even that a statue is pro 
duced 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. 

8 Since anything which is produced is produced by some 
thing (and this I call the starting-point of the production), 
and from something (and let this be taken to be not the priva- 25 
tion but the matter ; for the meaning we attach to this 
has already a been explained), and since something is pro 
duced (and this is either a sphere or a circle or whatever 
else it may chance to be), just as we do not make the sub 
stratum (the brass), so we do not make the sphere, except 
incidentally, because the brazen sphere is a sphere and we 
make the former. For to make a this is to make a this 30 
out of the substratum in the full sense of the word. 4 (I mean 

1 Aristotle uses the example of stone, but unfortunately we do not 
say stonen , 

2 Omitting 01 uXoi> in 1. 1 8. 3 Cf. 1032* 17. 
4 i. e. including form as well as matter (cf. lO29 a 3). 


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 
i033 b assumed. 1 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 thepro- 
5 cesses of making will regress to infinity. Obviously then the 
form also, 2 or whatever we ought to call the shape present 
in the sensible thing, is not produced, nor is there any pro 
duction 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 ; 

10 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 

J 5 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 

20 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 

1 a 25. 2 Sc. as well as the matter. 

BOOK Z. 8 i033 b 

father begets, a such out of a s this ; and when it has 
been begotten, it is a * this such V And the whole this , 
Callias or Socrates, is analogous to this brazen sphere , 
but man and animal to brazen sphere in general. Obvi- 2 5 
ously, 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 30 
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, 1034 a 
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, 5 
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. 

9 The question might be raised, why some things are pro 
duced spontaneously as well as by art, e. g. health, while 
others are not, e. g. a house. The reason is that in some i0 
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 

1 i. e. the artist, or the father, turns a mere piece of matter into 
a qualified piece of matter. 


way required, while other matter is incapable of this ; 
for many things can be set in motion by themselves but not 

J 5 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, 1 except by some 
thing 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 

20 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. 2 

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, q^ta produced by reason ; for the 
art of building is the form of the house), or from some 
thing which contains a part of it, if we exclude things 

25 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 3 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 con 

30 Therefore, as in syllogisms, substance 4 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. 5 

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 

iO34 b in a sense the same name as the offspring only in a sense, 

1 Sc. for building. 

2 i. e. an element of it pre-existing in the things themselves (cf. 

3 Sc. of the rubber s hand. 4 i. e. essence. 

5 Cf. TO eldos, 1. 24. 

BOOK Z. 9 i034 b 

for we must not expect parent and offspring always to 
have exactly the same name, as in the production of 
1 human being from human being ; 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. 1 The natural things which (like 
the artificial objects previously considered 2 ) can be produced 5 
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 pro 
duced 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 I0 
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 like 
wise ; for the quality does not come to be, but the wood ot 
that quality, and the quantity does not come to be, but the 15 
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. 

10 Since a definition is a formula, and every formula has 20 
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 35 
of the letters ; yet the circle is divided into segments as the 

1 Cf. 1033*33. 2 cf.*9- 3 2. 


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 

3 o prior to the right angle and the 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 4 part is used in 
several senses. One of these is l 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 
IO 35 a 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 
5 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 

10 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 

15 syllable, e. g. particular waxen letters or the letters as move 
ments in the air ; for in these also we have already some 
thing 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 com 
posed of these as parts of their essence, but rather as 

20 matter ; and these are parts of the concrete thing, but not 

BOOK Z. 10 i035 a 

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 2 5 
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 30 
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 it involves matter. 
For circle is used ambiguously, meaning both the circle. iO35 b 
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 5 
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 10 
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 15 


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 1 ), so that 
the parts of soul are prior, either all or some of them, to 
the concrete animal , and so too with each individual 

20 animal ; and the body and its 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 

25 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 sub 
stance but something composed of this particular formula 

30 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 ; 
1036* 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 intel 
ligible circles the mathematical, and by perceptible circles 
5 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 realiza 
tion it is not clear whether they exist or not ; but they are 
always stated and recognized by means of the universal for- 
1 And therefore not without soul. 

BOOK Z. 10 1036 

mula. But matter is unknowable in itself. And some matter 
is perceptible and some intelligible, perceptible matter being 10 
for instance bronze and wood and all matter that is change 
able, and intelligible matter being that which is present 
in perceptible things not qzia perceptible, i. e. the objects of 

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 15 
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 1 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 
part in one sense, i. e. to the parts included in the formula 
and to the parts of the individual right angle (for both the 20 
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 2 5 
others, must not. 

II 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 30 
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, 

1 Sc. to put it more widely so as to include the vegetable world. 

L 2 


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 

35 them. Of things which are not seen to exist apart, there 

1036** 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 

5 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 l 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 

10 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 2 make * two the line-itself, 

15 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 con 
fronted 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 defini 
tions 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 par 
ticular form in a particular matter, or particular things in 
a particular state. And the comparison which Socrates the 
younger 3 used to make in the case of animal 4 is not 

1 Aristotle is thinking of Pythagoreans. 

2 This probably includes Plato himself. 

3 Cf. PI. Theaet. 147 D ; Soph. 218 B ; Pol. 257 C ; Epp. 358 D. 

4 Cf. a 34~ b 7- 


BOOK Z. ii ios6 b 

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 30 
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, l because 
these parts are perceptible things ; for they are not. But 
perhaps this makes no difference ; for even some things 35 
which are not perceptible must have matter ; indeed there 1037** 
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 l ; for while one 
kind of matter is perceptible, there is another which is 

It is clear also that the soul is the primary substance and 5 
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, 2 has two 
meanings (for some mean by such a term the soul, and 
others mean the concrete thing), but if Socrates or 
4 Coriscus means simply this particular soul and this par 
ticular body, the individual is analogous to the universal in 
its composition. 3 

Whether there is, apart from the matter of such sub- 10 
stances, another kind of matter, and one should look for 
some substance other than these, e. g. numbers or some 
thing of the sort, must be considered later. 4 For it is for 

1 1035* 3o- b 3. 2 Cf. I036 a 16-17, H - i43 b 2-4. 

3 i.e. as man = soul -f body, Socrates = this soul + this body. 

4 Cf. M, N. 


the sake of this that we are trying- to determine the nature 
of perceptible substances as well, since in a sense the inquiry 

1 5 about perceptible substances is the work of physics, i. e. ot 
second philosophy ; for the physicist must come to know 
not only about the matter, but also about the substance ex 
pressed 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 

20 what is the thing one, although it has parts ?), this must 
be considered later. 1 

What the essence is and in what sense it is independent, 
has been stated universally in a way which is true of every 
case, 2 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 

25 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 ; 3 e. g. 

30 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. 4 And we have stated that the essence and the 
iO37 b thing itself are in some cases the same ; i. e. in the case of 
primary substances, e. g. curvature and the essence of curva 
ture, 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 
5 as their essences, nor are accidental unities like that of 

1 Cf. z. 12, H. 6. 2 Ch. 4. 

>J Chs. 10, ii. 4 Ch. 5. 

BOOK Z. ii io37 b 

Socrates and * musical ; for these are the same only by 
accident. 1 

12 Now let us treat first of definition, in so far as we have 
not treated of it in the Analytics 2 ; for the problem stated 
in them 3 is useful for our inquiries concerning substance. 
I mean this problem : wherein can consist the unity of 10 
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. 4 animal and * two-footed ? For in the 
case of man and * pale there is a plurality when one term 15 
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, 4 one does not share in 
the other ; the genus is not thought to share in its differ 
entiae (for then the same thing would share in contraries ; 
for the differentiae by which the genus is divided are con- 20 
trary). 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, feather- 
less. 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 25 
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 genus and the differentiae. The 30 
other genera are the first genus and along with this the 
differentiae that are taken with it, e. g. the first may be 
1 animal , the next * animal which is two-footed , and again 
1 animal which is two-footed and featherless , and similarly 
if the definition includes more terms. And in general it iO38 a 

1 Ch. 6. 2 Cf. An. Post. ii. 3-10, 13. 3 Cf. ib. 97*29. 

4 That of * animal and two-footed . 


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 4 animal is genus, and 
the other is differentia. 

5 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 differentia ; e. g. endowed with feet is a differentia 

10 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-footedness is 

15 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 

20 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 
1 animal endowed with feet and two-footed we have said 
nothing other than 4 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. 

35 If then a differentia of a differentia be taken at each step, 
one differentia the last will be the form and the sub 
stance ; 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 differ 
entiae as there are cuts. Therefore it is plain that the 

BOOK Z. 12 ioa8 a 

definition is the formula which contains the differentiae, or, 
according to the right method, the last of these. This 30 
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 3s 

13 Let us return to the subject of our inquiry, which is iO38 b 
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 l and about the substratum, 2 of which we have 
said 3 that it underlies in two senses, either being a 4 this 5 
which is the way in which an animal underlies its attri 
butes 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 10 
universal is common, since that is called universal which is 
such as to belong to more than one thing. Of which indi 
vidual 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 predi cable of 15 
a subject, but the universal is predicable of some subject 

But perhaps the universal, while it cannot be substance 
in the way in which the essence is so, can be present in this ; 

1 Chs. 4-6, 10-12. 2 Ch. 3. 3 io29 a 2-3, 23-4. 


e. g. * animal can be present in man and horse . Then 
clearly it is 1 a formula of the essence. And it makes 
no difference even if it is 2 not a formula of everything that 

20 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. 
4 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 

25 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 
4 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 separ 
able from it. Further, Socrates will contain a substance 
present in a substance 3 , so that this will be the substance 

30 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 parti 
cular 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 

35 plain that no universal attribute is a substance, and this is 
plain also from the fact that no common predicate indicates 
iO39 a a this , but rather a such . If not, many difficulties 
follow and especially the third man . 4 

The conclusion is evident also from the following con 
sideration. A substance cannot consist of substances present 
in it in complete reality ; for things that are thus in com- 
5 plete 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 

1 Reading in 1. 19 m . 2 Reading in 1. 

3 Reading in 1. 29 ovaia ova-ia. * Cf. A. 99O b 17. 

BOOK Z. 13 1039 

complete realization of the halves divides them from one 
another) ; therefore if the substance is one, it will not con 
sist of substances present in it and present in this way, 
which Democritus describes rightly ; he says one thing can 
not be made out of two nor two out of one ; for he identifies 10 
substances with his indivisible magnitudes. It is clear there 
fore that the same will hold good of number, if number is 
a synthesis of units, as is said by some 1 ; for two is either 
not one, or there is no unit present in it in complete 

But our result involves a difficulty. If no substance can 15 
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 thottght by all and 
was stated long ago 2 that it is either only, or primarily, 
substance that can be defined ; yet now it seems that not 20 
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. 3 

14 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 2 5 
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 same formula in either case.) If then there 30 
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 (i) if the animal in the horse and in man is 

1 Thales is said to have defined number as a system of units . 

2 Cf. 1031*11-14. 3 Cf. Z. 15, H. 6. 


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, (6) 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 
5 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 i 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 
10 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 
4 animal in each species derived, and how will it be derived 
15 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 con 
sequences 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. 

20 Since substance is of two kinds, the concrete thing and 15 
the formula (I mean that one kind of substance is the for 
mula 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 

BOOK Z. 15 io 3 9 b 

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 with- 25 
out generation and destruction formulae are and are not ; 
for it has been shown l 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 30 
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 1040** 
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- 5 
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 10 
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 15 
the elements ; e. g, l two-footed animal belongs to animal 

1 Ch. 8. 


and to the two-footed. (And in the case of eternal entities 1 
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 

20 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 

25 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, 2 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. 

30 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, 3 it will no longer be the sun ; but 
it is strange if this is so ; for the sun means a certain 
sitbstance] ; 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 
iO4o b 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. 

5 Evidently even of the things that are thought to be sub- 16 
stances, most are only potencies, both the parts of animals 
(for none of them exists separately ; and when they are 

1 i. e. the Ideas. 2 Cf. 1. 17. 3 Sc. at night. 

BOOK Z. 16 i040 b 

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 10 
the parts of living 1 things and the parts of the soul nearly 
related to them to turn out to be both, i.e. existent in com 
plete 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 15 
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 20 
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 com 
mon 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 25 
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 30 
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 io4i a 


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 be some. Clearly, 
then, no universal term is the name of a substance, and no 
5 substance is composed of substances. 

Let us state what, i. e. what kind of thing, substance 17 
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 pur- 

10 sue 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 

15 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 \ l unless one were 
to answer because each thing is inseparable from itself, 
and its being one just meant this ; this, however, is com 
mon to all things and is a short and easy way with the 

20 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 ? 

2 5 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 

1 Sc. and therefore in this case, when the fact is known, there is no 
question as to the why . 

BOOK Z. 17 i04i a 

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 3 
while the efficient cause is sought in the case of genesis 
and destruction, the final cause is sought in the case of being 

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 iO4i b 
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 5 
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 10 
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 2 a heap but like a syllable, 
now the syllable is not its elements, ba is not the same as b 
and #, 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 15 
earth) ; the syllable, then, is something not only its ele 
ments (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, 
(i) if it is an element the same argument will again apply ; ao 
for flesh will consist of this and fire and earth and some 
thing still further, so that the process will go on to infinity. 

1 Not even the protasis of the sentence beginning io4i b n is ever 
completed ; the parenthesis beginning 17 Se <7iAXa/3^, 1. 12, is so long 
that the original construction is forgotten. 

2 Omitting ai/ in 1. 12. 

645-28 M 


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. 

35 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 sitbstance 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 

3 of nature, their substance would seem to be this kind of 
nature V 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. 

1 Sc. the formal cause. Cf. A. ioi4 b 36 in contrast with ib. 27. 


I WE must reckon up the results arising from what has been 1042* 
said, and compute the sum of them, and put the finishing 
touch to our inquiry. We have said that the causes, princi- 5 
pies, and elements of substances are the object of our search. 1 
And some substances are recognized by every one, but some 
have been advocated by particular schools. Those gener 
ally recognized are the natural substances, i.e. fire, earth, 
water, air, &c., the simple bodies ; secondly, plants and 
their parts, and animals and the parts of animals ; and 10 
finally the physical universe and its parts ; while some 
particular schools say that Forms and the objects of mathe 
matics are substances. 2 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. 3 And with the universal 15 
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. 4 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 20 
the substance and what are not, and whether the parts of the 
substance are also parts of the definition. 5 Further, too, 
neither the universal nor the genus is a substance ; 6 we 
must inquire later into the Ideas and the objects of mathe 
matics ; 7 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, 25 
and sensible substances all have matter. The substratum is 

1 Cf. z. i. 2 Cf. z. 2. 3 Cf. Z. 3. io28 b 33-6. 

4 Cf. Z. 4-6, 12, 15. 6 Cf. Z. 10, ii. 

6 Cf. Z. 13, 14, 16. I04o b i6-i04i a 5. 7 Cf. M and N. 

M 2 


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 

30 thirdly the complex of these two, which alone is generated 
and destroyed, and is, without qualification, capable of 
separate existence ; for of substances completely expres 
sible in a formula some are separable and some are not. 

But clearly matter also is substance ; for in all the oppo 
site changes that occur there is something which underlies 
the changes, e. g. in respect of place that which is now here 

35 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 ; 
iO42 b and similarly in respect of substance there is something that 
is now being generated and again being destroyed, and 
now r l underlies the process as a l this and again 2 underlies 
it in respect of a privation of positive character. And in this 
change the others are involved. But in either one or two 
5 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. 3 

Since the substance which exists as underlying and 2 
as matter is generally recognized, and this is that which 

10 exists potentially, it remains for us to say what is the sub 
stance, in the sense of actuality, of sensible things. Demo- 
critus 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. 4 

15 But evidently there are many differences ; for instance, 
some things are characterized by the mode of composition 

1 Sc. in the case of destruction. 2 Sc. in the case of generation. 
8 Cf. Phys. 22 S a 12-20, De Gen. et Corr. 317* 17-31. 
4 Cf. A. 9 8s b 13-19. 

BOOK H. a i042 b 

of their matter, e. g. the things formed by blending, such as 
honey-water ; and others by being bound together, e. g. 
a 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 2 o 
and breakfast ; and others by place, e. g. the winds ; and 
others by the affections proper to sensible things, e. g. hard 
ness 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 ; 25 
a thing is a threshold because it lies in such and such a posi 
tion, 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 3 
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 charac- 35 
terized 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 1043** 
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 sub 
stance in each case ; and as in substances that which is 5 
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 

10 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, 

15 bricks, and timbers are speaking of the potential house, for 
these are the matter ; but those who propose 1 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 com 
posed of matter and form (for the formula that gives the 
differentiae seems to be an account of the form or actuality, 

20 while that which gives the components is rather an account 
of the matter); and the same is true of the kind of defi 
nitions 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 

25 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 sub 
stance 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 3 
30 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 
35 whether an animal is a soul in a body or a soul ; for 
1 Reading in 1. 17 

BOOK H. 3 i043 a 

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, 1 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 actu- iO43 b 
ality. 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 2 we find that the syllable does not consist 5 
of the letters + juxtaposition, nor is the house bricks + juxta 
position. 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 posi 
tion, the position is not constituted by the threshold, but 
rather the latter is constituted by the former. Nor is man 10 
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, 3 they will not be stating the substance itself. 

(This, then, must either be eternal or it must be destruc- 15 
tible 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 else 
where 4 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 20 
the case of things which cannot exist apart from the in 
dividual instances, e. g. house or utensil. Perhaps, indeed, 
neither these things themselves, nor any of the other things 

1 Sc. whether the name means the form or the concrete thing. 

2 Aristotle returns to the subject discussed in ch. 2. 

3 Cf. A. 1017^14-15. * Cf. Z. 8. 


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 

25 a certain timeliness. They said that the * what cannot be 
defined (for the definition so called is a long rigmarole l ) 
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 

30 be perceptible or intelligible ; but the primary parts of 
which this consists cannot be defined, since a defmitory 
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, 2 
as numbers of units. For a definition is a sort of number ; 

35 for (i) it is divisible, and into indivisible parts (for defini- 
tory 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 
ic>44 a 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 

5 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 

1 Sc. and therefore cannot give the essence, which is simple. For 
the contemptuous meaning of paKpos \6yos cf. N. ic>9i a 7. 

2 The Pythagoreans and Platonists (cf. M. 6, 7), 
8 Reading in 1. 35 arreipoi. &rreipos is a misprint. 

BOOK H. 3 1044* 

a complete reality and a definite nature. And (4) as 
number does not admit of the more and the less, neither does 10 
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 

4 Regarding material substance we must not forget that 15 
even if all things come from the same first cause 1 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 20 
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 35 
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 30 
moving principle, is the same ; for if both the matter and 
the moving cause were different, the product would be so 

When one inquires into the cause of something, one 
should, since l causes are spoken of in several senses, state 
all the possible causes. E. g. what is the material cause of 
man ? Shall we say the menstrual fluid ? What is the 35 

1 Sc. material cause. 


moving cause ? Shall we say the seed ? The formal cause ? 
His essence. The final cause ? His end. But perhaps the 
iO44 b 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 

5 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 

ic is the cause of eclipse ? What is its matter ? There is none ; 
the moon is that which suffers eclipse. 1 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. 2 E. g. what is eclipse ? Deprivation of 
light. But if we add 4 by the earth s coming in between , 

15 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 affection 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 

20 proximate subject is this due ? 

Since some things are and are not, without coming to be 5 
and ceasing to be, e. g. points, if they can be said to be, and 
in general forms (for it is not white that 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 
25 contraries can come from one another, but it is in different 

1 i. e. the substratum of a substance is bare matter, but the sub 
stratum of an attribute is a determinate substance such as the moon. 

2 Sc. the efficient cause. 

BOOK H. 5 i044 b 

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 an 
other. 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 30 
potentially healthy, and disease is contrary to health, is it 
potentially both healthy and diseased ? And is water poten 
tially 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), 35 
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 104 5 a 
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 5 
goes back to water, and only then becomes wine. 

6 To return to the difficulty which has been stated 1 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 besides the parts, 
there is a cause ; for even in bodies contact is the cause of 10 
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, 

1 Cf. Z. 12, H. io44 a 2-6. 


15 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 ? 

20 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 an 
other is form, and one is potentially and the other actually, 

25 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 ; l for this word would be 
a sign of the defmitory 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 

30 other form. What, then, causes this that which was poten 
tially 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. 2 Of matter some is intelligible, 
some perceptible, and in a formula there is always an 

35 element of matter as well as one of actuality ; e. g. the 
circle is a plane figure . 3 But of the things which have no 
matter, either intelligible or perceptible, each is by its 
iO45 b 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 defini 
tions), 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 
5 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. 

1 Cf. Z. I029 b 28, de Int. i8 a 19. 

2 i. e. it was the essence of the potential ball to become an actual 
ball, and of the actual ball to be produced from a potential ball. 

3 Aristotle does not give the whole definition, but only the genus, or 
material element. 

BOOK H. 6 i045 b 

Owing to the difficulty about unity some speak of par 
ticipation , 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 com- 10 
munion 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 con 
nexion 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 15 
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, 1 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, 20 
and the potential and the actual are somehow one. There 
fore 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 qualifi 
cation essentially unities. 

1 Cf. a 23-33. 


WE have treated l of that which is primarily and to which i 
all the other categories of being are referred i. e. of sub 
stance. For it is in virtue of the concept of substance that 

30 the others also are said to be quantity and quality and the 
like ; for all will be found to involve the concept of sub 
stance, as we said in the first part of our work. 2 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 

35 add a discussion of potency and complete reality. And first 
let us explain potency in the strictest sense, which is, hovv- 
I046 a ever, 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 3 explain 
the other kinds of potency as well. 

We have pointed out elsewhere 4 that potency and the 
5 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 4 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 

10 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 

1 Cf. ZH. 2 Cf. z. i. 

3 Cf. 0. 1048* 27- b 6. 4 Cf. A. 12. 

BOOK 0. i i046 a 

or by the thing itself qua other by virtue ot an originative 
source of change. In all these definitions is implied the 15 
formula of 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 20 
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 par 
ticular way can be crushed ; J and similarly in all other cases. 25 
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 
1 impotence and impotent stand for the privation which 
is contrary to potency of this sort, so that every potency 3 
belongs to the same subject and refers to the same process 
as a corresponding impotence. Privation has several senses ; 
for it means (i) 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 (/?) when it has not it at all. And in certain 
cases if things which naturally have a quality lose it by 35 
violence, we say they have suffered privation. 

2 Since some such originative sources are present in soul 
less things, and others in things possessed of soul, and in 
soul, and in the rational part of the soul, clearly some iO46 b 

1 i. e. the event would not happen if the passive factor were different. 
What is oily cannot necessarily be crushed, nor what is yielding burnt. 


potencies will be non-rational and some will be accom 
panied 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 
5 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 botli 
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 

10 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 

15 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 

20 produces both the contrary effects. For the rational for 
mula 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. 1 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. 

25 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 
1 i. e. with the rational formula. 

BOOK 0. 2 i046 b 

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. 

3 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 can- 30 
not build, but only he who is building, when he is building ; 
and so in all other cases. It is not hard to see the absurdi 
ties 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 35 
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 for- 1047* 
getfulness 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 ? 2 And similarly with regard to lifeless things ; 
nothing will be either cold or hot or sweet or perceptible 5 
at all if people are not perceiving it ; so that the upholders 
of this view will have to maintain the doctrine of Pro 
tagoras. 3 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 wall be blind many times in the day 
and deaf too. 

Again, if that which is deprived of potency is incapable, 10 
that which is not happening will be incapable of happen 
ing ; but he who says of that which is incapable of happen 
ing either that it is or that it will be will say what is untrue ; 
for this is what incapacity meant. Therefore these views 

1 The object of knowledge is always a form, which is eternal. The 
matter which makes things perishable is no object for knowledge. 

2 The protasis here states facts, the apodosis states a conclusion 
which follows from the Megaric theory, and the final question states 
a difficulty which follows from the apodosis. 

3 Cf. r. 5, 6. 

645-28 N 


15 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 ot 
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 

20 they are seeking to annihilate), so that it is possible that a 
thing may be capable of being and not be, and capable ot 
not being and yet be, 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 im- 

25 possible 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. 

30 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 

35 are moved ; and this because, while ex hypotkesi \hey do not 
actually exist, they would have to exist actually if they 
iO47 b were moved. For of non-existent things some exist poten 
tially ; but they do not exist ^ because they do not exist in 
complete reality. 

It what we have described l is identical with the capable or , 

convertible with it, evidently it cannot be true to say * this 

5 is capable of being but will not be \ which would imply that 

the things z>/capable of being would on this showing vanish. 

Suppose, for instance, that a man one who did not take 

Cf. 1047*24-26. 

BOOK 0. 4 i047 b 

account of that which is incapable of being- were to say 
that the diagonal of the square is capable of being 1 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 cap- 10 
able of being, to be or to have come to be, there will be 
nothing impossible in this ; but the result will be im 
possible, 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 15 
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 20 
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^ 
being thus related, 1 B is not possible on this condition, 2 A 25 
and B will not be related as was supposed. 3 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 w r hen 
and in the way in which it was supposed capable of being 
real, B also must then and in that way be real. 3 o 

5 As all potencies are either innate, like the senses, or come 
by practice, like the power of playing the flute, or by learn 
ing, like artistic power, those which come by practice or by 
rational formula we must acquire by previous exercise but 

1 Sc. so related that if the reality of A implies the reality of B the 
possibility of A implies the possibility of B. 
" Sc. if A is possible. 
3 Sc. so related that the reality of A implies the reality of B. 

N 2 


this is not necessary with those which are not of this nature 
and which imply passivity. 

35 Since that which is * capable is capable of something and 
iO48 a at some time and in someway (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 non-rational and their potencies are non-rational, and 
the former potencies must be in a living thing, while the 
5 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 non-rational 
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 

10 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 

! 5 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 no 
thing external prevents it is not further necessary ; for it has 
the potency on the terms on which this is a potency of act 
ing, and it is this not in all circumstances but on certain 
conditions, among which will be the exclusion of external 

20 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. 

BOOK 0. 6 1048* 

6 Since we have treated 1 of the kind of potency which is 25 
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 poten 
tial, 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, w r hich is the reason of 
the inquiry in the course of which we have discussed these pre- 3 
vious 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 \vho 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 mean- 35 
ing 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 w r aking to the sleep- 1048 
ing, 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. 5 
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 10 
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 

1 Cf. e. 1-5. 


15 potentially only for knowledge. For the fact that the pro 
cess of dividing never comes to an end ensures that this 
activity exists potentially, but not that the infinite exists 

Since of the actions which have a limit none is an end but 
all are relative to the end, e. g. the removing of fat, or fat- 
20 removal, and the bodily parts themselves when one is 
making them thin are in movement in this way (i. e. with 
out 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 
25 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 move- 
so ments, 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, or is 
thinking and has thought. The latter sort of process, then, 
I call an actuality, and the former a movement. 

35 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 7 
when it does not ; for it is not at any and every time. 
1049* E.g. is earth potentially a man ? No but rather when it 
has already become seed, and perhaps not even then. It is 

BOOK 0. 7 1049* 

just as it is with being healed ; not every thing 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 (i) the delimiting mark of that which as a result of 5 
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 10 
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 ex 
ternal 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 15 
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). 1 

It seems that when we call a thing not something else but 
thaten e. g. a casket is not wood but wooden , and 20 
wood is not l earth but 4 earthen , and again earth will illus 
trate 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 par 
ticular wood of this particular casket. And if there is a first 
thing, which is no longer, in reference to something else, 

1 The classes marked by (i) and (2) are the works of art and of 
nature respectively, but at the end (2) is illustrated by an example 
from (i). 


25 called l thaten , this is prime matter ; e.g. if earth is airy 
and air is not 4 fire but l 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 

30 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 4 pale , and not ambula- 
tion or movement but walking or * moving , which is 
akin to the thaten .) Wherever this is so, then, the ulti 
mate subject is a substance ; but when this is not so but the 

35 predicate is a form and a this , the ultimate subject is 
matter and material substance. And it is only right that 
6 thaten should be used with reference both to the matter 
iO49 b and to the accidents ; for both are indeterminates. 1 

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 , 2 it 8 
5 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 move 
ment or of rest. For nature also is in the same genus as 
10 potency ; for it is a principle of movement not, however, 
in something else but in the thing itself gtia 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. 

(i) Clearly it is prior in formula ; for that which is in the 
primary sense potential is potential because it is possible 

1 Aristotle points out that there are two kinds of derivative predi 
cates those derived from the matter of the subject, like wooden , 
and those formed from the accidents of the subject, like musical . 
Matter and accidents have this in common, that they are indetermi 
nate matter having (relatively) no character and accidents not being 
confined to one special subject as essential predicates are. He mentions 
at the same time that there are two kinds of substratum the bare 
matter which underlies form or essence, and the complete individual 
which underlies accidents. Cf. Z. iO38 b 5. 

2 Cf. A. ii. 

BOOK 0. 8 io49 b 

for it to become active ; e. g. I mean by capable of build 
ing that which can build, and by capable of seeing that 15 
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 prior to it. I mean that to this particular man 
who now exists actually and to the corn and to the seeing 20 
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 25 
always a first mover, and the mover already exists actually. 
We have said in our account of substance 1 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 3 
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 35 
have come to be, and, of that which, in general, is chang 
ing, some part must have changed (this is shown in the 
treatise on movement 2 ), 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 5 
1 Cf. Z. 7, 8. 2 Cf. Phys. vi. 6. 


being to seed ; for the one already has its form, and the other 
has not), and because everything that comes to be moves to 
wards 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 

10 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 

15 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 r , 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 

20 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. 1 For the 
action is the end, and the actuality is the action. And so 
even the word 4 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 

25 other product besides this results from sight), but from 
some things a product follows (e. g. from the art of build 
ing 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. 

30 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 

1 The reference is apparently to a tricky painting in which the 
figure was painted so as to stand out in high relief. 

BOOK 0. 8 ioso a 

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 beingmoved ; but where there is noproduct 
apart from the actuality, the actuality is present in the agents, 35 
e. g. the act of seeing is in the seeing subject and that of theo 
rizing in the theorizing subject and the life is in the soul (and 
therefore well-being also ; for it is a certain kind of life). iO5O b 

Obviously, therefore, the substance or form is actuality. 1 
According to this argument, then, it is obvious that actuality 
is prior in substantial being to potency ; and as we have 
said, 2 one actuality always precedes another in time right 
back to the actuality of the eternal prime mover. 5 

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 10 
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 15 
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, 20 
exist potentially ; and, if there is an eternal mobile, it is not 
in motion in virtue of a potentiality, except in respect of 
4 whence and* whither (there is nothing to prevent its having 

1 This follows from the whole section a 4~ b 2 ; cf. esp. a 15, 16. 


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. 1 Nor do they tire in this activity ; for movement is 

25 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 2 are imitated by those that are in 
volved in change, e. g. earth and fire. For these also are 
ever active ; for they have their movement of themselves 

30 and in themselves. 3 But the other potencies, according to 
our previous discussion, 4 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. 

35 If, then, there are any entities or substances such as the 
dialecticians 6 say the Ideas are, there must be something 
much more scientific than science-itself and something more 
1051* 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 9 

the good potency is evident from the following argument. 

5 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 

1 e. g. Empedocles (cf. De Caelo, 284* 24-6). 

2 Sc. the heavenly bodies. 

3 i.e. they are both movers and moved. 4 Cf. b 8-i2. 

5 The Platonists are meant; cf. A. 987 b 3i. 

6 The Idea, being the universal apart from its special manifestations, 
will be a potentiality, and will therefore be inferior to the correspond 
ing particulars e. g. the Idea of science will be inferior to particular 
acts of scientific thought. 

BOOK 0. 9 iosi a 

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 10 
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 15 
actuality must be worse than the potency ; for that which 
4 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. 1 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, 2 o 
nothing perverted (for perversion is something bad). 2 

B D C 

It is by an activity also that geometrical constructions 3 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. 

1 Sc. while the eternal and substantial must be better than the 

2 The paragraph seems to be directed against Plato ; cf. Rep. 402 C, 
476 A, Theaet. i;6E, Laws 896 E, 8980. 

3 The figures required for the two theorems are as above. 


Why are the angles of the triangle equal to two right 
angles ? Because the angles about one point are equal to two 

25 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 perpen 
dicular from the centre the conclusion is evident at a 
glance to one who knows the former proposition. Obvi 
ously, therefore, the potentially existing constructions are 

30 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 

The terms being and non-being are employed firstly 10 

35 with reference to the categories, and secondly with refer 
ence to the potency or actuality of these or their non- 
iO5i b potency or non-actuality, 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 

5 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 

10 separated, and others are always separated and cannot be 
combined, while others are capable either of combination 
or of vSeparation, 4 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 

15 for it to be at one time correct and at another erroneous ; but 
regarding things that cannot be otherwise opinions are not 

BOOK 0. 10 iosi b 

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 2 o 
1 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 
follows contact and assertion are truth (assertion not being 
the same as affirmation), and ignorance is non-contact. 25 
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 30 
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 35 
object is existent it exists in a particular way, and if it does 
not exist in this way it does not exist at all. 1 And truth io52 
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 

1 i. e. we have not here A and B, which may or may not be com 
bined, but A, which if it exists at all exists as A. 


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, how 
ever, to suppose that one member of such a class has 
a certain attribute and another has not ; e. g. while w r e 
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 
10 possible ; for we cannot in this case suppose that one in 
stance has an attribute and another has not, but whether 
our judgement be true or false, it is implied that the fact is 


I WE have said previously, in our distinction of the various 15 
meanings of words, 1 that one has several meanings ; the 
things that are directly and of their own nature and not acci 
dentally called one may be summarized under four heads, 
though the word is used in more senses, (i) There is the 
continuous, either in general, or especially that which is con 
tinuous by nature and not by contact nor by being tied to 
gether ; and of these, that has more unity and is prior, whose 20 
movement 2 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 25 
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 30 
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 3 must be one in the 
primary sense. l One \ then, has all these meanings the 
naturally continuous and the whole, and the individual and 35 
the universal. And all these are one because in some cases 

1 A. 6. 

2 Nature is defined (A. ioi5 a i3) as the essence of things which 
have in themselves, as such, a source of movement . 

8 Sc. the form. 

845-28 O 


the movement, in others the thought or the definition is 

iO52 b 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. 
4 One has all these meanings, and each of the things to 
5 which one of these kinds of unity belongs will be one ; but 
4 to be one will sometimes mean being one of these 
things, and sometimes being something else l which is even 
nearer to the meaning of the word one while these other 
things approximate to its application. This is also true of 
4 element or 4 cause , if one had both to specify the things 
of which it is predicable and to render the definition of the 

10 word. For in a sense fire is an element (and doubtlessalso 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 parti 
cular thing with a nature of its own fire is an element, the 
name 4 element means that it has this attribute, that there 
is something which is made of it as a primary constituent. 

15 And so with cause and one and all such terms. For 
this reason, too, 4 to be one means to be indivisible, being 
essentially 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. 

20 For measure is that by which quantity is know r n ; and 
quantity qua quantity is known either by a one or by 
a number, and all number is known by a one . There 
fore all quantity qua quantity is known by the one, and 
that by which quantities are primarily known is the one it 
self; and so the one is the starting-point of number qua 
number. And hence in the other classes too measure 

25 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 4 weight and 4 speed are common 

to both contraries 2 ; for each of them has two meanings 

1 Cf. I052 b 16-19. 2 Sc. heavy and light, fast and slow. 

BOOK I. i 1052 

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 30 
certain speed and the comparatively light a certain 

In all these, then, the measure and starting-point is some 
thing 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 35 
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 iO53 a 
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 5 
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 move 
ment and the quickest ; for this occupies least time. And 10 
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 predic- 
able in the same sense of all of these, but in the sense we 
have mentioned. 

But the measure is not always one in number some 
times there are several; e.g. the quarter- tones (not to the [5 
ear, but as determined by the ratios) are two, and the articu 
late 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 

O 2 


of unit. 1 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 

20 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 2 only to 
perception, for doubtless every continuous thing is divisible. 
The measure is always homogeneous with the thing 

25 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 

30 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 some 
thing 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 

35 a fraction of us. But Protagoras says man is the measure 
of all things , 3 as if he had said the man who knows or 
IO 53 b l t ^ e man w ^ 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 remark 

1 Alexander thinks this means that a line may be measured either 
by the ideal measure (e. g. the standard yard) or by the particular 
imperfect measure (the yard-wand, which slightly differs from the 
standard yard). This sense does not agree with the context, and 
no doubt the meaning is that incommensurables must be measured by 
different units. 

2 Cf. I052 b 33, io53 a 5. 3 Fr. I. 

BOOK I. i io53 b 

Evidently, then, unity in the strictest sense, if we define 
it according to the meaning of the word, is a measure, and 5 
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 qiia one. 

2 With regard to the substance and nature of the one we 
must ask in which of two ways it exists. This is the very 10 
question that we reviewed J 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, 15 
another says it is air, and another the indefinite. 2 

If, then, no universal can be a substance, as has been said 3 
in 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 predi 
cate, clearly unity also cannot be a substance ; for being 20 
and unity are the most universal of all predicates. There 
fore, 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 ge era. 

Further, the position must be similar in all the kinds ot 
unity. Now unity has just as many meanings as being ; 
so that since in the sphere of qualities the one is something 25 
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 

1 B. iooi a 4- b 25. 

2 The three thinkers referred to are Empedocles, Anaximenes, 

3 Z. 13. 


30 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 

35 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 
iO54 a 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 

5 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 sub 
stance is not just to be one, the same must be true of 
substances also ; for it is true of all cases alike. 

10 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, 

15 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. 

20 The one and the many are opposed in several ways, of 3 
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 

BOOK I. 3 io54 a 

four kinds, and one of these two terms is privative in mean 
ing, they must be contraries, and neither contradictory nor 25 
correlative in meaning. 1 And the one derives its name and 
its explanation from its contrary, the indivisible from the 
divisible, because plurality and the divisible is more per 
ceptible than the indivisible, so that in definition plurality is 
prior to the indivisible, because of the conditions of percep 

To the one belong, as we indicated graphically in our 30 
distinction of the contraries, 2 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 ; (i) we 
sometimes mean the same numerically ; again, (2) we call 
a thing the same if it is one both in definition and in num 
ber, e. g. you are one with yourself both in form and in 
matter ; and again, (3) if the definition of its primary 35 
essence is one ; e. g. equal straight lines are the same, and iO54 b 
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, 5 
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 the same 
e. g. whiteness in a greater or less degree, are called like i 
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 15 

1 Two of the kinds, contrariety and privation, are not mutually ex 
clusive, for contrariety is the relation between a form and its complete 
privation. Cf. r. ioo4 b 2;, I. io55 b 26. 

2 Cf. r. ioo4 a 2. 


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. 1 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 ; 

20 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 

25 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, 2 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), 3 and in species if they have the same 

3 o genus ( genus meaning that identical thing which is essen 
tially predicated of both the different things). 

Contraries are different, and contrariety is a kind of differ 
ence. That we are right in this supposition is shown by 
induction. For all of these too are seen to be different ; 

35 they are not merely other, but some are other in genus, 
iO55 a and others are in the same line of predication, 3 and there 
fore in the same genus, and the same in genus. We have 
distinguished 4 elsewhere what sort of things are the same or 
other in genus. 

Since things which differ may differ from one another 4 
more or less, there is also a greatest difference, and this 

1 Cf. a 35- b 3. 2 See note on io5; b 36. 

8 See note on A. 986*23. * A. 9. 

BOOK 1. 4 io55 a 

I call contrariety. That contrariety is the greatest differ- 5 
ence 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. 10 
For that is greatest which cannot be exceeded, and that is 
complete beyond which nothing can be found. For the com 
plete 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 ajl else, and 15 
therefore there is nothing beyond the end, and the complete 
needs nothing further. From this, then, it is clear that con 
trariety 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 cannot have 
more than one contrary (for neither can there be anything 20 
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 differ 
ence, must be between two things. 

And the other commonly accepted definitions of con 
traries are also necessarily true. For not only is (i) the 
complete difference the greatest difference (for we can get 25 
no difference beyond it of things differing either in genus 
or in species ; for it has been shown T 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 

1 Cf. a 6. But how can we reconcile this with io54 b 27-30, 35 ? 


30 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). 1 

The primary contrariety is that between positive state 
and privation not every privation, however (for priva 
tion has several meanings), but that which is complete. 

35 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 priva- 
iO55 b tion 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, is either that which is quite 
5 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 distin 
guished 2 elsewhere. Privation, therefore, is a contradiction 
or incapacity which is determinate or taken along with the 
receptive material. This is the reason why, while contra 
diction does not admit of an intermediate, privation some- 

10 times 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 presum- 

15 ably not all privation is contrariety (the reason being that 
that which 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 con- 

1 Punctuating in 11. 32-3 p.ia, Iv . . . /neyiVr^). 2 A. 22. 

BOOK I. 4 io55 b 

trariety 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 20 
described ; 1 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 25 
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. 

5 Since one thing has one contrary, we might raise the 30 
question how the one is opposed to the many, and the 
equal to the great and the small. For if we use the word 
4 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 pro 
ceeding on a prior assumption and asking something such 35 
as whether it was Cleon or Socrates that came but 
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 iO56 a 
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 5 
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 uneqiiaL There- 


fore 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 

10 will be opposite to both (and the difficulty supports those 
who say the unequal is a two 1 ), 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 inter 
mediate, or, from its definition, can be so ; for it would not 
be complete 2 if it were intermediate between any two things, 
but rather it always has something intermediate between its 
own terms. 

J 5 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 

20 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 

2 5 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 some- 

3 thing 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 inter 
mediate between the good and the bad as if there must 
1 This is a Platonic doctrine ; cf. N. io8; b 7. 2 Cf. 1055* 16. 

BOOK I. 5 ios6 a 

be an intermediate in all cases. But this does not necessarily 
follow. For the one phrase is a joint denial of opposites 35 
between which there is an intermediate and a certain natural 
interval ; but between the other two there is no differ- ios6 b 
ence l ; for the things, the denials of which are combined, 
belong to different classes, so that the substratum is not one. 

6 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 2 , 5 
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 10 
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 con 
tinuum), 3 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 4 much , it is with a difference ; e. g. water is much 15 
but not many. But * many is applied to the things that 
are divisible ; in 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 20 
to say 4 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. 

1 Cf. 105 s a 6, 2.6. 

2 The Greek is o\iyov 77 oX/ya, which, it might seem, should be trans 
lated a little or a few . But the singular oXiyov is used only because 
of the difficulty of predicating the plural oX/-ya of one . On the other 
hand, TTO\V and rroXXa are used in the really distinct senses of much 
and many . oXiyov has been translated few in this chapter except 
where it is opposed to TTO\V and must be translated * little . 

3 i. e. a fluid. Cf. 1. 16. 


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. 

25 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 qualifi 
cation two is few ; for it is the first plurality which is 
deficient (for this reason Anaxagoras was not right in 
leaving the subject with the statement 1 that all things 
were together, boundless both in plurality and in smallness 

3 where for * and in smallness he should have said and in 
fewness ; for they could not have been boundless in few 
ness), 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 2 elsewhere the two senses 

35 in which relatives are so called: (i) 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 is few T er, 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 
5 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 

10 measured, the fact is that all knowledge is knowable, but not 
all that is knowable is knowledge, because in a sense know 
ledge 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 
1 Fr. i. 2 A. 1021*26-30. 

BOOK I. 6 ios7 a 

every sense; but in 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 15 
knowledge is to knowable, if plurality is number and the 
one is a measure. 

7 Since contraries admit of an intermediate and in some 
cases have it, intermediates must be composed of the con 
traries. For (i) all intermediates are in the same genus as ao 
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 35 
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 30 
kind ; for only between these can change take place in 
virtue of their own nature (so that an intermediate is im 
possible 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 35 
opposition, one or other side of which must attach to any 
thing whatever, i. e. which has no intermediate. Of other 
opposites, some are relative, others privative, others con 
trary. 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 io57 b 
there zs one. 

(3) If intermediates are in the same genus, as has been 
shown, and stand between contraries, they must be com 
posed 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 

5 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, 1 these differentiae piercing and compressing 

10 are prior ; so that these are prior contraries of one an 
other.) But, again, the species which differ contrarywise are 
the more truly contrary species. 2 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. 

15 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 (d) with regard to these contraries which 
do not fall within a genus that we must first ask of what 

20 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. 3 ) 
Now contraries do not involve one another in their com 
position, and are therefore first principles ; but the inter 
mediates 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 

25 the other contrary ; for it will have less of the quality in 

1 Cf. PI. Tim. 67 E ff. 

8 I now make the parenthesis end at Trportpa (1. n) and treat aXXa 
fjtrjv as beginning a new argument. 

8 Aristotle has first (ei /xV, 1. 4) considered the case of contraries in 
a genus, and shown that they involve prior contraries which are not 
in the genus, but when added to the genus constitute its species. These 
are the primary contraries, and it is primarily of them that we must 
ask, Of what are their intermediates composed? The sentence, 
11. 20-22, in which he reverts to contraries in a genus must be paren 
thetical. A species in a genus must either contain an element (sc. the 
differentia) which does not itself contain the genus, or (which is incom 
patible with its being a species) be an unanalysable term. 

BOOK I. 7 i057 b 

question than the one contrary and more than the other. 
This also, 1 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 30 
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. 2 Clearly, then, intermediates are (i) 
all in the same genus and (2) intermediate between con 
traries, and (3) all compounded out of the contraries. 

8 That which is other in species is other than something 35 
in something, and this must belong to both 3 ; 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 acci 
dental way, whether conceived as matter or otherwise. iO58 a 
For not only must the common nature attach to the differ 
ent 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 

1 i. e. this intermediate differentia comes between the extreme 
differentiae, as the intermediate species comes between the extreme 

2 This seems to mean that each extreme as well as each intermediate 
species is compounded out of both the extreme differentiae. E. g. white 
would have to be to some extent compressing as well as piercing . 
But this is not in itself a likely doctrine, and it can hardly be said to be 
proved in the present passage ; the meaning probably is that each 
extreme species contains one differentia as a logical element, the other 
element being the genus ; while each intermediate contains both the 

3 It might seem that the respect in which things differ is just what 
does not belong to both. But Aristotle s meaning is this : If A differs 
from >, it must be a different something, and this something is the 
genus common to both. Horse and man are different animals. And 
when two things differ in their essence, they differ just in that in which 
(in another sense of in ) they agree. Difference in a genus makes 
the genus itself other (ic>58 a 7-8). Cf. io54 b 25-28. 


5 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 
1 difference in the genus to an otherness which makes the 
genus itself other. 

This, then, will be a contrariety (as can be shown also by 

10 induction). For all things are divided by opposites, and it 
has been proved that contraries are in the same genus 1 . 
For contrariety was seen 2 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 predica- 

IKk tion, 3 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 con 

This, then, is what it is to be * other in species to have 
a contrariety, being in the same genus and being indivis 
ible 4 (and those things are the same in species which have 
no contrariety, being indivisible 5 ); we say being indi 
visible , for in the process of division contrarieties arise 

20 even in the intermediate stages before we come to the 
indivisibles. 4 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, 6 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 7 ), nor is it so with reference 

25 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 

1 Ch. 4. 2 io55 a i6. 

3 Cf. I054 b 35 and note on A. 986* 23. 

4 Sc. individuals or infimae species. 

5 Sc. individuals. 

6 i. e. by eliminating the form which characterizes the concrete thing. 

7 Cf. A. io24 a 3i-6, b 4-6. 

BOOK I. 8 ios8 a 

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. 

g One might raise the question, why woman does not differ 
from man in species, when female and male are contrary and 3 
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 35 
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 io58 b 
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 con- 5 
sidered 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 l is the ultimate indivisible 
kind. Callias is definition + matter ; the pale man, then, is 10 
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 I5 
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 

1 i. e. that in whose definition no contrarieties are included. 

P 2 


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 

30 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 4 animal , 
are so not in virtue pf its essence but in the matter, i. e. the 
body. This is why the same seed becomes female or male 
by being acted on in a certain way. We have stated, then, 

25 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 10 
and the imperishable are contraries (for privation is a deter 
minate incapacity), the perishable and the imperishable 
must be different in kind. 1 

Now so far we have spoken of the general terms them- 

3 o selves, 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 

35 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 

1 To translate ytvos and ei<W as genus and species makes non 
sense of the argument of this chapter. They have therefore been 
rendered kind and form . The only trace of the technical distinc 
tion is found in the last sentence of the chapter, and there it is not 
justified by what precedes. It looks as if the first part of the chapter 
had been written before the distinction was drawn, and io59 a 10-14 
(or perhaps only 1. 14) added under the supposition that a generic 
difference between the perishable and the imperishable had been 
proved. For the absence of distinction between yews and fl&os cf. A. 
1071*25 with 27, Cat. 8 b 27 with 9 a 14, Hist. An. i. 49O b 16 with 17, 
Pol. iv. 1290^33 with 36. To read eifift in io5& b 28 is useless in view 
of 1059* 10-14. 

BOOK I. 10 io59 a 

imperishable . For nothing is by accident perishable. For 1059** 
what is accidental is capable of not being present, but 
perishableness is one of the attributes that belong of neces 
sity to the things to which they belong ; or else one and 
the same thing may be perishable and imperishable, if 5 
perishableness is capable of not belonging to it. Perishable- 
ness then must either be the essence or be present in the 
essence of each perishable thing. The same account holds 
good for im perishableness 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 i 
maintain, for then one man l would be perishable and an 
other 2 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 3 are 
farther apart than those which differ in form. 

1 The sensible individual. 2 The ideal man. 

3 As the perishable and the imperishable have been shown to do. 


THAT Wisdom is a science of first principles is evident i 
from the introductory chapters, 1 in which we have raised 
objections to the statements of others about the first prin- 
20 ciples ; 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 con 
traries, but the first principles are not contrary. If it is 
not one, what sort of sciences are those with which it is to 
be identified ? 2 

Further, is it the business of one science, or of more than 
one, to examine the first principles of demonstration ? If of 
2 5 one, why of this rather than of any other? If of more, 
what sort of sciences must these be said to be ? 3 

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. 4 

Further, does it deal with substances only or also with 
3 their attributes ? If in the case of attributes demonstration 
is possible, 5 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 title. 6 

But again the science we are looking for must not be 
supposed to deal with the causes which have been mentioned 
35 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 

1 Cf. Bk. A. 3-10. 2 Cf. B. 996 a i8- b 26. 

3 Cf. B. 996 b 26-997* 15. 4 Cf. B. 997 a 15-25. 

5 Reading in 1. 31 an-ada^is (<TTIV. 6 Cf. B. 997 a 25-34. 

1 The material, formal, efficient, and final causes (Pkys. ii. 3). 

BOOK K. i i059 a 

first), 1 and (B) in general it is hard to say whether per 
chance the science we are now looking for deals with 
perceptible substances or not with them, but with cer 
tain others. If with others, it must deal either with the 
Forms or with the objects of mathematics. Now (a) evi 
dently 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 5 
place the objects of mathematics between the Forms and per 
ceptible 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 10 
none of these is the sort of thing which the mathematical 
sciences demand.) Nor (6) 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 perish 
able. 2 

In general one might raise the question, to what kind of 15 
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 20 
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 25 
every definition and every science is of universals and not 
of infimae species f so that as far as this goes it would deal 

1 Cf. B. 996 a 2i- b i. 2 Cf. B. 997* 34-998* 19. 3 Cf. B. 998 b 15. 


with the highest genera. These would turn out to be being 
and unity ; for these might most of all be supposed to con 
tain all things that are, and to be most like principles 

30 because they are first 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 

35 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 
io6o a it. 1 These and others of the kind are the subjects that 
involve difficulties. 

Further, must we suppose something apart from indi- 2 
vidual things, or is it these that the science we are seeking 
5 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. 2 Indeed, it 
is in general hard to say whether one must assume that 
there is a separable substance besides the sensible sub 
stances (i.e. the substances in this world), or that these are 

10 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 ? 

15 Why should one suppose men or horses to have it, more 
than either the other animals or even all lifeless things? 

1 Cf. B. 998*20-999*23. 2 io59 b 24-38. 

BOOK K. 2 io6o a 

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 than matter ? 
This, however, does not exist in actuality, but exists in 20 
potency. And it would seem rather that the form or shape 
is a more important principle than this ; but the form is 
perishable, 1 so that there is no eternal substance at all 
which can exist apart and independent. But this is para 
doxical ; for such a principle and substance seems to exist 
and is sought by nearly all the most refined thinkers as some- 25 
thing that exists ; for how is there to be order unless there 
is something eternal and independent and permanent ? 2 

Further, if there is a substance or principle of such a 
nature as that which \ve 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 30 
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. 3 35 

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 sub 
stance, how will they be separable and independent ? Yet io6o b 
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 sub- 5 
stance is false. Further, how can they 4 be right who say that 

1 It must be remembered that A. is only stating common opinions 
and the consequent difficulties. 

2 Cf. B. 999 a 24- b 24. s Cf. B. iooo a 5-iooi a 3. 
4 The Pythagoreans and Plato. 


the first principle is unity and this is substance, and generate 
number as the first product from unity and from matter, 

10 and 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 sur 
faces) to be principles, these at least are not separable sub 
stances, but sections and divisions the former of surfaces, 
the latter of bodies (while points are sections and divisions 

J 5 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. 1 

20 A further difficulty is raised by the fact that all know 
ledge 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 prin 
ciples, the question arises, how are we to suppose the first 
principle to be substance ? 2 

Further, is there anything apart from the concrete thing 
(by which I mean the matter and that which is joined with 

2 5 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. 3 

Further, are the principles the same in kind or in num- 

3 ber ? If they are one in number, all things will be the 
same. 4 

Since the science of the philosopher treats of being qua 3 
being universally and not in respect of a part of it, and 
1 being has many senses and is not used in one only, it 
follows that if the word is used equivocally and in virtue of 

1 Cf. B. iooi a 4-ioo2 b ii. 2 Cf. B. 1003* 5-17. 

3 Cf. B. 999 a 24- b 24. 4 Cf. B. 999 b 24-1000* 4. 

BOOK K. 3 io6o b 

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 35 
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 io6i a 
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 5 
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 q^la being 
or a permanent or a transient state or a movement of it, or 
something else of the sort. And since everything that is TO 
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 dis 
cussed. 1 It makes no difference whether that which is be re- 15 
ferred 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 20 
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. E. g. if the just man is by virtue of some per 
manent disposition obedient to the laws \ 2 the unjust man 25 

1 Cf. Fr. I478 b 35-1479* 5, M97 a 32-149^43- 

2 Cf. [PL] Zte/. 411 E. 


will not in every case have the whole definition denied of 
him, but may be merely 4 in some respect deficient in obedi 
ence 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 

30 beginning his investigation he strips off all the sensible quali 
ties, 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 

35 the attributes of these qiia quantitative and continuous, and 
does not consider them in any other respect, and examines 
the relative positions of some and the attributes of these, 
io6i b 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 
5 far as it is being, and the contrarieties in it qua being, it is 
the business of no other science than philosophy to investi 
gate ; for to physics one would assign the study of things 
not qzta being, but rather qua sharing in movement ; while 
dialectic and sophistic deal with the attributes of things that 
are, but not of things qita being, and not with being itself 

10 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 said 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), 

15 and things of this sort can fall under one science, the diffi 
culty we stated at the beginning l appears to be solved, I 
mean the question how there can be a single science ot 
things which are many and different in genus. 

Since even the mathematician uses the common axioms 4 
only in a special application, it must be the business of first 
philosophy to examine the principles of mathematics also. 

1 I059 a 20-23. Cf. r. 2. The question raised in 1059* 29-34 has 
also incidentally been answered. 

BOOK K. 4 io6i b 

That when equals are taken from equals the remainders 
are equal, is common to all quantities, but mathematics ao 
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 25 
philosophy does not inquire about particular subjects in so 
far as each of them has some attribute or other> but specu 
lates 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 qita being (whereas the primary 30 
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. 1 

5 There is a principle in things, about which we cannot be 
deceived, but must always, on the contrary, recognize the 35 
truth, viz. that the same thing cannot at one and the same 
time be and not be, or admit any other similar pair of oppo- io62 a 
sites. 2 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 prin 
ciple, yet this is necessary if there is to be completed proof 
of it in the full sense. 3 But he who wants to prove to the 5 
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 oppo- 10 
site 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 15 

1 Cf. r. ioos a i9- b 2, K. 1059*23-26. 2 Cf. r. ioo5 b 8-34. 

3 Cf. r. ioc6 a 5-18. 


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 some 
thing, one cannot truly assert its contradictory. 1 

Further, if the word signifies something and this is 

20 asserted truly, 2 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/ 1 Fur 
ther, if the affirmation is no more true than the negation, 
he who says man will be no more right than he who says 

25 4 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. 4 

30 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 

35 opinion without understanding what his statement involves. 5 
But in any case if what is said by him is true, not even this 
io62 b 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 state 
ments are separated, the affirmation is no more true than the 
negation, in the same way the combined and complex 
5 statement being like a single affirmation the whole taken 
as an affirmation will be no more true than the negation. 6 
Further, if it is not possible to affirm anything truly, 
this itself will be false the assertion that there is no true 

1 Cf. r. ioo6 a i8-ioo7 a 2o. 

2 Sc. of that of which the word is asserted. 

3 Cf. r. ioo6 b 28-34. 4 Cf. r. ioo; b 18-1008*2. 
6 Cf. r. ioos b 23-26. 6 Cf. r. ioo8 a 6-7. 

BOOK K. 5 io62 b 

affirmation. 1 But if a true affirmation exists, this appears 
to refute what is said by those who raise such objections 10 
and utterly destroy rational discourse. 

6 The saying of Protagoras is like the views we have men 
tioned ; he said that man is the measure of all things, 2 
meaning simply that that which seems to each man also 
assuredly is. If this is so, it follows that the same thing 15 
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 20 
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. 3 

That nothing comes to be out of that which is not, but 
everything out of that which is, is a dogma common to 2 5 
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 3 
not hard to solve this difficulty ; for we have said in our 
works on physics 4 in what sense things that come to be 
come to be from that which is not, and in what sense from 
that which is. 5 

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 35 
of sensation ; for the same thing never appears sweet to some 
and the contrary of sweet to others, unless in the one case 1063** 

1 Cf. r. ioi2 b 13-18. Fr. i. 

3 Cf. r. ioo9 a 6-i6, 22-30. 

4 Phys. i. 7-9, De Gen. et Corr. i. 3l7 b 14-319^. 

5 Cf. r. 1009* 30-36. 


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 
5 not. And I 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). 1 

10 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 

15 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. 2 

Further, if there is movement, there is also something 
moved, and everything is moved out of something and into 
something ; it follows that that which is moved must first 
be in that out of which it is to be moved, and then not be in 

20 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 qualify ? For the assertion of contradictory 
statements about the same thing seems to have arisen 

35 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. 3 

Further, when the doctor orders people to take some 

1 Cf. r. ioio b i-26, ioii a 3i-4. 2 Cf. r. ioio a 25-32. 

3 Cf. r. 1010*22-25. 

BOOK K. 6 io63 a 

particular food, why do they take it ? In what respect is 30 
4 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. 1 

Again, if we are always changing and never remain the 35 
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 1063 
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 5 
the aforesaid 2 change takes place.) But if we do not 
change but remain the same, there will be something that 
endures. 3 

As for those to whom the difficulties mentioned are 
suggested by reasoning, it is not easy to solve the diffi 
culties to their satisfaction, unless they will posit something 
and no longer demand a reason for it ; for it is only thus 10 
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 per 
plexity. This is evident from what has been said. 4 

It is manifest, therefore, from these arguments that con- 15 
tradictory statements cannot be truly made about the same 
subject at one time, 5 nor can contrary statements, because 
every contrariety depends on privation. This is evident if 
we reduce the definitions of contraries to their principle. 6 

Similarly, no intermediate between contraries can be 
predicated of one and the same subject, of which one of the 

Cf. r. ioo8 b 12-27. 2 Cf. io63 a 35. 

3 Cf. r. ioo9 a 38- b 33. 4 In io62 b 2o-io63 b 7. 

5 Cf. r. ioo9 a 16-22, ioii a 3-i6. 6 Cf. r. ioii b 15-22. 

645-28 O 


jo 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 l is true of it, and this is 
the contradictory of white. 2 

We could not be right, then, in accepting the views 

25 either of Heraclitus 3 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 con 
traries, since in everything everything is present not poten- 

30 daily only, but actually and separately. And similarly all 
statements cannot be false nor all true, both because ot 
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 

35 to say all are false. 4 

Every science seeks certain principles and causes for each 7 
1064 o f it s 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 exist 
ing and real, not however qua real; the science that does 
this is another distinct from these. Of the sciences men- 
5 tioned each gets somehow the l 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 
1 what . 

10 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 move 
ment is in the producer and not in the product, and is either 
an art or some other faculty. And similarly in practical 

1 Sc. not white and not black . 

2 Cf. r. ioii b 23-iol2 a 24. 3 Cf. io62 a 3i- b 2. 
4 Cf. r. ioi2 a 24- b i8. 

BOOK K. 7 io64 a 

science the movement is not in the thing done, but rather 
in the doers. But the science of the natural philosopher 15 
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 theoreti 
cal (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 fail to observe 20 
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 defini 
tion of snub includes the matter of the thing, but that of 
concave is independent of the matter ; for snubness is 2 5 
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 30 
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 35 
there is. 1 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 io64 b 
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 5 
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. 

1 Cf. A. 6, 7. 



Each of the mathematical sciences deals with some one 
determinate class of things, but universal mathematics ap 
plies alike to all. Now if natural substances are the first of 
10 existing things, physics must be the first of sciences ; but if 
there is another entity and substance, separable and un- 
movable, the knowledge of it must be different and prior 
to physics and universal because it is prior. 1 

15 Since being in general has several senses, of which one 8 
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 archi 
tecture consider what will happen to those who are to use 

20 the house (e. g. whether they will have a painful life in it 
or not), nor does weaving, or shoemaking, or the con 
fectioner 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 will be both at once, not having been 

25 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 \vrong 
when he says 2 that the sophist spends his time on non- 

3 o That a science of the accidental is not even possible \vill 
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 

35 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 dog- 
days, but this occurs neither always and of necessity, nor 
io65 a 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 

1 Cf. E. I, K. I059 a 26-29. 2 Cf. Sophistes 254 A. 

BOOK K. 8 io6s a 

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 5 
these classes. 

Evidently there are not causes and principles of the acci 
dental, 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 ro 
will exist of necessity, do\vn 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. 15 
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 20 
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 25 
unordered and indefinite. 1 

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 2 happens by accident. For as a thing may 
exist, so it may be a cause, either by its own nature or by 
accident. 15 Luck is an accidental cause at work in such 3 
events adapted to an end as are usually effected in accor 
dance with purpose. And so luck and thought are concerned 

1 Cf. E. 2-4. 

2 Sc. which happen usually by nature or as the result of thought. 

3 Cf. Pliys. ii. I96 b 21-25. 


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 

35 sense a cause of nothing. 1 It is good or bad luck when 

io6s b the result is good or evil ; and prosperity or misfortune 

when the scale of the results is large. 2 

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. :3 

5 Some things are only actually, some potentially, some 9 
potentially and actually, what they are, viz. in one case 
a particular reality, in another, characterized by a particular 
quantity, or the like. 4 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 

10 subjects in either of two ways (e. g. this-ness for one 
kind of it is * positive form , and the other is * privation ; 
and as regards quality one kind is white and the other 
black , and as regards quantity one kind is complete 
and the other * incomplete , and as regards spatial move 
ment 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 

J 5 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 V 5 exists actually, 
it is being built, and this is the process of building. Simi 
larly with learning, healing, walking, leaping, ageing, ripen- 

20 ing. G Movement takes place when the complete reality itself 
exists, and neither earlier nor later. 7 The complete reality, 

1 Cf. Phys. ii. I97 a 5-14. 2 Cf. Phys. ii. I97 a 25-27. 

3 Cf. Phys. ii. 198* 5-13. 4 Cf. Phys. iii. 200^26-28. 

6 i. e. not as so much matter, but as matter capable of being made 
into a building. 

fi Cf. Phys. iii. 2OO b 32-201* 19. 7 Cf. Phys. iii. 2oi b 6, 7. 

BOOK K. 9 io6s b 

then, of that which exists potentially, when it is completely 
real and actual, not q2ia 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 qzia bronze that 
is movement. For it is not the same thing to be bronze 25 
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 30 
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 move 
ment takes place when the complete reality itself exists, and 35 
neither earlier nor later, is evident. For each thing is io66 8 
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^ 5 
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 other class. This is evident from what people say. i 
Some call it otherness and inequality and the unreal ; 2 
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 move 
ment in these classes is that it is thought to be something 

1 The argument is that the house cannot be the eW/ryeia of the 
buildable, for when the house exists the buildable has ceased to exist ; 
therefore its eV/ryeia must be \\\& process of building. 

2 The Pythagoreans and Platonists are meant; cf. PI. Soph. 256 D, 
Tim. 57Eff. 


indefinite, and the principles in one of the two columns of 

15 contraries l 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 neces- 

20 sity 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 actu 
ality, but evidently none of these is possible. Therefore 

25 what remains is that it must be what we said both actu 
ality and the actuality we have described which is hard to 
detect but capable of existing. 2 

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 

30 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. 3 

35 The infinite is either that which is incapable of being 10 
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 subtrac- 

1 Cf. note on A. 986** 23. 

" With io65 b 22-io66 a 27 cf. Phys. iii. 2oi a 27-202* 3. 

3 Cf. Phys. iii. 2O2 a 13-21. 

BOOK K. 10 io66 b 

tion, or both. The infinite cannot be a separate, indepen- io66 b 
dent thing. For if it is neither a spatial magnitude nor a 
plurality, but infinity itself is its substance and not an acci 
dent 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 5 
this, nor are we examining this sort of infinite, but the in 
finite as untraversable. 1 Further, how can an infinite exist 
by itself, unless number and magnitude also exist by them 
selves, since infinity is an attribute of these ? 2 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 10 
element in speech, though the voice is invisible. 3 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 in 
finites ; but the same thing cannot be many infinites (as a 15 
part of air is air, so a part of the infinite would be infinite, 
if the infinite is a 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 4 ) it cannot be it that is a prin- 3 o 
ciple, but that of which it is an accident the air or the 
even number. 5 

This inquiry is universal ; but that the infinite is not 
among sensible things, is evident from the following argu 
ment. 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 25 
number or that which has a number is numerable. 5 Con 
cretely, 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 

1 Cf. Phys. iii. 2O4 a 3-14. 2 Cf. Phys. iii. 204* 17-19. 

3 Cf. Phys. iii. 2O4 a 14-17. 4 1. 9. 

5 Cf. Phys. iii. 2O4 a 20-32. 6 Cf. Phys. iii. 2O4 a 34~ b 8. 


in multitude. For the contraries must be equal and no one 
of them must be infinite ; for if one of the two bodies falls 

30 at all short of the other in potency, the finite will be de 
stroyed 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 direc 
tion. Nor (d) can the infinite body be one and simple 

35 neither, as some say, 1 something apart from the elements, 
from which they generate these 2 (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 
io67 a 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 Hera- 

5 clitus says 3 all things sometime become fire. The same 
argument applies to this as to the One which the natural 
philosophers posit besides the elements. 4 For everything 
changes from contrary to contrary, e. g. from hot to cold. 5 
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 

10 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 in 
finite 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 

15 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 can- 

1 Anaximander is meant. 2 Cf. Phys. iii. 2O4 b 10-24. 

3 Fr. 30, 64, 66, 90. 4 For this argument cf. io66 b 35~io67 a I. 

5 Cf. Phys. iii. 204* 32-205* 7. 

BOOK K. 10 io67 a 

not be ; for then those of one kind will be infinite in quan 
tity 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. 1 
But if the parts are infinite and simple, their places also 20 
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. 2 

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 25 
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, 3 but 
these cannot exist in an infinite body. In general, if there 30 
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. 4 

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 35 
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 it. 5 

ii Of things which change, some change in an accidental 1067 
sense, like that in which the musical may be said to walk, 

1 Cf. Phys. iii. 205* 10-25. Cf. also io66 b 28-34, from which it appears 
that the argument is as follows. If a finite number of kinds is to make 
an infinite whole, at least one kind must be infinite in extent. They 
cannot all be infinite, for they limit one another. But if one is infinite 
and another finite, the former destroys the latter and there ceases to be 
the variety of kinds within the whole which is at present presupposed. 
Aristotle omits to mention that the supposition of a finite kind co 
existing with an infinite kind is in itself absurd, because the finite 
limits the infinite. But this would only make his case stronger. 

2 Cf. Phys. iii. 205* 29-32. 

3 Sc. up and down, right and left, before and behind. 

4 Cf. Phys. iii. 20^24-206^ 7. 5 Cf. Phys. iii. 2o; b 21-25. 


and others are said, without qualification, to change, because 
something* in them changes, 1. 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 
5 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. 1 But the forms and 
the affections and the place, which are the terminals of the 

10 movement of moving things, are unmovable, e.g. know 
ledge or heat ; it is not heat that is a movement, but heat 
ing. 2 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. 3 

15 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 ; for that from 

20 negative into negative is not change, because (since the 
terms are neither contraries nor contradictories) there is no 
opposition. 4 The change from the negative into the posi 
tive 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 

25 partial change partial destruction. If, then, that which is 
not has several senses, 5 and movement can attach neither 
to that which implies putting together or separating, 6 nor 

1 Cf. Phys. v. 224 a 2i- b i. 

2 Cf. Phys. v. 224 b 11-16. * Cf. Phys. v. 224 b 28-30. 
4 1067^ 20-21. I now read ovre yap . . . Icrnv as a parenthesis giving 

the justification for OVK dvTidfo-is and idiomatically thrown forward. 

8 Cf. E. I026 a 33- b 2, I027 b i8-i9. 

6 i. e. to that which is not in the sense of the judgement which is 
false . 

BOOK K. ii io67 b 

to that which implies potency and is opposed to that which 
is in the full sense l (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, 30 
generation cannot be movement ; for that which is not is 
generated ; for even if we admit to the full that its genera 
tion is accidental, yet it is true to say that not-being is 
predicable of that which is generated absolutely). 2 Simi 
larly rest cannot belong to that which is not. These con 
sequences, then, turn out to be awkward, and also this, 35 
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 move 
ment is movement or rest, but the contrary of destruction 
is generation. Since every movement is a change, and the io68 a 
kinds of change are the three named above, 3 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 5 
contrary or intermediate (for even privation must be 
regarded as contrary), and are expressed by an affirmative 
term, e. g. naked or toothless 4 or black . 

12 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 10 
(because there is nothing contrary to substance), nor of 
relation (for it is possible that if one of two things in rela 
tion changes, the relative term which was true of the other 
thing ceases to be true, though this other does not change 

1 i. e. a thing cannot be moved when it does not exist actually, but 
exists potentially. 

2 i. e. even if the not-being (privation) which is the starting-point of 
generation can exist only as an accident of prime matter, still not- 
being is the starting-point of absolute generation (i.e. generation of a 
substance, not of a quality). 

3 In io6; b 19. 

4 Toothless is more obviously negative in form than the corre 
sponding Greek word. 


at all, so that their movement is accidental), nor of agent 
and patient, or mover and moved, because there is no 

15 movement of movement nor generation of generation, nor, 
in general, change of change. For there might be move 
ment of movement in two senses; (i) 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 sub- 

20 ject. 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 incident 
ally. For every movement is change from something into 

25 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. 1 ) 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 2 ), and, further, into a determinate 
change each time ; and that new change will be from some- 

30 thing 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 pro cess 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 

35 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 
io68 b comes to be something was also once coming to be ; there 
fore 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 

1 Change between contraries is movement, change between contra 
dictories is generation or destruction. 

2 This is possible, though excluded by the theory in question. 

BOOK K. 12 io68 b 

once coming 1 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 will exist. 
Nothing, then, can either come to be or move or change. 5 
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 TO 
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 some 
thing into something. How, then, can this condition be 
fulfilled ? There can be no learning of learning, and there 
fore no becoming of becoming. 2 

Since there is not movement either of substance or of 15 
relation or of activity and passivity, it remains that move 
ment 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. 3 
The immobile is either that which is wholly incapable of 20 
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 

1 If that which comes to be comes to be coming to be, it also ceases 
to be. When ? Not when it is only coming to be coming to be, for then 
it is not and . . cannot cease to be ; nor after it has come to be, for then 
also that which comes to be is not and . . cannot cease to be. /. It 
is ceasing to be, at the very time when it is coming to be Which is 

2 W 7 ith io67 b !4-io68 b 15 cf. Phys. v. 225* 3-226** 16. 
5 Cf. Phys. v. 226 a 23-29. 


25 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 2 continuously according to 
its nature, naturally arrives before it arrives at the extreme 

3 o 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.) 

35 For the successive succeeds something and is something 
later ; * one does not succeed two , nor the first day of 
io6g a the month the second. That which, being successive, 
touches, is contiguous. (Since all change is between oppo- 
sites, and these are either contraries or contradictories, and 
there is no middle term for contradictories, clearly that 
which is between is between contraries. 4 ) The continuous 
5 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 

10 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 suc 
cession : and there is something between two of the former, 
but not between two of the latter. 5 

1 Cf. Phys. v. 226 b io-i6. 

2 io68 b 29 omit TO. 3 Cf. Phys. v. 226 b 21-25. 

4 This sentence should probably come after the first in this para 
graph. 5 Cf. Phys. v. 226 b 32-227* 31. 


i 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 20 
succession, on this view" also substance is first, and is suc 
ceeded 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 V Further, none 
of the categories other than substance can exist apart. And 25 
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 2 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 com 
mon to both, body. 

There are three kinds of substance one that is sensible 3 
(of which one subdivision is eternal and another is perish 
able ; 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 35 
the objects of mathematics, and others positing, of these 
two, only the objects of mathematics. 3 The former two 
kinds of substance are the subject of physics (for they 

1 This is an implication of the ordinary type of judgement, x is not 
white . 

2 The Platonists. 

3 The three views appear to have been held respectively by Plato, 
Xenocrates, and Speusippus. 

645-28 R 


io6g b 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 pro 
ceeds from opposites or from intermediates, and not from 
all opposites (for the voice is not-white(, but it does not 
5 therefore change to white}), but from the contrary, there 
must be something underlying which changes into the con 
trary state ; for the contraries do not change. Further, 2 
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 

10 or of the place, and change in respect of thisness J 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 

15 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 

33 which is, but is potentially, and is not actually. And this 
is the One of Anaxagoras ; for instead of * all things 
were together c 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, 

25 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 
1 Reading in I. 1 1 TO ro 8f. 2 Anaxagoras, fr. I. 

BOOK A. 2 io6g b 

generation proceeds ; for non-being has three senses. 1 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 satis 
factory to say that all things were together ; for they 30 
differ in their matter, since otherwise why did an infinity of 
things come to be, and not one thing ? For reason 2 is 
one, so that if matter also were one, that must have come 
to be in actuality which the matter was in potency. :i 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. 

3 Note, next, that neither the matter nor the form comes 35 
to be and I mean the last matter and form. For every 
thing that changes is something and is changed by some 
thing and into something. That by which it is changed iO7o a 
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 5 
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 some 
thing other than the thing moved, nature is a principle 
in the thing itself (for man begets man 4 ), and the other 
causes are privations of these two. 

1 Alexander points out that aTrop^o-fie . . . 6V refers to 1. 20. The 
three senses are probably the non-being that answers to the categories 
of being, the false, and the potential (cf. N. io89 a 26-28). 

2 Sc. the voiis of Anaxagoras doctrine, summarized by D. L. (II. 3. 
l) in the words, irdvra xprjfiara rjv 6/j.oii etra 6 vovs eXOav aura Su/cdo-fi^o-ev. 

3 Sc. an undifferentiated unity. 

4 This is not a good instance of what A. says about nature, for the 
principle of generation is not in the child but in the father. The 
definition of nature applies better to other natural functions, such as 
growth. The note ai Spano? yap av6pu>7rov yfwa is hastily thrown in 
because A. is thinking mainly of his favourite thesis of ycvco-is ex 

. Hence Alexander says TOVTO crvvexf? earn TCO /uera ravra 

OTl fKCKJTT] K (TVVtOVV[J.OV y L V T (1 L O V (T I a. 

R 2 


There are three kinds of substance the matter, which is 

10 a * this in appearance (for all things that are characterized 
by contact and not by organic unity are matter and sub- 

i 9 stratum, e. g. fire, flesh, head ; for these are all matter, and 
the last matter is the matter of that which is in the full 

1 1 sense substance T ) ; 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 
4 this does not exist apart from the composite substance, 
e.g. the form of house does not so exist, unless the art of 

15 building exists apart (nor is there generation and de 
struction 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 

21 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 

25 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 

30 the medical art is the formal cause of health. 

The causes and the principles of different things are in 4 
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 

1 I adopt Alexander s suggestion that olov . .. reAevrm a (11. 19-20) 
should be placed after {nr-jKfipevov (1. u). 

BOOK A. 4 io7o a 

different or the same for substances and for relative terms, 
and similarly in the case of each of the categories. But it 35 
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 ? io7o b 
For (i) (a) there is nothing common to and distinct from sub 
stance and the other categories, viz. those which are predi 
cated ; but an element is prior to the things of which it is 
an element. But again (6) 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 5 
is composed of elements, e. g. b or a cannot be the same 
as ba. (None, therefore, of the intelligibles, 1 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 10 
a sense they have not ; e. g. perhaps the elements of per 
ceptible bodies are, zsform, 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 com 
posed 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. 15 
These things then have the same elements and principles 
(though specifically different things have specifically differ 
ent 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. 20 
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 

1 This is apparently almost a technical name for the abstract terms 
which are found in all the categories alike. 


while * principle and element are different both are causes, 
and principle is divided into these two kinds 1 : and that 
which acts as producing movement or rest is a principle 

25 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, dis 
order of a particular kind, bricks ; the moving cause is the 

30 building art. And since the moving cause in the case ol 
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 ; 2 
further, besides these there is that which as first of all 

35 things moves all things. 

Some things can exist apart and some cannot, and it is 5 
io7i a the former that are substances. And therefore all things 
have the same causes, 3 because, without substances, modi 
fications and movements do not exist. Further, these causes 
will probably be soul and body, or reason and desire and 

And in yet another way, analogically identical things are 

5 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. 4 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 

10 disease ; but the matter exists potentially ; for this is that 

1 i.e. the principles which are elements and those which are not. 

2 i. e. the efficient cause is identical with the formal. 

3 i. e. the causes of substance are the causes of all things. 

4 i. e. the division into potency and actuality stands in a detinite 
relation to the previous division into matter, form, and privation. r<> 
e | a/z0oty is not strictly in point, but is suggested by the frequent 
division of ova-ia into v\rj, eldos, and ro e aptyolv. 

BOOK A. 5 1071* 

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 (i) 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 15 
course, which are neither matter nor form nor privation of 
man nor of the same species with him, but moving causes. 1 

Further, one must observe that some causes can be ex 
pressed 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. 2 
The universal causes, then, of which we spoke :i do not 
exist. For it is the individual that is the originative prin- 20 
ciple 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 4 ; the causes of things that are not in the same 25 
class, e. g. of colours and sounds, of substances and quan 
tities, 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 

1 Aristotle distinguishes two ways in which things may be related as 
& and eWpyeia. (i) The same thing is <Wa/iei what it later comes 
to be evepyei a. But (2) one thing may be called Svvanis and another 
eWpyeui though they have nothing in common. Here duvams and eWp- 
yeia almost = cause and effect, and dvvafjus is the duvajus Kara Kivrjcriv 
\eyofjievr) (transeunt potentiality or rather power) spoken of in (3. i. 
The movement of the sun in the ecliptic is the cause of generation and 
decay (Phys. ii. I94 b 13, De Gen. et Corr. ii. 356* 3i- b 9) and is thus 
a transeunt dvvapis of each man who is born. 

2 e. g. the proximate causes of a child are the individual father (who 
on Aristotle s view is the efficient and contains the formal cause) and 
the germ contained in the individual mother (which is the material 

3 In 1. 17. 4 In io;o b 17. 


different, your matter and form and moving cause being 
different from mine, while in their universal definition they 

3 o 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 different 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 (i) the 
same or analogous in this sense, that matter, form, priva 
tion, 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 

35 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 1 first causes, viz. all 
the contraries which are neither generic nor ambi 
guous terms ; 2 and, further, the matters of different things 
io7i b 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 8 three kinds of substance, two of them 6 
physical and one unmovable, regarding the latter we must 
assert that it is necessary that there should be an eternal 
5 unmovable substance. For substances are the first of exist 
ing 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. Move 
ment also is continuous, then, in the sense in which time is ; 
for time is either the same thing as movement or an attri- 
10 bute of movement. And there is no continuous movement 
except movement in place, and of this only that which is 
circular is continuous. 

1 First is now taken in the sense of proximate , not of* ultimate 
as in TO TrpcoTov (i>T(\e\(ia. 

z Sc. but taken as individual qualities. All things include f!8os and 
<TTcpr)<ris, but each thing has a distinct ddos and oWpgo-if of its own. 

8 Cf. io69 a 3o. 

BOOK A. 6 ioyi b 

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 15 
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, 20 
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, 25 
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, 1 or the natural philosophers who say that * all 
things were together , 2 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 30 
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. Leucip- 
pus 3 and Plato 4 ; for they say there is always movement. 
But why and what this movement is they do not 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 ; 

1 Cf. Hesiod, Op. et D. 17, Theog. 116 ff., Orpheus fr. 12, Diels, 
Musaeus fr. 14, Epimenides fr. 5, Acusilaus fr. i, 3, Aristoph. Av. 693. 

2 Anaxagoras, fr. I. 

3 Cf. De Caelo, iii. 3oo b 8. 4 Cf. Timaeus, 30 A. 


35 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 
iO72 a 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. 2 To suppose potency 
prior to actuality, then, is in a sense right, and in a sense 
not ; and we have specified these senses. 3 That actuality 
5 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, 4 acting in 

J the same way. And if there is to be generation and de 
struction, there must be something else 5 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. 

15 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 (i) this is a possible account of the matter, and (2) 7 
if it were not true, the world would have proceeded out 
of night and 4 all things together 6 and out of non-being, 
20 these difficulties may be taken as solved. There is, then, 

1 Cf. Phaedrus, 245 C; Laivs, 894 E. 

2 Cf. Timaeus, 346. 3 Cf. io;i b 22-26. 
4 i. e. the sphere of the fixed stars. 

G i. e. the sun. Cf. De Gen. et Corr. ii. 336* 23 ff. 
6 Anaxagoras, fr. i. 

BOOK A. 7 i072 a 

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 1 must be 
eternal. There is therefore also something which moves it. 
And since that which is moves and moved is intermediate, 
there is something which moves without being moved, 
being eternal, substance, and actuality. And the object of 25 
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 30 
thought, and one of the two columns of opposites 2 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 35 
any class is always best, or analogous to the best. 3 

That a final cause may exist among unchangeable en- iO72 b 
tities 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. 

1 i. e. the outer sphere of the universe, that in which the fixed stars 
are set. 

2 Cf. note on A. 986*23. 

3 Sc. where there is no best in the strict sense. The argument for 
the identity of the primary forms of TO opfKrov and TO VOI]TOV is not very 
clearly stated, but seems to be as follows. The opfKrov is the Ka\6i>. 
(In parenthesis it is stated that desire depends on thought rather than 
thought on desire.) The positive side of the list ot contraries is the 
object of thought, and the first term on this side (which must be the 
primary object of thought) is simple actual substance. But the object 
of desire, which we have seen to be the Ka\of, is on the same side of the 
list, and therefore the first member of that list (the primary object of 
thought) must be the primary object of desire. 


Now if something is moved it is capable of being otherwise 
5 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 

10 mover produces?- The first mover, then, exists of necessity ; 
and in so far as it exists by necessity, its mode of being is 
good, 2 and it is in this sense a first principle. For the 
necessary has all these sensesthat which is necessary 
perforce because it is contrary to the natural impulse, that 
without which the good is impossible, and that which can 
not 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 

15 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 3 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 

20 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 

1 If it had any movement, it would have the first. But it produces 
this and therefore cannot share in it ; for if it did, we should have to 
look for something that is prior to the first mover and imparts this 
motion to it. 

2 i. e. it is necessary in the sense of /jn] ev^f\6^vov aXXcos e ^ft", and is 
. . good. 

3 Sc. because they are activities or actualities. 

BOOK A. 7 io72 b 

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 25 
God ts 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 l and Speusip- 30 
pus 2 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, 3 are wrong in their opinion. For the 35 
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 io73 a 
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 5 
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 10 
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 4 change of place. 
8 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 15 
opinions expressed by others, that they have said nothing 
about the number of the substances that can even be clearly 

1 Cf. io75 a 36. 2 Cf. Z. io2S b 2i, N. I09i a 34, io92 a u. 

;! i. e. the animal or plant is more beautiful and perfect than the 

4 i. e. impossible without. 


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, 

20 now 1 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 dis 
cuss the subject, starting 1 from the presuppositions and 
distinctions we have mentioned. The first principle or 
primary being is not movable either in itself or accident- 

25 ally, 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 eter 
nal movement must be produced by something eternal and 
a single movement by a single thing, and since we see that be 
sides the simple spatial movement of the universe, which we 

3 o 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 2 ), each of these movements also must be caused by 
a substance both unmovable in itself and eternal. For the 
nature of the stars 3 is eternal just because it is a certain kind 

35 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. 4 
iO73 b 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 mathe 
matical sciences which is most akin to philosophy viz. of 
5 astronomy ; for this science speculates about substance 

1 The reference is to Plato Ccf. Phys. 2c6 b 32). 

2 Cf. Phys. viii. 8, 9 ; De Caelo, i. 2, ii. 3-8. 

3 This is to be understood as a general term including both fixed 
stars and planets. 

4 Cf. 11. 5-n. 

BOOK A. 8 io73 b 

which is perceptible but eternal, but the other mathema 
tical 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 10 
actual number of these movements, we now to give some 
notion of the subject quote what some of the mathema 
ticians 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 1 5 
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 20 
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 25 
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 30 
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 35 
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 hither 
to 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 1 the star in 
5 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 

I0 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, 2 the whole set of spheres will be 
forty-seven in number. 

Let this, then, be taken as the number of the spheres, 

15 so that the unmovable substances and principles also may 
probably be taken as just so many ; the assertion of neces 
sity 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, 

20 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 be other 
movements besides those mentioned. And it is reasonable 
to infer this from a consideration of the bodies that are 

25 moved ; for if everything that moves is for the sake of that 
which is moved, and every movement belongs to something 

1 i. e. inwards from, the universe being thought of as a system of 
concentric spheres encircling the earth. 

2 In I073 b 35, 38-1074*4. 

BOOK A. 8 i074 a 

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 30 
of the divine bodies which move through the heaven. 1 

(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. 2 But 35 
the primary essence has not matter ; for it is complete, 
reality. So the unmovable first mover is one both in defini 
tion and in number ; so too, therefore, is that which is 
moved always and continuously ; therefore there is one 
heaven alone.) 3 

Our forefathers in the most remote ages have handed iO74 b 
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 5 
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 10 
that, while probably each art and each science has often 

1 The argument is : Each unchangeable perfect substance is an end 
and must cos 6/>eKrdz> produce a distinct motion. But every motion is 
ultimately for the sake of a <f)(p6fj.(t>ov, and as we have enumerated the 
motions necessary for the fapdpcva, there can be no more motions and 
therefore no more unchangeable perfect substances. 

2 i. e. the \6yos is common to all men, so that it must be matter 
which gives Socrates his uniqueness, 

3 This paragraph appears to be an early fragment embedded in 
a chapter written rather late in Aristotle s life, ovroi in b 3 refers back 
to rooi/ (frepofjLevcov 6ei<av (ra)/Lidra)j/ in a 30. 


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. 

15 The nature of the divine thought involves certain pro- 9 
blems ; 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 

20 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 itselt 
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 

25 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. 1 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 

30 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. 

35 But evidently knowledge and perception and opinion 
and understanding have always something else as their 

1 Sc. while vovs is ex hypothesi unmovable. 

BOOK A. 9 i074 b 

object, and themselves only by the way. Further, if think 
ing and being thought of are different, in respect of which 
does goodness belong to thought ? For to be an act of think 
ing and to <e 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 5 
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 10 
throughout eternity is the thought which has itself for its 

IO 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 15 
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 20 
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, 

S 2 


for instance, that all must at least come to be dissolved into 
their elements, 1 and there are other functions similarly in 
which all share for the good of the whole. 

25 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 

3 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. 2 These thinkers how 
ever 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. 3 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, 

35 partake of evil ; for the bad itself is one of the two elements. 
But the other school 4 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. 

IO 75 Empedocles 5 also has a paradoxical view ; for he identi 
fies 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 
5 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 

1 Sc. in order that higher forms of being may be produced by new 
combinations of the elements. 

2 i. e. the substratum. 

3 The reference is to Platonists. 

The reference is to the Pythagoreans and Speusippus ; cf. A. 1072 

b 3I 

6 Cf. A. 985* 4. 

BOOK A. 10 i075 b 

should be imperishable ; the nature of his * evil is just 

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 10 
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 non-existent ; and T 5 
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 parti 
cipate, in the Forms? And all other thinkers 1 are con- 20 
fronted 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 2 ; but what is primary has 
no contrary. 

Again, if besides sensible things no others exist, there 25 
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. 

1 The special reference is to Plato ; cf. Rep. 477. 

2 If there were an ignorance contrary to philosophy, it would have 
an object contrary to TO TT/JWTOI;, which is the object of philosophy. But 
TO npa>Tov has no contrary. 


a continuum, to be produced out of unextended parts ? 
For number will not, either as mover or as form, produce 

30 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. 1 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. 2 
Further, in virtue of what the numbers, or the soul and the 

35 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 a mathematical number is first and go on to 
generate one kind of substance after another and give 
iO76 a 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 non-existence), 
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. 4 

1 Since contraries must contain matter, and matter implies potentiality 
and contingency. 

2 Cf. I07i b i9, 20. 

8 Speusippus is meant ; cf. Z. io28 b 2i, N. iO9o b 13-20. 
4 Cf. Iliad) ii. 204. 


WE have stated what is the substance of sensible things, 
dealing in the treatise on physics with matter, and later 2 
with the substance which has actual existence. Now since 10 
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 15 
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 since (i) some recognize these as two different classes 
the Ideas and the mathematical numbers, and (2) some 20 
recognize both as having one nature, while (3) some others 
say that the mathematical substances are the only sub 
stances, 15 we must consider first 4 the objects of mathematics, 
not qualifying them by any other characteristic not ask 
ing, 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 25 
they exist or not, and if they exist, how they exist. 
Then after this we must separately consider 5 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 30 

1 Phys. i. " Met. ZH0. 

3 Plato, Xenocrates, and the Pythagoreans and Speusippus, respec 
tively, are meant. 

4 Cf. chs. 2, 3. 5 Cf. chs. 4, 5. 


examine l whether the substances and the principles ot 
existing things are numbers and Ideas ; for after the dis 
cussion of the Ideas this remains as a third inquiry. 

If the objects of mathematics exist, they must exist either 
in sensible objects, as some say, or separate from sensible 
35 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 

That it is impossible for mathematical objects to exist in 2 
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 2 ; we have pointed out that it is 
IO 76 impossible for two solids to be in the same place, and also 
that according to the same argument the other powers and 
characteristics also 3 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 
5 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 

10 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 

15 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 

1 Cf. chs. 6-9. 2 Cf. B. 998 a ;-i9. 

8 Which nevertheless the theory in question represents as Ideas 
apart from sensible things. 

BOOK M. 2 1076* 

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 20 
themselves must be prior to those which are in the motion 
less 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, there 
fore, there will be, belonging to these planes, lines, and 25 
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 ( i ) the accumulation 
becomes absurd ; for we find ourselves with one set of 
solids apart from the sensible solids ; three sets of planes 30 
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 35 
what is prior. And (2) 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 l ? 
For the objects of astronomy will exist apart from sensible IO 77 a 
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 5 
individual voices and sights. Therefore it is plain that the 
1 B. 997^ 12-34. 


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 

10 universal, extending beyond these substances. Here then 
we shall have another intermediate substance separate both 
from the Ideas and from the intermediates, 1 a substance 
which is neither number nor points nor spatial magnitude 
nor time. And if this is impossible, plainly it is also 
impossible that \hzformer entities should exist separate 
from sensible things. 

And, in general, conclusions contrary alike to the truth 

15 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. 

20 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 ; 2 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 mathe 
matics show that we are right. For the dimension first 

25 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, 

1 A Platonic expression for ra pad yuan mi, which were regarded as 
intermediate between Ideas and sensible things. 

2 Reading in 1. 22 euAoyw. 

BOOK M. 2 io77 a 

could a line or a plane be animate ? The supposition passes 30 
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 any 
thing that can be put together out of lines or planes or 
points, while if these had been a sort of material substance, 35 
we should have observed things which could be put to 
gether out of them. 

Grant, then, that they are prior in definition. Still not all iO77 b 
things that are prior in definition are also prior in substan 
tiality. 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 co- ex 
tensive. For if attributes do not exist apart from their sub- 5 
stances (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. There 
fore it is plain that neither is the result of abstraction prior 
nor that which is produced by adding determinants pos 
terior ; for it is by adding a determinant to pale that we 10 
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 some 
where apart. But since it was not possible for them to 
exist in sensibles either, 1 it is plain that they either do 15 
not exist at all or exist in a special sense and therefore 
do not exist without qualification. For exist has many 
3 senses. For just as the universal propositions of mathematics 
deal not with objects which exist separately, apart from ex 
tended magnitudes and from numbers, but with magnitudes 
and numbers, not however qita such as to have magnitude or 
1 Cf. I076 a 38- b u. 


20 to be divisible, 1 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. 2 For as there are many propo 
sitions about things merely considered as in motion, apart 

25 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 q^la 

30 planes, or only qua lines, or qua divisibles, or qua indivi 
sibles 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 

35 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 
io78 a 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 
5 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 attri 
butes peculiar to the animal qiia 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 

1 Cf. E. 1026*25, M. io;7 a 9. 

2 i. e. as universal mathematics abstracts from the distinctions 
between different kinds of /za^/zartKa, so geometry abstracts from the 
sensible characteristics of magnitudes and attends only to their spatial 

BOOK M. 3 1078 

are dealing with things which are prior in definition and 
simpler, our knowledge has more accuracy, i. e. simplicity, ro 
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 [ 5 
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 ao 
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 attri 
bute belongs to a man qua indivisible. But the geometer 35 
treats him neither qita man nor qzta indivisible, but as 
a solid. For evidently the properties which would have 
belonged to him even if perchance he had not been indivi 
sible, can belong to him even apart from these attributes. 1 
Thus, then, geometers speak correctly ; they talk about 
existing things, and their subjects do exist ; for being has 3 
two forms it exists not only in complete reality but also 

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 2 are in error. For these sciences say 

1 Sc. indivisibility and humanity. 

2 The reference is apparently to Aristippus ; cf. B. 996*32. 


35 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 
iO78 b and symmetry and definiteness, which the mathematical 
sciences demonstrate in a special degree. And since these 
(e. o-. order and definiteness) are obviously causes of many 
things, evidently these sciences must treat this sort of causa 
tive principle also (i. e. the beautiful) as in some sense 
5 a cause. But we shall speak more plainly elsewhere l about 
these matters. 

So much then for the objects of mathematics ; we have 4 
said that they exist and in what sense they exist, 2 and in 
what sense they are prior and in what sense not prior/ 
Now, regarding the Ideas, we must first examine the 

10 ideal theory itself, not connecting it in any way with the 
nature of numbers, but treating it in the form in which 
it w r as 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 

15 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 Demo- 

20 critus 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 
definitions -e. g. those of opportunity, justice, or marriage 4 
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 syllo- 

1 Apparently an unfulfilled promise. 

2 Chs. 2, 3. * io;7 a 17-20, 24- b ii. 
4 Cf. Diels, Vorsokratiker^ ed. 3, i. 346. 27-347. 11. 

BOOK M. 4 1078* 

gisms; for there was as yet none of the dialectical power which 25 
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 3 
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 35 
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 pro- 1079* 
ceeded 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 5 
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 accord 
ing to the argument of the one over many there will be 
Forms even of negations, and according to the argument 10 
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 argu 
ments, some lead to Ideas of relations, of which they say 
there is no independent class, and others introduce the 
third man Y* 

1 Reading in 1. 2 OUWW/JLOV TL (with A. 990^6). 

2 Cf. Z. 1039* 2, Soph. El. I78 b 36-i79 a 10, and Plato, Parmenides, 
132 AB, 0-133 A. 


And in general the arguments for the Forms destroy 
things for whose existence the believers in Forms are more 

15 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 1 
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 which the belief 

20 in the Ideas rests, there will be Forms not only of sub 
stances 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 2 sciences of other things 
than substance ; and a thousand other such difficulties 
confront them. But according to the necessities of the case 

25 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 4 double 
itself, it shares also in eternal , but incidentally ; for the 

30 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 ?). :i 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 

35 perishable 2 s, or in the 2 s which are many but eternal, 4 

and not the same in the 2 itself as in the individual 2 ? 

io?9 b But if they have not the same form, they will have only the 

1 i. e. the relative in general is more general than, and therefore (on 
Platonic principles) prior to, number. Number is similarly prior to the 
dyad. Therefore the relative is prior to the dyad, which yet is held to 
be absolute. 

2 Reading rrjs ovcrins eiVt in 1. 23. 

3 This seems to be an enthymeme, the conclusion to be supplied 
being that the Forms, since they are substances, must be 0/ substances. 

4 Sc. the abstract (eternal) 2 s of which we can say e.g. 2 + 2 = 4, 
i. e. TO. /zerau, which like the Ideas are eternal, but like sensible things 
are many. 

BOOK M. 4 io79 b 

name in common, and it is as if one were to call both Callias 
and a piece of wood a man , without observing any com 
munity between them. 1 

But if we are to suppose that in other respects the com 
mon definitions apply to the Forms, e.g. that plane figure 
and the other parts of the definition apply to the circle- 5 
itself, but 4 what really is 2 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. l animal and two-footed . 3 Further, 
there must be some Idea answering to plane above, some 10 
nature which will be present in all the Forms as their 

5 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 sub 
stance 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 20 
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 25 
are patterns and the other things share in them is to use 
empty w r ords 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 

1 With ic78 b 34-io79 b 3 cf. A. 99O b 2-99i a 8. 

2 Reading ro 6 6 errn in 1. 6 (cf. Io86 b 27) with P. Shorey (Class. 
Phil. xx. 271-3). 

3 Sc. in the essence of man. 


else, so that, whether Socrates exists or not, a man like 

30 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 l 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 forms-of-a-genus ; 

therefore the same thing will be pattern and copy. 

35 Again, it would seem impossible that substance and that 

io8o a whose substance it is should exist apart ; how, therefore, 

could the Ideas, being the substances of things, exist apart ? 

In the Pkaedo 1 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) 

5 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, 2 and not owing to the Forms. 

But regarding the Ideas it is possible, both in this way and 

10 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 5 
again the results regarding numbers which confront those 
who say that numbers are separable substances and first 

15 causes of things. If number is an entity and its substance 
is nothing other than just number, as some say, it follows 
that either (i) 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 

20 unit, or (6) 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 

1 ico D. 2 With io79 b !2-io8c a S cf. A. 99i a 8- b 9. 

BOOK M. 6 io8o a 

is first after i, and then comes 3 and then the rest of the 
number series, and the units in each number are associable, 25 
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 30 
number is counted thus after i, 2 (which consists of 
another i besides the former i), and 3 (which consists of 
another i besides these two), and the other numbers simi 
larly, ideal number is counted thus after i, a distinct 2 
which does not include the first i, 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 35 
named, 1 one like that which the mathematicians speak 
of, and that which we have named last 2 must be a third 

Again, these kinds of numbers must either be separable 
from things, or not separable but in objects of perception io8o b 
(not however in the way which we first considered, 3 but in 
the sense that objects of perception consist of numbers 
which are present in them) either one kind and not an 
other, or all of them. 

These are of necessity the only ways in which the numbers 5 
can exist. And of those who say that the i is the begin 
ning and substance and element of all things, and that 
number is formed from the i 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 TO 
besides those mentioned. Some 4 say both kinds of number 
exist, that which has a before and after 5 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 G say mathe- 

1 11. 15-20. 2 11.23-35. 

3 Cf. io;6 a 38- h u. 4 Plato is meant. 

5 i. e. in which the numbeis differ in kind. 

6 Speusippus is meant. 

T 2 


15 matical 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 

20 the units to have spatial magnitude. But how the first i 
was constructed so as to have magnitude, they seem unable 
to say. 

Another thinker l says the first kind of number, that of 
the Forms, alone exists, and some 2 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 

35 different from those which come after the Ideas ; 3 and of 
those who express themselves otherwise some speak of the 
objects of mathematics and in a mathematical way viz. 
those w r ho do not make the Ideas numbers nor say that 
Ideas exist ; 4 and others speak of the objects of mathe 
matics, but not mathematically ; for they say that neither is 
every spatial magnitude divisible into magnitudes, nor do 

30 any two units taken at random make 2. 5 All who say the i 
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. 6 It is clear from this statement, then, in how many 
ways numbers may be described, and that all the ways have 

35 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 inas- 7 
io8i a sociable, and if inassociable, in which of the two ways we dis 
tinguished. 7 For it is possible that any unit is inassociable 
with any, and it is possible that those in the 2 -itself are 
inassociable with those in the 3 -itself \ and, generally, that 
those in each ideal number are inassociable with those in 

1 Some unknown Platonist. 2 Xenocrates is meant. 

3 This refers to Plato; cf. A. 992^ 13-18. 

4 Speusippus is meant. 5 Xenocrates is meant. 

R 1. 19. 7 Cf. io8o a 18-20, 23-35. 

BOOK M. 7 ic8i a 

other ideal numbers. Now (i) if all units are associable and 5 
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 i 
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 i and the indefinite dyad, and 15 
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 20 
proved of it suit this character. Nor can it be ideal number. 
For 2 will not proceed immediately from i and the indefi 
nite dyad, and be followed by the successive numbers, as 
they say 2, 3, 4 for the units in the ideal 2 are generated 
at the same time, whether, as the first holder of the theory l 
said, from unequals (coming into being when these were 
equalized) or in some other way since, if one unit is to 25 
be prior to the other, it will be prior also to the 2 com 
posed 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. 2 

Again, since the i -itself is first, and then there is a parti- 30 
cular i which is first among the others and next after the 
i -itself, and again a third which is next after the second 
and next but one after the first i, so the units must be 
prior to the numbers after which they are named when we 

1 Plato. 

2 The theory of ideal number holds that 2 comes next after the 
original i, which with the indefinite 2 is the source of number. But 
if all units are different in species, one of the units in 2 is prior to the 
other and . . to 2, and comes next after the original I. Similarly 
between 2 and 3 there will be the first unit in 3, and so on. 


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 

35 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 
io8i b 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 i, and also that the 2 s should if there is 
a first 2 ; for after the first it is reasonable and necessary 

5 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 i, and that a 2 is first after it, is 
impossible.) But they make a first unit or i, but not also 
a second and a third, and a first 2, but not also a second and 
a third. 

10 Clearly, also, it is not possible, if all the units are in 
associable, 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 i to 

15 the one, 3 by adding another i to the two, and 4 similarly. 
This being so, numbers cannot be generated as they gene 
rate them, from the 2 and the i ; for 2 becomes part of 3, 

20 and 3 of 4, and the same happens in the case of the suc 
ceeding numbers, but they say 4 came from the first 2 and 
the indefinite 2, which makes it two 2 s other than the 
2-itself 1 ; 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 

25 i -itself and another i ; 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*3 and 2 s ? And how do they consist of prior 

30 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 i and the indefinite dyad are to be the elements. But 

1 The indefinite 2 being bvorroios produces two 2 s by operating on 
the ideal 2, and it is these two 2 s which are distinct from the ideal 2. 

BOOK M. 7 io8i b 

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 35 
(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 lo-itself there are ten units, and the 10 is com- io8a a 
posed both of them and of two 5*8. But since the lo-itself 
is not any chance number nor composed of any chance 5*3 
or, for that matter, units the units in this 10 must differ. 
For if they do not differ, neither will the 5*3 of which the 5 
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 10 in the 10 
10 but itself. But it is actually necessary on their view that 
the 4 should not consist of any chance 2 s ; for the indefinite 
2, 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, 15 
and the 3 an entity apart from its three units, how is this pos 
sible ? 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 inter- 2 o 
mixture, 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 25 
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 s, and similarly 
with the other numbers. For let the 2 s in the 4 be simul 
taneous ; yet these are prior to those in the 8, and as the 2 30 
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 

35 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. 

io82 b 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 
5 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 s in the lo-itself will be 

10 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 (/3) will 
it be prior to the 3 or posterior ? It rather seems that it 

15 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 i and T, 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 linits are 2. 

20 If the number of the 3-itself is not greater than that ot 
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. 1 

Nor will the Ideas be numbers. For in this particular 
point they are right who claim that the units must be 
1 i. e. if there is a difference of kind between the numbers. 

BOOK i\l. 7 io82 b 

different, if there are to be Ideas ; as has been said before. 1 2 5 
For the Form is unique ; but if the units are not different, 
the 2 s and the 3*8 also will not be different. This is also 
the reason why they must say that when we count thus 
i , 2 we do not proceed by adding to the given number ; 
for if we do, neither will the numbers be generated from 30 
the indefinite dyad, nor can a number be an Idea ; for then 
one Idea will be in another, and all the 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 difficulty whether, when we 35 
count and say i, 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. 

8 First of all it is well to determine what is the differentia 1083** 
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 5 
of units. Again, are the first units greater or smaller, and 
do the later ones increase or diminish ? All these are irra 
tional suppositions. But neither can they differ in quality. 
For no attribute can attach to them ; for even to numbers I0 
quality is said to belong after quantity. Again, quality 
could not come to them either from the i or from 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 15 
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 can 
not all be associable, nor can they be inassociable in either 
of the two ways. 2 But neither is the way in which some 20 
others speak about numbers correct. These are those who 

1 1081*5-17. 2 Cf. io8o a 18-20, 23-35. 


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 i -itself is the starting-point of them. It is 
paradoxical that there should be a i which is first of I s, as 

25 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 i is not the starting-point (for 

30 this sort of i 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 i 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 the numbers must not be associable with one another. 

3 But if on the other hand one supposes this, many impossible 
results, as we have said, 1 follow. But either this or the 
other must be the case, so that if neither is, number cannot 
exist separately. 

io83 b It is evident, also, from this that the third version 2 is the 
worst, the view ideal and mathematical number is the same. 
For two mistakes must then meet in the one opinion, (i) 
5 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 diffi 
culties than those before named, but in another way has 

10 others peculiar to itself. For not thinking of number as 
capable of existing separately removes many of the im 
possible 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 ; 

1 5 and how can a magnitude be composed of indivisibles ? 
But arithmetical number, at least, consists of units, while 
1 Cf. ioSo b 37-io83 a 17. 2 That of Xenocrates ; cf. io8o b 22. 

BOOK M. 8 io8 3 b 

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 20 
been mentioned, 1 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 ele- 25 
ments, 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 i -itself the middle place in 
odd numbers. 2 (6) But if each of the two units consists of 30 
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 35 
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 i operates on an even number, an 
odd number is produced ; in another way, when 2 operates, 5 
the numbers got from i 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 

2 Cf. Diels, Vorsokratiker, ed. 3, i. 346. 17-22. 


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. 

10 But if number infinite, 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, 1 firstly the 
Forms will soon run short ; e. g. if 3 is man-himself, what 

15 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 

ao numbers are similar), so that there will be an infinite num 
ber 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 associ- 
able), 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 

25 is 2. It is paradoxical also that there should be an Idea of 
10, but not of 1 1, 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 

30 real thing and a Form than 10 itself. There is no genera 
tion 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 

35 to the originative principles, and the others to the numbers. 
This is why they identify the odd with i ; for if the odd 
1 This includes Plato (cf. Phys. 2o6 b 32) and probably Speusippus. 

BOOK M. 8 io84 a 

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, 2 then io84 b 
the 2, &c. ; these entities also extend only up to io. 3 

Again, if number can exist separately, one might ask 
which is prior i, or 3 or 2 ? Inasmuch as the number is 
composite, i is prior, but inasmuch as the universal and the 
form is prior, the number is prior ; for each of the units is 5 
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 io 
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 i the starting- 
point ? Because it is not divisible, they say ; but both the 
universal, and the particular or the element, are indivisible. 
But they are starting-points in different ways, one in 15 
definition and the other in time. In which way, then, is i 
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 i the starting- 
point in both ways. But this is impossible. For the uni 
versal 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 20 
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 

1 i. e. to account for the oddness of odd numbers they identify the 
odd with the i, which is a principle present in all numbers, not with 
the 3, which on their theory is not present in other numbers. 

2 Cf. A. 992*22. 

3 Cf. N. io9o b 21-24. i answers to the point (the indivisible line ), 
2 to the line, 3 to the plane, 4 to the solid, and 1+2 + 3+4= io. 


the same time from the standpoint of mathematics and from 
25 that of universal definitions, so that (i) 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 1 also 
have done. Therefore the unit becomes the matter of num 
bers and at the same time prior to 2 ; and again posterior, 2 
3 being treated as a whole, a unity, and a form. But (2) 
because they were seeking the universal 2 they treated the 
unity w ich can be predicated of a number, as in this 
sense also 3 a part of the number. But these characteristics 
cannot belong at the same time to the same thing. 

If the i -itself must be unitary 4 (for it differs in nothing 

from other I s except that it is the starting-point), and the 

2 is divisible but the unit is not, the unit must be liker the 

35 i -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 

io85 a 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, g 
viz. between the units between which there is nothing, e. g. 
K betw r een those in 2 or in 3, one might ask whether these suc 
ceed the i -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 5 construct these out of the species of the great 
10 and small ; e. g. lines from the 4 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 

1 Sc. the atomists. 

2 Inserting TO before in 1. 31. 

3 i. e. they treated the unity which is predicable of a number, as well 
as the unit in a number, as a part of the number. 

4 Reading conjecturally in 1. 33 p-ovaSiKov for povo 

5 This probably includes Plato himself. 

BOOK M. 9 1085* 

the i l different thinkers describe in different ways. And 
in these also the impossibilities, the fictions, and the contra- 1 5 
dictions of all probability are seen to be innumerable. For 
(i) the 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 a line and the solid 
a plane ; 2 again, how will angles and figures and such 
things be explained ?). And (ii) the same happens as in 20 
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 . 3 

(All these views share a difficulty which occurs with re 
gard to species-of-a-genus, when one posits the universals, 
viz. whether it is animal-itself or something other than 25 
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 i 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- 30 
itself or something else ?) 

Some, then, generate spatial magnitudes from matter of 
this sort, others 4 from the point and the point is thought 
by them to be not i but something like i and from other 
matter like plurality, but not identical with it ; about which 
principles none the less the same difficulties occur. For if 35 
the matter is one, line and plane and solid 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 io85 b 
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 

1 i. e. that which is to the geometrical forms as the primary i is 
^according to the Platonic theory) to numbers. 

2 With 1085* 7-19 cf. A. 992 a 10-19. 
" Cf. A. 992 b 1-7, N. io88 a 15-21. 

4 Speusippus is probably meant. 


that the same results will follow even so ; for either the plane 
will not contain a line or it will be a line. 

Again, how number can consist of the one and plurality, 
5 they make no attempt to explain ; but however they ex 
press themselves, the same objections arise as confront 
those who construct number out of the one and the in 
definite dyad. 1 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 plural- 

10 ity . 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 

15 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 

20 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, 2 whether the number 
is infinite or finite. For there was at first, as it seems, 

2 - a plurality that was itself finite, from which and from the 
one comes the finite number of units. And there is an 
other plurality that is plurality-itself and infinite plurality ; 
which sort of plurality, then, is the element which co-oper 
ates 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 other 

30 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 
1 i. e. probably Plato and Xenocrates. a Cf. io83 b 36. 

BOOK M. 9 io85 b 

to be made are indivisible parts of plurality ; for number 
consists of indivisibles, but spatial magnitudes do not. 1 

All these objections, then, and others of the sort make it 
evident that number and spatial magnitudes cannotexist apart 35 
from things. Again, the discord about numbers between the 
various versions is a sign that it is the incorrectness of the io86 a 
alleged facts themselves that brings confusion into the 
theories. For those who make the objects of mathematics 
alone exist apart from sensible things, 2 seeing the diffi 
culty about the Forms and their fictitiousness, abandoned 
ideal number and posited mathematical. But those who 5 
wished to make the Forms at the same time also numbers, but 
did not see, if one assumed these principles, how mathe 
matical number was to exist apart from ideal, 3 made ideal 
and mathematical number the same in words, since mfact 
mathematical number has been destroyed; for they state 10 
hypotheses peculiar to themselves and not those of mathe 
matics. And he who first supposed that the Forms exist and 
that the Forms are numbers and that the objects of mathe 
matics exist, 4 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 15 
their hypotheses and their principles are false. And it is 
hard to make a good case out of bad materials, according 
to Epicharmus 5 : as soon as tis said, tis seen to be 

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 20 
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 

1 The point cannot have for an element of it (a) a distance, for this 
would destroy the simplicity of the point ; or (b) part of a distance, for 
any part of a distance must be a distance. 

Speusippus is meant. 3 Xenocrates is meant. 

4 Plato. 5 Fr. 14, Diels, Vorsokratiker. 


stated in our works on nature, 1 and partly do not belong 
to the present inquiry ; but the views of those who assert 

25 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, 

30 must be considered later 2 ; 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 

35 not possible has been argued before. 3 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 in 
io86 b 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, 4 by reason of his definitions, but 
he did not separate universals from individuals ; and in this 
5 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 suc 
cessors, 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 sepa- 

10 rate 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 IO 

1 Phys. i. 4-6 ; De Caelo, iii. 3-4 ; De Gen, et Corr. i. i. 
? Speusippus is meant; cf. N. 1090*7-15, 2o- b 2o. 
8 B. ioo3 a 7-17. 

BOOK M. 10 io86 b 

difficulty both to those who believe in the Ideas and to those 
who do not, and which was stated before, at the beginning, I5 
among the problems. 1 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 c 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 20 
will be just of the same number as the elements, and (d) the 
elements will not be knowable. For (a) let the syllables in 
speech be substances, and their elements elements of sub 
stances ; then there must be only one ba and one of each of 
the syllables, since they are not universal and the same in 25 
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 2 is in each case one). And if the 
syllables are unique, so tooare the parts ofwhich they consist; 
there will not, then, be more as than one, nor more than 
one of any of the other elements, on the same principle on 30 
which an identical syllable cannot 3 exist in the plural number. 
But if this is so, there will not be other things existing 
besides the elements, but only the elements. (6) 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 tw r o right 
angles, unless every triangle has its angles equal to two 35 
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 io87 a 
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 prin 
ciple or element. 

1 B. 999 b 24-iooo a 4, ioo3 a 5-i;. 

2 i.e. the Idea ; cf. I079 b 6. 

3 Omitting aXXo>i> in 1. 30 ; there is no trace of it in ps. -Alexander. 

U 2 


5 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 as and the s may quite well 
be many and there need be no ^-itself and ^-itself besides 
the many, there may be, so far as this goes, an infinite 

ic number of similar syllables. The statement that all know 
ledge 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 

1 5 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 

20 colour ; and this individual a which the grammarian in 
vestigates is an a. For if the principles must be universal, 
what is derived from them must also be universal, as in 
demonstrations l ; 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 

25 it is not. 

1 Sc. universal premisses do not give singular conclusions. 


I REGARDING this kind of substance, what we have said 
must be taken as sufficient. All philosophers make the 
first principles contraries : as in natural thing s, so also in 30 
the case of unchangeable substances. But since there can 
not 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 qiia 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 35 
absurd, for then that subject will be prior. But all things 
which are generated from their contraries involve an under 
lying subject ; a subject, then, must be present in the case 
of contraries, if anywhere. All contraries, then, are always io87 b 
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 T making the unequal which they take to be the 5 
essence of plurality matter for the One, and others 2 
making plurality matter for the One. (The former gene 
rate 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 philo 
sopher who says the unequal and the One are the elements, 
and the unequal is a dyad composed of the great and small, 10 
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 

1 Plato is meant. 2 Speusippus is probably referred to. 


some 1 name the great and the small with the One and treat 

15 these three as elements of numbers, two being matter, one 
the form ; while others 2 name the many and few, because 
the great and the small are more appropriate in their 
nature to magnitude than to number ; and others 3 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 2 does ; for number is more universal 
than 2, as the exceeding and the exceeded are more uni- 

2 5 versal 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, 4 and others 
oppose plurality to the One. 5 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, 

30 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 

35 of its ow r n, 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 
io88 a 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 

1 This includes Plato. 2 Unidentifiable Platonists. 

3 Perhaps Pythagoreans. 

4 Probably certain Pythagoreans are referred to. 

5 Probably Speusippus is meant. 

BOOK N. i io88 

substance of anything-. And this is reasonable ; for 4 the 
one means the measure of some plurality, and number 5 
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 10 
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 num 
ber, 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 15 
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 20 
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 l 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 25 
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 30 
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. 
1 Omitting r&v K.arriyopi.u>v in 1. 23 as a gloss. 


In respect of relation there is no proper change ; for, with 
out changing, a thing will be now greater and now less or 
35 equal, if that with which it is compared has changed in 
io88 b 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 
5 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, i would be few), there must be also one which is 
10 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 2 
15 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 con 
sists it would necessarily also, if it had come into being, have 
come into being, 1 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 poten- 
20 tial 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. 

1 Punctuating in 11. l6, 17 ft KCU ati eon, } d eyevero, e< TOVTOV 

BOOK N. 2 1088* 

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. 1 If that which we are now saying is 25 
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 2 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 3 
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 35 
explanations, and especially the fact that they framed the 1089* 
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: 3 

For never will this be 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 5 
the things that are be composed, if they are many. 

But, first, if being has many senses (for it means some 
times 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 10 
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 4 should bring it about 
that part of that which is is a this , part a * such , part 
a so much , part a here . 

1 Cf. 0. io5o b 7 ff., De Caelo, i. 12. 

2 Probably Xenocrates is meant. 3 Fr. 7. 4 i. e. non-being. 


15 Secondly, of what sort of non-being and being do the 
things that are consist? For non-being 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 ? 

20 This thinker 1 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 in- 

25 ference), nor is it non-being in this sense that the things 
that are are generated from or resolved into. But since 
4 non-being taken in its various cases 2 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 

30 man, and white from that which is not white but potentially 
\vhite, and this whether it is some one thing that is gene 
rated or many. 

The question evidently is, how being, in the sense of the 
siibstances\ 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 

35 not how either qualities or quantities are many. For surely 
the indefinite dyad or 4 the great and the small is not a 
reason why there should be two kinds of white or many 
io89 b colours or flavours or shapes ; for then these also would be 
numbers and units. But if they had attacked these other 
categories, they w r ould have seen the cause of the plurality 
in substances also ; for the same thing or something analo 
gous is the cause. This aberration is the reason also why 
5 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 
1 Plato ; cf. Soph. 237 A, 240. 2 Cf. 11. 16-19. 

BOOK N. 2 

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 i, but do not go on to 10 
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 pro 
ceed 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 T 5 
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 20 
more necessary, as we said, 1 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 exist 
ence of plurality. Since they are not separable from substances, 25 
qualitiesand quantities aremanyjust 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. 2 The difficulty arising 3 
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 

1 a 34- 

2 Which, Aristotle thinks, the Platonists assert the Idea to be. 


many, but how quantities are many. For all number 

35 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 

iO9O a 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 
5 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 mathema- 
10 tical number, 1 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 any 
thing ; for the theorems of arithmeticians will all be found 
15 true even of sensible things, as was said before. 2 

As for those, then, who suppose the Ideas to exist and to 3 
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 

20 of number. Again, the Pythagoreans, because they saw 
many attributes of numbers belonging to sensible bodies, 
supposed real things to be numbers not separable num 
bers, 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 

25 things. 3 Those, however, who say that mathematical num- 

1 Speusippus is meant. 2 Cf. M. 3, esp. io77 b 17-22. 

3 Cf. A. 989** 29-99o a 29. 

BOOK N. 3 io90 a 

her alone exists 1 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. 2 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 3 
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 separ- 35 
able 3 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 ; 4 
and similarly with the spatial magnitudes of mathematics. 
It is evident, then, both that the rival theory 5 will say the iogo b 
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 5 
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 sub 
stances, but rather all these things are limits. For even 10 
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, regard 
ing all number and the objects of mathematics, press this 
difficulty, that they contribute nothing to one another, the 15 

1 Speusippus is meant. 2 Cf. M. 3. 3 The Platonists. 

4 This seems to be a quotation from some poet or writer of poetical 

5 Sc. of the Pythagoreans ; cf. 11. 20-25. &2 9- 


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, 1 
and if spatial magnitudes did not exist, soul and sensible 
bodies would exist. But the observed facts show that 

20 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 2, planes doubtless out of 
3, solids out of 4, or they use other numbers, which 
makes no difference. But will these magnitudes be Ideas, 

25 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. 

30 But it is not hard to assume any random hypotheses and 
spin out a long string of conclusions. These thinkers, 2 
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 

35 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 3 makes 
spatial magnitudes out of some other small and great 4 ). 
iogi a 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 i, unity will be something 
common to these, and we must inquire how the one is 
these many things, while at the same time number, accord 
ing to him, cannot be generated except from one and an 
indefinite dyad. 

5 All this is absurd, and conflicts both with itself and with 
the probabilities, and we seem to see in it Simonides long 

1 Speusippus is meant. 

2 11. 20-32 seem to refer to Xenocrates. 3 Sc. Plato. 

4 Cf. I090 b 2I, 22. 

BOOK N. 3 i09i a 

rigmarole 1 ; 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 10 
cannot in any way generate numbers other than those got 
from i 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 Pytha 
goreans attribute generation to them or not ; for they say 15 
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 ao 
principles at work in unchangeable things, so that it is 
numbers of this kind whose genesis we must study. 

4 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 equal 
ized. The inequality, then, must belong to them before 25 
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. 2 

A difficulty, and a reproach to any one who finds it no 
difficulty, are contained in the question how the elements 3 
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 

1 Sim. Ceius, Fr. 189. Bergk. 

2 Cf. De Caelo, i. 279* 32-280* 10. 


35 present day, 1 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 
iogi b 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 
5 not those who are first in time, e. g. Night and Heaven 2 or 
Chaos 3 or Ocean 4 , reign and rule, but Zeus. 5 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 

10 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. 

15 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-sufficiency 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 

20 principle is good is probably correct ; but that this prin 
ciple should be the One or, if not that, at least an element, 
and an element of numbers, is impossible. Powerful ob 
jections arise, to avoid w r hich some have given up the 
theory 6 (viz. those who agree that the One is a first 

1 Speusippus is meant; cf. A. 1072* 31. 

2 The reference is to the Orphic cosmogony. 

3 Cf. Hes. Theog. 116. 4 Cf. Horn. //. xiv. 201. 

5 Cf. A. ic7i b 26. 

6 i. e. Speusippus gave up the identity of the One with the Good. 

BOOK N. 4 i09i b 

principle and element, but only of mathematical number). 
For on this view all the units become identical with species 25 
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 sub 
stances, all animals and plants and all individuals that share 
in Ideas will be good. 

These absurdities follow, and it also follows that the 30 
contrary element, whether it is plurality or the unequal, 
i.e. the great and small, is the bad-itself. (Hence one 
thinker 1 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 2 say inequality is the nature of the bad.) It follows, 35 
then, that all things partake of the bad except one the 
One itself, and that numbers partake of it in a more un 
diluted form than spatial magnitudes, and that the bad is 1092* 
the space in which the good is realized, 3 and that it par 
takes in and desires that which tends to destroy it ; for 
contrary tends to destroy contrary. And if, as we were 
saying, 4 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 5 
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. 

5 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 de- 10 
scribed, nor are the first substances. Nor does any one 
conceive the matter correctly if he compares the principles 

1 Speusippus. 2 Plato and Xenocrates. 

3 Cf. PI. Tim. 52 A, B. 4 io88 b I. 


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 1 to say that 
this is also true of the first principles of reality, so that the 
r 5 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 ; 
20 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 (i) not everything is capable of 
2 5 intermixture, and (2) that which is produced by it is differ 
ent 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 (i) 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 

30 that they are not ; in 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 

1 Speusippus ; cf. A. io;2 b 30-34. 

BOOK N. 5 iog2 a 

else which does persist. 1 Since, then, one thinker 2 places 35 
the i as contrary to plurality, and another 3 places it as 
contrary to the unequal, treating the i as equal, number iog2 b 
must be being 1 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 con 
traries, 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 5 
present in the compound the contrary destroys it, e. g. 
strife destroys the mixture 4 (yet it sho2ild not ; for it is 
not to that that it is contrary). 5 

Once more, it has not been determined at all in which 
way numbers are the causes of substances and of being 
whether (i) as boundaries (as points are of spatial magni 
tudes). This is how Eurytus decided what was the number 10 
of what (e. g. one of man and another of horse), viz. by 
imitating the figures of living things 6 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 15 
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 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 . T 
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 20 
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. 

1 Cf. A. io69 b 3~9, Phys. \. 7. 2 Speusippus. 

3 Plato. 4 Cf. Empedocles, Fr. 17. 

5 a I7~ b 8 seem to refer mainly to Speusippus. 

6 Eurytus may have used (pvrd in this wider sense, as Plato some 
times does. The ordinary Aristotelian sense plants would be difficult 

7 Cf. Empedocles, Fr. 96. 

645-28 X 2 


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. 
25 Nor, of course, is it the final cause. 

One might also raise the question what the good is that 6 
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 

3 o 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 i, and 4 x 5 x 6 by 4, and therefore all pro 
ducts into which the same factor enters must be measur- 

35 able by that factor. The number of fire, then, cannot be 

2x5x3x6, and at the same time that of water 2x3. 
IO 93 a 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, 
5 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. 

10 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 

BOOK N. 6 logs 3 

seven animals lose their teeth (at least some do, though 
some do not), and the champions who fought against 15 
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 E, IF, and Z are concords, 20 
and that because there are three concords, the double con 
sonants also are three. They quite neglect the fact that 
there might be a thousand such letters ; for one symbol 
might be assigned to PP. 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 con 
cords are three ; since as a matter of fact the concords are 25 
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 1 , and 30 
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. iO93 b 
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 5 
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 con 
traries of these, and generally the mathematical relations, 
as some describe them, making them causes of nature, 

1 The ratios corresponding to the fourth and the fifth are respectively 
8 to 6 and 9 to 6. 

2 i. e. first. 


10 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. 1 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 2 of the 
beautiful. For the seasons and a particular kind of number 

15 go together ; and the other agreements that they collect 
from the theorems of mathematics all have this meaning. 3 
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 

20 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 

25 might be brought together. The fact that our opponents 
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 

1 Cf. A. I, 2. 2 Cf. note on A. 986*23. 

3 Sc. that numerical relations are found in things, but are not the 
cause of anything that happens. 


o a 93 b = looo a 

a privative, its meanings 22" 32. 

Abstraction 36 b 3, 23, 6i a 29 ; 
)( qualification 982 a 27, 30* 33, 
77 b 10. 

Accident, accidental A. 30, E. 2, 3, 
K.8, 7 a I5,2i- b 16, 13 b 34-i4 a 20, 
1 5 b 1 7, 1 7 a 7, 27 b 33 ; not knowable 
26 b 3, 64 b 30, 65 a 4 ; its cause 
matter 27 a 13; twofold 3i b 22; 
the same by accident 37 b 6 ; 
nothing accidentally perishable 
59 a i ; )( essential 65* 6. 

Action, concerned with individuals 
981* 17 ; )( motion 48 b 21. 

Actuality (eYe pyfia) 0. 6-9, K. 9 ; 
)( potency 3 a I, 7 b 28, 69 b 16, 7i a 
6, b 22 ; coni. substance, form, 
definition, essence 42 b 10, 43 a 18, 
25,28, 30, 5<D a 16, b 2, 5i b 3i,7i a 
8; )( matter 43 a 6, 45 a 35 7i b 2i, 
76* 10 ; differs with different 
matter 43 a 12 ; the actual identi 
cal with the potential 45 b 21 ; coni. 
complete reality (eVreXe ^aa) 47 a 
30, 5o a 22 ; )( knowledge 48 b 15 ; 
)( motion 48 b 28 ; coni. action 5o a 
22 ; God s actuality pleasure 72 b 
16; actual, syn. individual I4 a 21. 

Aegina I5 a 25. 

Affection, modification, attribute 
(rrddos), its meanings A. 21 ; 
)( substance 983 b 10, g85 b 11, 
38 b 28, 7i a 2; coni. states 986 a 
17, 2o a 19; coni. accidents, 
movements 98c; b 3, 7i a 2 ; )( sub 
stratum 49 a 29 ; essential, proper 
4 b 6, 58 a 37, b 22, 78 a 16 ; change 
in respect of 69 b 12. 

Alcmaeon 986 a 27. 

All (Traira), coni. total 24 a 8. 

Alteration 989 a 27, 42 a 36, 69 b 12, 
88 a 32. 

Analogy 43 a 5, 48 a 37, b 7, 89 b 4, 
93 b 19; the same by i6 b 32, i8 a 

18-21, 988 a 17, 28, 

3o- b 21, 

99i a 1 6, 9 a 27, i2 a 26, 63 b 25-30, 
b 20-32, 7i b 27, 72 a 5, 20, 75 b 
79 b 20, 9i b ii ; quoted 7 b 25, 

9 25, 56 b 2 
15, 28 b 5, 69 b 3i. 

Anaximander 69 b 22 ; referred to 
988 a 30, 52 b 10, 53 b 16, 66 b 35. 

Anaximenes 984 a 5 ; referred to 
984 a 27, 988 a 30, 9 96 a 9, i a 15, 
53 b 16. 

Antisthenes 24 b 32 ; referred to 5 b 
2-5(?),6 a 5(?),u a 7(?), I2 a 2i; 
his school 43 b 24. 

Appearance (^aiveadai, ^avraala) Y. 
5, 6, 98o b 26, 7o a 10. v. Image. 

Archytas 43 a 21. 

Aristippus 996 a 32 ; referred to 78 a 
3i- b 6. 

Aristotle, references to An. Post. 
25 a 34, 37 b 8; Phys. 983** 33, 
98s a 12, 986 b 30, 988 a 22, 993* 
ii,42 b 8(?), 49 b 36, 59 a 34, 62 b 
3i(?), 73 a 32(?), 76 a 9, 8 a 23 
(?) ; De Caelo 986 a I2(?), 989** 
24, 73 a 32(?), 86 a 2 3 (?), 88 b 
24 (?) ; De Gen. et Corr. 42* 8 (?), 
62 b 3i (?),86 a 23(?); Met. A.995 b 
5, 996 b 8, 14, 997 b 4, 59 a 19 5 B - 
993 a 26, 4 a 32, 53 b 10, 76 b I, 77* 
i, 86 a 34(?), b i55 A. 26 a 34 , 2 8 a 


b 7, 56 b 355 Z. 
1 6, 45 a 7(?) 5 b 
17, 7 6 a 9; H. 


52 a 15, 55 a 2, 
4, 18, 20, 43 b 

32, 49 b 27, 53 



, 26, 

Anaxagoras 984 a 11-16, b IS, 985** 

, 39 a 22(?), 

45 b 27, 76 a 9; 9. i7 9, 2i a 20, 
27 b 29, 76 a 9, 88 b 24(?) ; A. 27 a 
19, 64 a 36; M. 37* i 3 (?), 4 2 a 
22 (?), 9o a 15, 28; N. 37 a i 3 (?), 
42 a 22 (?), 86 a 30 ; Eth. Nic. 98 i b 
25 ; lost works 986 a 12 (?), 4 a 2, 
b 34, 2i a 20(?), 54 a 30, 6i a 15. 

Arithmetic 982 a 28, 5 a 31, 9o a 14 ; 
arithmetical number 83 b 16. 

Art 98o b 28 ; comes by experience 
98i a 3; )( science 98i b 26 ; )( ex- 


perience 981* 25, b 8, 31 ; genera 
tion by nature, art, spontaneity 
Z. 7-9, 7o a 6, 17; by reason, art, 
faculty 25 b 22 ; = form 34 a 24, 70* 
15; comes by learning 46 b 37, 47 b 
33 ; architectonic arts 13* 14. 

Assertion, syn. affirmation 8 a 4- b i, 
62 a 24 ; )( affirmation, syn. con 
tact 5i b 24. 

Associable numbers M. 6-8. 
b 33, 997 

16, 35, 

Astronomy 98g b 

9 9 8 a 5, 53 a 10 
Athens io b 10. 
Atlas 23 a 20. 

Atomists referred to 28 b 5, 84 b 27. 
Attribute )( substance 995 b 20, 3 a 25. 

v. Affection. 


26, 5 a 20, b 33, 90* 36. 

Beautiful, syn. good I3 a 22, 9i a 31 ; 
)( good 78* 3i- b 5 ; an original 
principle 72 b 32. 

Becoming, .v. Generation. 

Being (ov) A. 7, I9 a 4, 28 a lo, 3o a j 
21, 42 b 25, 45 b 32, 6i a 8, 78 a 30, j 
89 a 7 ; not a genus 998 b 22, 45 b 6 ; 
and unity I. 2, 986 b 15, 9g8 b 22, 
i a 5- b i, 3 b 22, 4o b i6, 45 b 6, 53 b 
25 ; being qua being, in general, 
without qualification )( particu 
lar being r. i -2, E. i , 6o b 3 1 ; acci 
dental being E. 2, 3, I7 a 7 ; being 
as truth E. 4, e. 10, 65 a 21 ; in 
full sense 27 b 31, 5i b i ; primary 
being, substance 28 a 14, 30; being 
of a thing 29 a 22, $2 b 11, 75 b 5 ; 
being not the substance of things 
i a 5~ b i, 4o b 1 8 ; completely real 
)( material 78 a 30; non-being is 
non-being 3 b 10 ; subject of so 
phistic 26 b 14 ; as falsity E. 4, 0. 
lo ; source of becoming 62 b 26, 
69 b 1 8 ; three kinds 69 b 27 ; am 
biguous 89 a 1 6 ; proof of its reality 
(Platonists) 89 a 2. 

Between, v. Intermediate. 

Broad and narrow (Platonists) 992 a 
12, 88 b 8. 

Callias 981* 8, 33 b 24, 34 a 6. 

Callippus 73 b 32. 

Categories 4 a 29, 1 7 a 23, 24 b 13, 
2 6 a 36,27 b 3i, 28 a 13, 33, 29*23, 
34 b 10, 5i a 35, 55 a i, s8 a 14, 7o b 
i, 88* 23, 89 a 27, b 24. 

Cause A. 2, I3 a 16, 26 a 17 ; philo 
sophy a study of first causes 98i b 

28 ; of all causes ? 995 b 6, 996 a 
1 8 ; primary g83 a 25, 3 a 31 ; 
proximate 44 b i ; four causes 983 a 
26, 7o b 26 ; formal = final 44 b I ; 
= efficient 7o b 26 ; causes not 
infinite in number a. 2, 74 a 29 ; 
cause of accident accidental 27 a 
8, 65 a 6 ; generable without being 
generated E. 3. v. End, Essence, 
Final, Form, Formula, Matter, 
Motive, Principle. 

Change, by something to something 
984 a 22, 69 b 36 ; from opposite 
to opposite or intermediate n b 
34, 57 a 21, 31, 69 b 3; contraries 
do not change 69 b 7 ; coni. non- 
being, substratum, matter, po 
tency io a 15, 42 a 33, 69 b 14, 24; 
four kinds 42 a 32, 69 b 9, cf. 72 b 8 ; 
changeable substance 69* 3. 

Complete A. 16, 23 a 34 ; def. 55 a 1 1 ; 
said to proceed from incomplete 
72 b 34, 92 a 13. 

Compound, composite (o-vvOfros) 23 a 

31, b i, 2 9 b 23, 43 a 30, 75 a 8, 88 b 


Concrete (o-^oXo?) 995 b 35, 999 a 33, 
29 a 5, 35 b 22, 37 a 26, 30, 77 b 8. 

Contact 2 a 34, I4 b 22, 68 b 27, 7o a 
10, 82 a 20, 85 a 3 ; coni. intuitive 
thought 5i b 24, 72 b 21. 

Contiguous 69 a i. 

Continuous, def. 69 a 5 ; by nature, 
art, force i6 a 4, 23 b 34, 4o b 15 ; in 
one, two, three dimensions 6i a 33; 
continuity )( form l6 b 9. 

Contradiction, law of F. 3-6, K. 5, 
6 ; no intermediate r. 7, 55 b j, 
69* 35 )( privation, contrariety 
55 a 38- 

Contrary I. 4, 5, 7, i3 b 12, i8 a 25, 
54 a 25, b 31, 58 b 26, 92 a 2 ; con 
traries said to be principles of 
being 986 a 22, b i, 4 b 30, 7s a 28, 
87 a 30 ; knowledge of them one 
996 a 20, 6i a 19, 78 b 26; reducible 
to one principle 4 a i, b 27; con 
trariety )( difference, otherness, 
contradiction, privation, 4 a 20, 54 b 

32, 55 b I ; one of two contraries 
always privative 4 b 27, n b 18, 
55 b 14, 27, 6i a 19, 63 b 17; con 
traries incompatible n b 17, 63 b 
26 ; coni. negation I2 a g ; contra 
riety in substance i8 b 3 ; con 
traries have same form 32 b 2 ; not 
produced from, compounded of, 


affected by one another 44 b 2 5, 57 b 
22, 69^ 7, 75 a 30; contrariety = 
greatest, complete, difference 5 5 a 
4, 1 6, 58* II ; one term one con 
trary 55 a 19; contraries relative 
56 b 36 ; intermediate composed 
of contraries I. 7 ; which contra 
rieties make difference of species 
T. 9 ; prime contrarieties in being 
6i a 12, b 5, 13 ; sensible con 
trarieties 6i a 32 ; in place 68 b 30 ; 
)( opposite 69 b 4 ; contraries in 
volve matter 75 b 22, 87 b i. 

Coriscus I5 b 17-32, 26 b 18, 37 a 7. 

Counter-earth 86* 12. 

v) 3<D b 

Coupled term (a-v 
1 6, 3i a 6, 43 a 4- 
Cratylus 987 a 32, lo a 12. 

Definition (6piarp.6s t opos) Z. 10-12, 
H.6, 3i a 2, 43 a 21 ; starting-point 
of discussion I2 a 22, b 7; coni. 
essence 3o a 7, 3i a n, 44 a I ; not 
of the concrete and sensible 36 a 
2, 39 b 28 ; of the universal 36 a 28; 
why one Z. 12, H. 6; definition | 
by division 37 b 28 ; scientific 39 b 
32 ; no Idea definable 4O a 8 ; 
coni. number 43 b 34, 45 a 7. v. 


5-20, 9 a 27, b n 



23, 4 17, 

J 5> 39 9? 4 2 II, 09 22, 78 20; 
referred to 29 b 21. 

Demonstration 992 b 31 ; principles 
of993 b 28, 996 b 26, 5 b 9, ii, 13, 
18, 22, 62 a 3 ; not everything de 
monstrable 997 a 7, 6 a 8, ii a 13; 
essence not demonstrable 25 b 14, 
64 a 9 ; sensible things not de 
monstrable 39 b 28 ; demonstra 
tion of necessary truths 39 b 31 ; 
absolute and ad hominem 62* 2 ; 
demonstrative science 997 a 5-30. 

Destructible, destruction, perish 
able 994 b 6, o a 6, 22, 27, b 25, 27 a 
29, 42 a 30, 43 b 15, 44 b 36, 59 a i, 
67 b 24, 69 a 31, b u, 7o a 15. 

Differentia, difference 985 b 13, 
23, 4 a 14, 2o a 33, 35, b 2, 15, 
42 b 15, 58 a 7; its meanings i8 a 
12 ; )( otherness, contrariety 4 a 
21, 54 b 23, 55 a 4, 1 6, 58* u ; j 
opposite, prior, contrary differen 
tiae i6 a 25, 57 b 5, ii ; generic, 
specific i8 a 26, 54 b 28 ; kinds of 

42 b 32; definition by 43* 19; 
what makes it I. 9 ; matter does 
not make it 58 b 6; first differ 
ences 6i b 14; of numbers, units 
M. 8 ; three differences (Demo 
critus) 985 b 13, 42 b 12. 

Diogenes 984 a 5 ; referred to 996 a 
8, i a 15. 

Dionysia 23 b 10. 

Disposition A. 19. 

Divine, the 26 a 20, 64* 37 ; not 
jealous 983 a 2 ; encloses the uni 
verse 74 b 3 ; visible divine bodies 
26* 1 8 ; the divinest knowledge 

9?3 a 5- 

Division, mathematical 994 b 23, 2 a 
19, b 3, 10, 4 8 b 1 6, 6o b 14, 19; 
logical 37 b 28. 

Dyad (two), indefinite 987 b 26, 33, 
988 a 13, 8i a 14, 22, b 21, 32, 82 a 
I3, b 3o, 8 3 b 3 6, 8 5 b 7, 87 b 7, 88 b 
28, 89 a 35, 9i a 5 ; ideal 36 b 14, 8i a 
23, b 27, 82 b 9, 12, 20, 22 ; the 
first number 999 a 8, 85 b 10, 88 b 9. 

29, 986 b 

Egypt 98i b 23. 

Eleatics referred to 
10, 28 b 4, 75 b 15. 

Element A. 3, M. 10, 989* 4, 992 b 18, 
i a 1 8, 59 b 23, 88 b 4 ; whether only 
potential 2 b 33 ; coni. principle, 

four elements (Empedocles) 984 a 
8, 985 a 32, 998 a 30 ; of Ideas 987 b 

Empedocles 984 a 8, 985** 2-10, 
2i- b 4, 988 a 1 6, 27, 989 a 20-30, 
993 a 17, 996 a 8, 998* 30, a 24- 
b 20, i a 12, 69 b 21, 72 a 6, 75 b 2, 
9i b ii ; quoted o a 29, b 2, 6, 14, 
9 b 17, I4 b 37 ; referred to 984 b 
5, 994 a 7, 4 b 33, 28 b 5, 5o b 24, 

53 b 15, 92 b 7- 
End, syn. final cause 994 b 9, 16, 

!3 a 33, 59 a 37, 74 a 3; c ni - 

shape 23 a 34 ; coni. actuality 

5i a 1 6. 

Epicharmus io a 6, 86 a 16. 
Equal, def. 2i a 12, 56 a 22, 82 b 7 ; 

how opposed to great and small 

I. 5 ; syn. one (Plato) 75 a 33. 
Equivocal, equivocation 3 a 34, 3o a 

32, 35 b 25, 4 6 a 6, 6o b 33, 86 b 27. 
Eristic I2 a 19. 
Error )( ignorance 52 a 2. 
Essence ( rjv flvai) Z. 4-6, 8, 993* 

1 8, 994 b i7,25 b 28,3S b i4, 45 b 3J 


coni. definition 3O a 6 ; coni. form 

33 b 5- 

Eternal 987 b 16, I5 b 14, 5o b 7, 51* 
20 ; eternal sensible substance 69 a 
3i, b 25; necessity of an eternal 
substance A. 6 ; time eternal 
7i b 7; eternal things, whether 
composite 8b b 14 ; ungenerated 
9i a 12. 

Eudoxus 99i a 17, 73 b 17, 79 b 21. 

Eurytus 92 b 10. 

Even (Pythagoreans) 986* 18, 99o a 
9; (Plato) 9i a 24. 

Evenus I5 a 29. 

Evil, none apart from particular 
bad things 5i a 17; none among 
eternal things 5i a 20; said to be 
a first principle 75 a 35, 9i b 34 ; 
caused by strife (Empedocles) 
9 8 4 b 32. 

Excess and defect 992 b 6, 4 b 12, 
42 b 25, 35, 52 b 30, 57 a 13, 8; b 18. 

Experience 98o b 28 ; coni. science, 
art 98i a I, b 31 ; = knowledge 
of individual facts g8i a 15. 

Falsity, def. n b 25; its meanings, 
A. 29; non-being in sense of 
falsity E. 4, e. 10 ; )( impossi 
bility 47 b 14; a first principle 
(Plato) 89 a 20. 

Female sex, coni. matter 24 a 35 ; 
not a species I. 9. 

Final cause (ov eWa) 

31, 994 

9, I3 a 2i, 33, b 26, 44 a 36, 5 a 8, 
59 a 36, 72 b 2. v. .Z^/. 

First, its meanings 28 a 31. v. 

Form, things referred to by naming 
their form 35 a 8 ; more real than, 
cause of, matter 29 a 5 ; coni. 
essence 32 b I, 33 b 5, 35 b 32 ; syn. 
shape 999 b 16, i5 a 5, i7 b 25, 33 b 
5, 44 b 22, 52 a 23, 6o a 22, b 26 ; = 
art 34 a 24, 7o a 15 ; not generated 
34 b 7, 42 a 30, 4 3 b 17, 44 b 21, 
69 b 35, 7o a 15; coni. definition, 
formula i6 b 9, 35 a 21, 36 a 28, b 5, 
42 a 28, 43 a 19, 44 b 12, 69 b 33, 84 b 

10 ; syn. substance 32 b i, 4i b 8, 
5o b 2, 84 b 10 ; = final cause 44 b 
i; = efficient 7o b 30 ; syn. posi 
tive state 44 b 33 ; )( becoming 
5o a 4 ; )( matter 5o a 15, 7o a i, 
84 b 10 ; )( privation 44 b 33, 7o b 

11 ; its parts Z. 10, 11. v. Shape, 

Forms (Platonic), v. Ideas. 
Formula, definition, account (\6yos) 
987 b 31, i6 a 33, b 9, 28 a 34,42* 

28, 43 a I9,47 b 34> 5 b 33 I prin 
ciples in the 996 a I ; formula of 
the essence is one 998 b 12; )( 
word 6 b i, 3o a 7 ; formula )( 
definition (opio-^os-j 3o a 7, 14, 37 b 
II ; parts of Z. 10, n, i6 a 35, 
23 b 23, 33 a 2; prior in i8 b 31, 

2 8 a 3 2, 3 8 b 27,4 9 b ii, 54 a 28,77 b 
i, 78 a 10 ; )( concrete individual, 
matter 39 b 20, 58 b 10, 18, 64 a 23, 
74 a 34 ; separable in 42 a 29 ; 
coni. science 46 b 7, 59 b 26 ; 
analysis of 63 b 18 ; cause as de 
finition 7o a 22 ; primary in de 
finition, in time &4 b 15 ; one in 
definition, in number 87 b 12. 

( From , its meanings A. 24, 99i a 19, 
994 a 22, 44 a 23, 92 a 23. 

Full (Democritus) 985 b 5, 9 a 28. 

Generation, production, becoming, 
is of the concrete thing Z. 8, 98 i a 
17, 34 b 7, 42 a 30, 43 b 17, 44 b 2i, 
6 9 b 35* ?o a !5; posterior in 
generation, prior in nature, form, 
substance 9&9 a 15, 5o a 4, 77 a 26 ; 
two types 994 a 22 ; from non- 
being, matter, privation, con 
traries, the potential 994 a 27, 32* 

20, 33 a 9> 55 b n,62 b 26, 69 b 18, 
88 b 17, 9i b 34; of something 
from something by something 
999 b 6, io a 20, 3 2 a 13, b 3i, 33 a 
24, 44 b 24, 49 b 28 ; by nature, art, 
spontaneity Z. 7, 9 ; )( making 32 a 
26; the product must be divisible 
33 b 12, 49 b 35; from a member 
of the same species 34 a 21, 49 b 

29, 7o a 5 ; absolute and partial 
42 b 7, 67 b 22, 69 b 10, 88 a 33. 

Genus A. 28, 54 b 30, 57 a 27, b 38, 
59 b 27; proximate, ultimate 995 b 
29, 998 b 15, 99 9 a 31, 23 a 27, 
34 a I, 37 b 3<^ 59 b 27; whether 
genera are first principles 998 a 

21, I4 b 11, 42 a 14, 69 a 27; 
part of species 23 b 24 ; coni. 
definition, differentia, species Z. 
12, 998 b 5, i3-999 a 23, M b 9, 
i6 ft 24, b 32, 23 a 27, b 18, 37 b 19, 
39 a 26, 54 b 27, 57 b 7, 59 b 36 ; 
being and unity not genera 998 b 

22, 45 b 6 ; is matter of species 
24 b 8, 38 a 6; other in genus 


24 b 9; )( universal 28 b 34; not 
substantial Z. 13, 42* 21, 53 b 21 ; 
otherness of the genus $8 a 7. 

Geometry 983* 20, 992 a 21, 997 b 
27, 998 a i, 5 a ii, 31, 5i a 21, 6i b 
3, 78 a 25, 89 a 22. 

God, a first principle 983 a 8 ; is life 
72 b 14 ; identified with the One 
by Xenophanes 986 b 24 ; gods 
in human form 997 b 10, 74 b 5 ; the 
stars held to be gods 74 b 2. 

Good, syn. final cause 983 a 31, 
59 a 36; syn. beautiful I3 a 22, 
91 a 30 ; )( apparent good I3 b 27 ; 
how a first principle 75 a 12, 38 ; 
)( beautiful 78 a 31; whether 
discussed by mathematics 78 a 3 1 ; 
how related to first principles 
9i a 30, 92^ 9 ; Idea of 996 a 28. 

Great and small, how opposed to 
equal I. 5 ; (Plato) 987 b 20, 26, 
988* 26, 992 a 12, 998 b 10, 83 b 23, 
32 ; kinds of 992 a n, 85 a 9. 

Habit, having, state (cgis) A. 20, 
986* 17, I5 b 34, 44 b 32, 46 a 13, 
70 a 12 ; )( privation 55 b 13. 

Harmonics 997 b 21, 77* 5, 78* 14. 

Have, hold, its meanings A. 23. 

Hearing 98o b 23. 

Heaven, only one 74 a 31. 

Hellen24 a 33. 

Hellenes 24 a 33. 

Heraclidae 58 a 24. 

Heraclitus 98 4 a 7, 987 a 33, 5 b 25, 
io a ii, 13, I2 a 24, 34, 62 a 32,63 b 
24, 78 b 14; referred to 984 a 27, 
9 89 a 2, 99 6 a 8, i a 15. 

Hermes 2 a 22, I7 b 7, 48 a 33, 5o a 

Hermotimus 94 b 19. 

Hesiod g84 b 23, 989 a 10, o a 9 ; re 
ferred to 983 b 27, 23 a 19, 9i b 6 ; 
quoted 984 b 27. 

Hippasus 984 a 7 ; referred to 996 a 
8, i a 15. 

Hippo 984 a 3. 

Homer 9 b 28; quoted 76 a 4; re 
ferred to 983 b 30, 9t b 6 ; Homeric 
scholars 95 a 27. 

Homoeomerous 984 a 14. 

Hot, the (Parmenides) 987** I. 

Hypothesis )( necessary principle 
5 b IS- 

Ideas (Platonic) A. 6, 9, B. 6, Z. 6, 
M, M. 4, 5, 988 b i,997 b 2, i a 4, 

28 b 20, 33 b 27, 36 b 13, 42 a ii, 
59 a 10, 7o a 27, 73 a I7 75 b 18, 
7 6 a 3 i,83 b 34, 86 a 31, b 14, 9 a 
16, b 20, 9i b 28 ; elements of 987 b 
19; of negations 99o b 13, 79 a 9 ; 
of relations 99o b 16, 79 a 12; of 
manufactured objects 99 i b 6, 6o b 
28, 7o a 14 ; coni. numbers 99 i b 
9, 76 a 20, 8o b 12, 22,8i a 21, 83 b 
3, 86 a 4, 88 b 34, 9 b 33, 35, 9i b 
26 ; participate 99o b 28, 40* 27 ; 
eternal sensibles 997 b 12; as 
causes 33 b 26 ; how related 39 b 
4 ; indefinable 4o a 8 ; transcen 
dent 40 a 9, 86 a 33 ; universal 42 a 
15, 86 a 33 . 

Ignorance )( falsity, error 52 a 2. 

Iliad, an artificial unity 3O a 9, b 9 

45 a 13- / 

Image (fyavraa p.o) 99o b 14, 79 a ii. 
v. Appearance. 

Imitation (Pythagoreans) 987 b n. 

Imperishable I. 10, 4o b 3i. 

Impossible I9 b 22 ; )( false 47 b 14. 

In , its meanings 23 a 24. 

Inassociable numbers M. 6-8. 

Incapacity, impotence, its mean 
ings I9 b 15, 46 a 29. 

Incomposite entities 5i b 17, 27. 

Increase 42 a 35 ; )( diminution 
6o. b n, 88 a 31. 

Individual (aro^ 

12 ; (naff eKaarov acton con 
cerned with individuals 98 i a 17 ; 
is there anything apart from 
individuals ? 999 a 26, 6o a 3 ; syn. 
numerically one 999 b 33 ; are 
the first principles individual ? 
M. 10, 3 a 7, 7i a 20; syn. actual 
I4 a 21 ; prior in order of percep 
tion i8 b 33- v. This. 

Indivisible (udiaipeTov) I. i ; in 
quantity, in kind 999 a 2, i4 a 27, 
l6 a 19, 21 ; (iiTOfjiov) lines, magni 
tudes 992 a 22, 83 b 13, 84 b i ; 
species, form 998 b 29, 34 a 8, 
58 a 18; indivisible in genus 
i8 b 6. 

Induction )( demonstration, defini 
tion 992 b 33, 48 a 36 ; used 25 b 
15, 54 b 33, 55 a 6, b 17, 5 a 9 64* 
9 ; Socratic 78 b 28. 

Infinite, the a. 2, K. 10 ; as sub 
stance and principle 987 a 16, 

995 b 29, 

9, 4 b 33 ; composed of great and 
small 987 b 26 ; causes not infinite 
in number a. 2, 74* 29 ; not 


thinkable 994 b 22, 30, 999 a 27 ; 
by addition 994 b 30 ; how poten 
tial 48 b 9 ; has no separate exis 
tence 48 b 14 ; infinite regress 994 a 
3, 8, 20, b 4, o b 28, 6 a 9, ic a 22, 

I2 a 12, b 22, 22 b 9, 30 b 35, 32* 

3, 33 b 4, 41 b 22, 6o a 36, 7o a 2, 
74 a 29; no infinite magnitude 
73 a 10; whether number is in 
finite 83 b 36 ; principles infinite 
in number (Anaxagoras) 984 a 13. 

Intelligible )( sensible 99o a 31, 
999 b 2, 36 a 3, 10, 45* 34. 

Intermediate, def. 57 a 21, 68 b 27; 
no intermediate between contra 
dictories r. 7, 55 b i, 69 a 3 ; com 
posed of contraries 1. 7 ; (Plato) 
987 b 1 6. 

Intuition (vorjo-is), coni. perception, 
definition 36* 6. v. Thinking. 

Ion 24 a 34. 

lonians 24 a 33. 

Italian school 987 a 10-31, 988 a 26. 

Itself, used to signify Ideas 4o b 34. | 

Knowledge, science (eVaa-T^/), de- j 
sired by all 98o a 21 ; springs i 
from sensation o.8o a 28 ; )( art j 
98 i b 26 ; theoretical, productive, j 
practical 982 a i, 993 b 20, 25 b 21, 
46 b 3 ; pure, applied, superior, 
ancillary o,S2 a 14, 30, b 4, 27, 
996 b 10 ; its highest object 982 b 
I, 996 b 13; the divinest know 
ledge 983 a 5 ; is of causes 983 a 

25, 993 b 23, 994 b 29, 25 b 6 ; not 
of the sensible or accidental Z. 15, 
987 a 34, 26 b 3, 27 a 20, 64 b 30, 
65 a 5, 77 b 35 ; knowledge of con 
traries one 996 a 20, 6i a 19, 78 b 
26 ; is of species, form 998 b 7, 
3i b 6; )( sensation 999 b 3; of 
universals, individuals 3 a 14, 59 b 

26, 6o b 20, 86 b 6, 87 a 15 ; one 
science to one genus 3 b n, 55 a 
31 ; )( opinion 8 b 27, 30, 39 b 32 ; 
prior in l8 b 30, 28 a 32 ; ratio- 
cinative 25 b 6 ; not of matter 
36 a 8 ; coni. definition, formula 
28 a 32, 46 b 7, 59 b 26 ; )( actuality 
48 b 15 ; how a measure of ob 
jects 57 a 9 ; its two meanings 
87 a 15- 

Leucippus 985 b 4, y 
referred to 84 b 27. 
Libya io b u. 

32, 72 a 7; 

Like, def. i8 a 15, 2i a 11, 54 b 3; 
said to be known by like o b 5. 

Limit, its meanings A. 17; of bodies 
2 b 10, 6o b 16; (Pythagoreans) 
987 a 15, 99o a 8, 4 b 32. 

Line 2 a 5, i6 b 26, 36 b 12, 43 a 33; 
perceptible lines 998 a i ; not com 
posed of points i b 18 ; indivisible 
line 9p2 a 22, 84 b i. 

Logic (dva\VTid) 5 b 4. 

Love (epos) (Parmenides) 984 b 24, 
988 a 34; ((piXia, (j>i\oTr)s) (Em- 
pedocles) g85 a 3, 24, 988 a 33, 
o b n. 

Luck (TVXI) 98i a 5, 984 b 14, 32 a 29, 
5-a 30- generation by nature, art, 
spontaneity, luck Z. 7, 49 a 3, 
7o a 6. 

Lycophron 45 b 10. 

Magi 9i b 10. 

Making )( production 32 a 26; )( 

thinking 32 b 15. 
Male and female I. 9. 
Many )( one I. 3, 6 ; )( much 56 b 

15 ; matter of the one 75 a 33; 

and few (Platonists) 87 b 16. 
Mathematics 98i b 23,985 b 24, 992 a 

32, 996 a 29,4 a 9, 2 6 a 7, 9, 12, 19, 

6i a 28, b 32, 6 4 a 32, 77 b i,78 a 33; 
mathematical objects )( sensible 
989 b 32, 99o a 15, 36 a 4l )( Ideas 
B. 6, 28 b 20, 76* 20, 83 a 23, 9o b 
26 ; many of one species 2 b 14; 
whether substances M. 1-3, 42 a 
n, 69 a 35 ; not separable 59 b 13; 
mathematical matter 992 b 2, 59 b 
16; language 995 a 6, 8o b 26; 
parts of mathematics 4 a 7 ; 
mathematical sciences )( produc 
tive 64 a i ; mathematical number 
M. 6, 76 a 20, 86 a 5. 
Matter H. 3, 4, 983* 7-94 a 18, I5 a 
7, I7 a 5, 42 a 26, 58 b 6, 14; def. 
29 a 20 , syn. substratum 983 a 29, 
985 b 10, 988 a u, 992 b i, 22 a 18, 
24 b 8,42 a 26, 32, b 9, 6i b 22, 7o a n; 
a principle 983 b 7,986 a 17,46* 23 ; 
)( definition, form, complete re 
ality, actuality 986 b 20, 29 a 5, 

35 a 8, 3 8 b 6,4i b 7, 43 a 6, 45 a 35, 
5o a 15, 7o a i, 7i b 21, 74 a 34, 76 a 
9, 78 a 30, 84 b 9 ; coni. female sex 
2 4 a 35 I genus matter of species 
24 b 8, 38 a 6 ; coni. motion 26 a 3; 
cause of accident 27 a 13 ; whether 
substance Z. 3, 4 2 a 27, 49 a 36, 77 a 


36 ; necessary, to explain genera 
tion and change 32* 17, 42* 32, 
44 b 27, 69 b 3 ; unknowable in it 
self 36* 8 ; perceptible )( intelli 
gible 36* 9, b 35, 45 a 34; indefi 
nite 37 a 27, 49 b i ; coni. potency 
39 b 29, 42* 27, b 9, 49 a 23, 50* 
15, 6o a 20, 69 b 14, 7o b I2,7i a 10, 
88 b i, 92 a 3; indestructible 42* 
30 ; matter for locomotion, gene 
ration, &c. 42 a 34, b 6, 69 b 26 ; 
actuality varies with it 43 a 12 ; 
proximate matter 44 a 17; )( sub 
stratum 44 b 9 ; proximate matter 
= shape 45 b 18 ; of mathematical 
objects 992 b 2, 59 b 16 ; different 
things have different matter 69 b 
25 ; individual in appearance 7o a 
10 ; involved in contraries 75 b 
22, 87 b i. 

Measure, def. of unity $2 b 18, 87 b 
33 ; exact, homogeneous with 
thing measured, indivisible 52 b 
3 6 ) 53 a 25, 88 a 2; how know 
ledge is a measure 57 a 9 ; man 
the measure of all things (Prota 
goras) 53 a 36, 62 b 14, 19, 63 a 4. 

Megaric school 46 b 29; referred to 

5 b 35 (?). 

Melissus 986 b 19. 

Memory 98o a 29. 

Middle, excluded r. 7. 

Mixture, intermixture 989 b 2, 42 b 
29, 82 a 2i, 92 a 24. 

Monists 986 b 21. 

Motion, spatial (<#>pa) 6g b 12, 26, 
72 b 5 ; the first kind of change 
72 b 8, 73 a 12; simple 73 a 29 ; of 
the planets A. 8. 

Motive cause A. 3, 4, 983 a 30, 984 a 
27, 988 b 27, 9 9 6 b 6, I3 b 9,24; 
necessity of 991 b 5, 8o a 4 ; prior 
to the moved io b 37, 7o a 21 ; 
unmoved prime mover A. 7, i2 b 
31 ; fire a motive cause 984 b 6; 
the self-mover (Plato) 72 a i. 

Movement (KIVTJO-IS), coni. sensation, 
matter 989 b 32, 26 a 3, 36 b 29 ; 
)( rest 4 b 29, io a 36, I2 b 23, 25 b 
20, 49 b 7 ; coni. activity, action 
20 b 20, 22 a 7, b 5, 23 a 18 ; coni. 
nature 25 b 20 ; )( action 48 b 18 ; 
)( actuality 48 b 28; eternal 7i b 
7, 33 ; simple, continuous, un 
resting, uniform movement 53 a 
9, 7i b 9, 72 a 2i,78 a 13. 

Music of the spheres gS6 & 2, 93 b 4. 

Mutilated A. 27. 

Myth 982 b 18, 983 b 29,995 a 4, o a 9, 
I8,7i b 27,74 b i,4,75 b 26,9i a 34. 

Nature, its meanings A. 4 ; )( habit, 
spontaneity, luck, thought 98 i b 4, 
32 a 12, 65 a 27, 7o b 30, 7i b 35 ; 
)( generation 989** 15 ; not the 
whole of reality 5 a 34 ; syn. 
matter I4 b 33, 24 a 4; )( force I5 b 
15, 52 a 23, 7i b 35 ; = that which 
contains its principle of motion 
in itself I4 b 18, 25 b 20, 49 b 8, 
7o a 7; by nature )( to us 29 b 
7 )( art 32 a 12, 7o a 7, 17; 
syn. form, complete reality, posi 
tive state 32 a 24, 44 a 9, 7o a 1 1 ; 
the only substance in destructible 
things 43 b 23 ; )( potency 49 b 8 ; 
natural objects,bodies, substances 
I4 b 19, 32, 28 b 10, 42 a 7, 7o a 5, 
90 a 32 ; )( unnatural 33 b 33. 

Necessity, def. 6 b 32 ; its meanings 
26 b 28, 64 b 33 ; necessary, its 
meanings A. 5, 72 b II ; )( usual, 
accidental 25 a 15, 1 8, 20, 26 b 28, 
27 b 8, 64 b 33-65 a 3 ; objects of 
demonstration necessary truths 

39 b 3i- 

Negation )( privation 4 a 12; coni. 
contrariety 1 2 a 9, 46 b 13; privative 
negation 56 a 17, 29 ; Ideas of 
negation 99o b 13, 79 a 10. 

Nemean games i8 b 18. 

Non-rational potencies 46 b 2, 48 a 

4, 5 b 33- 

Number M. 6-9, N. 1-3, 5, 6, 2O a 13, 
39 a i2, 53 a 3o, 57 a 3,85 b 22,8S a 5; 
numerical ratio 985 b 32, 99i b 13, 
J 7> J 9, 993 a i7> i b 3o, 53 a i6,6i b i, 
92 b 14, 31 ; said to be limited by 
ten 986 a 9, 73 a 20, 84 a 12, 32; ele 
ments, attributes, generation of 
number 986 a 17, 4 b 10, 84 a 3, b 28, 
87 b 15, 89 b 12, 9o a 2i, 9i a 23, 29 ; 
numbers as principles, substances 
985 b 26, 986 a 16, 987 a 19, b 24, i a 
25, b 26, 36 b I2,76 a 3i, 8o a 13, 83 a 
23, 9o a 4, 23, 92 b 16, 26; prime 
numbers 987*^34, 52 a 8, 8i a 5; sen 
sible )( intelligible, ideal 99o a 31, 
9o b 36 ; coni. Ideas 99 i b 9, 76 a 20, 
8o b 12, 22, 8i a 7, 21, 83 b 3, 86 a 6, 
88 b 34,9o a 1 6, b 33, 37, 9 i b 26; 
wherein does its unity consist? 
992 a i, 44 a 3, 45 a 8; numerical 
unity 999 b 26, 33, i6 b 31, i8 a 13, 


33 b 3i,39 a 28, 54 a 3 4, 6o b 2 9 , 87 b 
12: unity the origin and measure 
of number i6 b 18, 2i a 13, 52 b 24, 
88 a 6; quality, differentia of num 
ber M. 6-8, 2o b 3; coni. definition 
43 b 34, 45 a 8 ; associable )( in- 
associable M. 6-8 : mathematical, 
arithmetical number 76 a 20, 8o a 
21, 30, b 13, 8i a 6, 83 b 3, 16, 86 a 
5, 9 b 33i 35, 9i b 24 ; related as 
prior and posterior, 8o b 1 2 ; num 
ber composed of abstract units 
So b 19, 30, 82 b 6, 83 b 17, 92 b 
20 infinite or finite ? 83 b 36 ; 
powers of two 84* 6 ; )( definition 
87 b 12; one not a number 88 a 
6 ; numerical succession 85 a 4 ; 
square, cube 93 a 7. 

Ocean 983 b 30, 9i b 6. 

Odd (Pythagoreans) 986 a 1 8, 99o a 
9, 9l a 23. 

One I. 1-3 ; its meanings A. 6, 52 a 
15; one over many 99<D b 7, 13, 
99l a 2, 4o b 29; unity and being 
I. 2, 998 b 22, i a 5, 3 b 22, 4o b 16, 
45 b 6 ; not a genus 998 b 22, 45 b 
6; = indivisible 999 a 2, 4i a 19; 
in quantity, species, number, ge 
nus, by analogy 999 a 2, b 25, 32, 
I6 b 3 i, i8 a i 3 , 33 b 3 i, 39 a 28, 54 a 
34, 6o b 29, 87 b 12 ; unity of com 
mon reference, of succession, of 
common predicability, of signifi 
cance 3 a 33, 5 a 10, 6 b 15 ; one in 
continuity, form, definition i6 b 9; 
origin and measure of number 
i6 b 18, 52 b 24 ; the one not sub 
stance I. 2, 4o b 1 8 ; unity of num 
ber and of definition Z. 12, H. 6, 
992 a i, 44 a 3 ; the one a measure 
52 b 1 8, 87 b 33 ; one and many I. 
3, 6, 87 b 28; )( simple 72 a 32; 
the many, matter of the one 75 a 
33 ; one by contact, intermixture, 
&c. 82 a 20; primary one 83 a 25; in 
what sense a starting-point 84 b 
1 8; one in definition, in number 87 b 
J2; i not a number 88 a 6; (Pytha 
goreans) 986 a 19, 987 a 1 8, 27, i a 
10 ; (Eleatics) 986 b 15, i a 33; 
(Plato) M. and N. passim, 987"^ 
21, 992 a 8, i u s; (Anaxagoras) 
989 17. 

Opinion )( knowledge 8 b 28, 30, 

39 b 33- 
Opposition, its kinds A. 10, 54 a 23, 

14, b 5, 

i 55 a 38,57 a 33;changetoopposites 
n b 34, 57 a 3i 69 b 4; opposite 
differentia i6 a 25 ; potency of 
opposites 5o b 8, 30; opposite )( 
contrary 69 b 4. 

Order 984 b 17, 985 b 14 ; not in sub 
stance 38 a 33. 

Orphic cosmogony referred to 9i b 5. 

Other, def. i8 a 9 ; its meanings 54 b 
14 ; in species 1. 8, 9, i8 a 38 ; in 
genus 24 9 ; otherness of the ge 
nus 58 a 7 ; otherness )( difference 
54 b 23; (Pythagoreans) 87 b 26. 

Parmenides 984 b 3, 986 b iS~987 a 2, 
l a 32 ; quoted 984 b 25, 9 b 21, 89 a 
3 ; referred to 4 b 32. 

Part, its meanings A. 25, 34 b 32 ; 

parts of definition, of concrete 

thing Z. 10, ii. 

I Participation 987 b 13, 

30 a 13, 3i b i8, 37 b i8/45 a i8, b 8, 
79 b 1 8 ; Ideas participable 99O b 
28, 40 a 27, 79 a 25. 

Pauson 5o a 20. 

Perceptible, v. Settsible. 

Perception, v. Sensation. 

Perishable, v. Destructible. 

Persian war i8 b 16. 

Petitio principii 6 a 17, 20. 

Pherecydes 9i b 9. 

Philosophy is knowledge desirable 
for its own sake, most accurate, 
communicable, most divine and 
honourable A. 2 ; starts from 
wonder 982 b 12; turned into 
mathematics 992 a 32 ; is know 
ledge of the truth 993 b 20 ; treats 
of the axioms r. 3, K. 4, 995 b 8 ; 
treats of being as being r. i, 2, 
K. 3 ; has distinct parts 4 a 2, 26 a 
18; )( dialectic, sophistic 4 b 17 ; 
theoretical, practical, &c. E. i ; 
first philosophy 26 a 24 ; the philo 
sopher fond of myth 982 b 18 ; can 
speculate about anything 4 a 34. 
! Phrynis 993 b 16. 

I Physics, natural philosophy, philo 
sophers 986 b 14, 989 b 3o, 99o a 3, 
7,992 b 4,995 a i8,i a i2,s a 31, 34, 
b i, 6 a 2, 25 b 19, 26, 26 a 4, 12, 
37 a 14, 1 6, 59 b 1 6, 6i b 6, 28, 62 b 

22, 26, 

7 8 b 19 

Place 92 a i7; changeof42 a 34,69 b i3. 
i Planets A. 8. 
Plato A. 6, 9, 988 a 26, 990* 30, 996 a 

36, 7i b 27, 75 b 27, 


6, i a 9, I9 a 4, 28 b 19, 53 b 13, 83 a 
32 : referred to Z. 14, M. and N. 
passim (esp. 76 a 19, 77 a n, 8o b 

11, 24, 8i a 24, 84 a 13, 85 a 9, b 7, 
86 a ii, 87 b 5, 13, 9i a i, b 35,92 b 
i), 983 b 27, 995 b 16, 997 b i, 
998 b 9, i b 19, 2 a ii, b 13, i7 b 19, 
28 b 19, 3o a 26, 3i a 30, 33 b 19, 34 a 
2, 36 b 14, 39 a 26 - b 19, 5o b 35, 
5i a 17-21, 59 a 10, b 3, 6o b 6, 
69 a 34, 7o a 27, 7i b 15, 73 a 17, 20, 
75 b 19-28 ; his works quoted, 
Hippias Mi?ior 25 a 6, Laws 72 a 
I (?), Phaedo 99 i b 3, 8o a 2, Phae- 
drus 72 a I (?), Republic 992* 
33, Sophistes 26 b 14, 64 b 29, 
89 a 20, Theaetetus lo b 12, 7Y- 
maeus 57 b 8, 7i b 32, 72 a 2, 92 a i. 

Platonists referred to M. and N. 
passim, 99o b 9, 997 b 3, 998 a 7, 
2 b 14, 4 b 32, 28 b 24, 3i a 31, 3 6 b 
13, 4o b 2, 43 b 34, 45 a 16, 5o b 35, 
56 a 10, 66 a ii, 6g a 26, 75 a 32. 

Plurality 57 a 3, 87 b 6, 9i b 34; def. 
2o a 8, 54 a 22 ; )( unity 4 a 10, 87 b 
28 ; first plurality 85 b 9. 

Point 992 a 19, i6 b 26, 6o b 18, 85 b 

Polus98i a 4. 

Polyclitus I3 b 35~i4 a 15. 

Position 985 15, i6 b 26, 22 b 2, 4 b 
19, 77 b 30. 

Possible 0. 4, I9 b 28. 

Potency, power, potentiality, def. A. 

12, 0. 1-9 ; whether the elements j 
exist potentially 2 b 33; potency 
or actuality prior? 0. 8, 3 a i ; )( ac- | 
tuality 7 b 28, 69 b 15, 7i a 6, b 23 ; j 
power in geometry I9 b 33, 46 a 7 ; j 
)( reason, art, nature 25*22, 27 a 
6, 33 b 8, 49 b 8, 64 a 13 ; coni. 
matter 42 a 27, b 10, 5o a 15, 6o a 


14, 7o 12, 7i a 10, 

92 a 3 ; irrational, rational 0. 2, 
47 b 3i 5o b 33; the potential 
and the actual are one 45 b 21 ; in 
what sense the infinite and the 
void exist potentially 48 b 9 ; when 
a thing exists potentially 0. 7 
primary potency 49 b 13 ; the eter 
nal not potential 5o b 7 ; potency 
is of opposites 5o b 8, 30, 5i a 6, 
7i b 19. 

Practical knowledge 993 b 21, 25 b 
21, 25. 

Primary 3o a 10, 37 b 3, 75 b 24; syn. 
self-subsistent3i b 14 ; substance 

32 b 2 ; coni. categories 34 b 9. v. 

Prime numbers 987 b 34. 

Principle, beginning, starting-point, 
originative source (apx^), its 
meanings A. I ; material 9>3 b 7, 
24, 9 8 4 a 6, 9 86 a 17, 9 87 a 4, 46 a 
23 ; efficient 984 a 27, 46 a 14, b 3, 
49 b 6, 7o a 7, b 25; final so a 7; 
formal 69 a 28, 76 a 24, 8o b 6, 32 ; 
God a first principle 983** 8 ; con 
trary principles 986 a 22, b I, 4 b 
31, 75 a 28, 87 a 30; principles of 
demonstration 993 b 28, 996 b 26, 
5 b 9, 11, 13, 1 8, 22, 6 a 5, 62 a 3; 
a first principle necessary a. 2 ; 
whether genera are first princi 
ples 998 a 21 ; whether one in 
kind or in number A. 4-5, 999 b 
24, 6o b 29 ; whether the same for 
things perishable and imperish 
able o a 6 ; whether potential or 
actual 2 b 32 ; whether universal 
or individual M. 10, 3 a 7, 6o b 20, 
6g a 26-30, 7i a 20; of being as 
such r. i, E. i ; the simple a 
principle 59 b 34 ; )( element 4i b 
31, 7 b 23 ; in what sense unity 
is a starting-point 84 b 18; the 
principles, how related to the 
good 9i a 30, 92 a ii ; infinity of 
principles (Anaxagoras) 984 a 13; 
ten (Pythagoreans) 986 a 22. 

Prior, its meanings A. n ; in 
generation, nature 989 a 15 ; in 
knowledge, definition, perception 
l8 b 30 ; in formula, time, genera 
tion, 38 b 27 ; in formula, sub 
stantiality, time 49 b 1 1 ; in gene 
ration, form, substantiality 5O a 4 ; 
in definition 54 a 28, 78 a 9; in 
definition, substantiality 77 b i ; 
no Idea of a class which includes 
prior and posterior members 
999 a 6 ; numbers related as prior 
and posterior 8o b 12. 

Privation 4 a 12, ig b 7, 58 b 27 ; its 
meanings A. 22, 46 a 31 ; one of 
two contraries privative 4 b 27, i i b 
1 8, 55 b 14, 27, 6i a 20, 63 b 17 ; 
)( state, form I9 b 7, 44 b 32, 55 b 
13, 7o b 12; primary 46 b 14; per 
fect 55 a 35 ; )( negation, con 
trariety 4 a 12, 55 a 33; privative 
negation 56 a 17, 29. 

Production, v. Generation. 

Productive knowledge 982* I, b II, 


25 b 21, 25 ; )( mathematical 

6 4 a i. 

Proof, negative (t\eyx os ) 6 a 18. 
Protagoras r. 5, 6, K. 6, 998** 3, ; b 

22, 47 a 6, 53 a 35; referred to 

999 b 3- 
Pythagoreans 985^ 23~986 b 8, 987** 

13-27, ii, 23, 31, 989 29-990 a 
2 9 , 99 6 a 6, i a 10 36*18, 53 b i2, 
72 b 31, 78 b 21, 8o b 16, 31, 8s b 8- 

19, 9o a 20-35, 9 ia 1 3) referred 
to 99 S b 9, 2 a ii, 4 b 31, I 7 b i 9 , 

20, 28 b 5, 1 6, 36 b 8, 43 b 34, 6o b 6, 
66 a u, 75 a 36, b 28, 76 a 2i, 87 b 
I7(?), 26, 9o b 2. 

Pythian games i8 b 18. 

Qua, def. 65 b 23. 

Quality A. 14, 28 a 15, 68 b 18; of 
number 2o b 3 ; definite 63* 27 ; 
change of 6g b 10 ; posterior to 
quantity 83 a n. 

Quantum, quantity, A. 13 ; attri 
butes of 2o a 19; known by a 
measure 52 b 20; indefinite 63 a 
28 ; change of 69 b 10; prior to 
quality 83 a 1 1 ; motion and time 
incidentally quantitative 2O a 29. 

Ratio (Actyos) 98$ b 32, 991 b 13, 17, 

I9 993 a I7> i b 3, 53 a 16, 6i b I, 
92 14,31. 

Reality, realization, complete (eWe- 
AeV") 7 b 28; )( matter 38 b 6, 
78 a 30 ; separates 39 a 7 ; coni. 
substance 44 a 9 ; )( actuality 47 a 
30, 5o a 23. 

Reason, thought, mind (vovs) A. 7, 
9 , 7o a 26; in nature 9 84 b 15; 
human 99 3 b n, 75 a 7; )( art, 
faculty 2fj b 22 ; acts by contact 
72 b 21; divinest of things 74 b 16; 
(Anaxagoras) 984 b 15, 9&9 b 15, 
17, 69 b 3i ; (Parmenides) 9 b 23. 

Relation A. 15, 56 b 34, 89 b 6, 14; 
Ideas of 99o b 16, 79 a 12 ; rela 
tive )( absolute 9 9 o b 20; least 
substantial of the categories 88 a 
22, 30. 

Same, the 9 95 b 21, 2i a n ; its 
meanings A. 9, 54 a 32 ; in species 
i8 b 7, 49 b 1 8, 29, 58 a 18 ; by 
accident 37 b 6. 

Scale 985 b 31, 986 a 3 ; seven notes 
in the scale 93 a 14. 

Science, v. Knowledge. 

! Sensation, sense, perception (ai- 

ff@rip.a) IO b 32, 63 4 ) (a io OrjO is) 

sight our most precious sense 
98o a 23 ; sensation the source of 
memory 98o a 28 ; )( wisdom 98 i b 
10 ; )( knowledge 999 b 3 ; not a 
physical alteration 9 b 13 ; special 
sensation always true io b 2 ; con 
flict of sensations io b 4, ll a 25 ; 
coni. intuition 36 a 6. 

Sensible, perceptible 987 a 33, 997 b 
12, io a 3, 42 a 25, 6 9 a 30, b 3, 78 b 
16 ; )( mathematical 989 b 31, 
99o a 15 ; no knowledge of sensi 
ble things Z. 15, 987 a 34; )( in 
telligible, ideal 99o a 31, 999 b 2, 
36 a 3> 9, 45 a 34, 9 b 35 5 are 
there non-sensible substances ? 
997 a 34, 2 b 12, 59 a 39; coni. 
movement 989" 31, 36 b 28; con 
trarieties 6i a 32. 

Sense-organ 63 a 2. 

Separable, capable of existing apart 

I7 b 25 

28, 26 a 9, 28 a 34, 
a b a 

9, 59" !3> 6o a 8 > 7 b 30, 86 a 33 ; 
in formula )( without qualification 
42 a 29 ; actually )( for knowledge 
48 b 15. 
Separate (verb) 989* 3, 4o b 28, 78 b 

3 i,86 b 4- 

Seven (Pythagoreans) 93 a 13. 
i Shape, coni. end 23 a 34 ; coni. 
formula 42 a 28 ; coni. actuality 
43 a 25, 28, 31; = proximate 
matter 45 b 18; coni. form 999 b 
16, I5 a 5, i7 b 25, 33 b 5, 52 a 22, 
6o a 22, b 26. 
Sight, the most precious sense 

98o a 23. 

i Simonides 982 b 30, 9i a 7. 
Simple, coni. necessary I5 b 12; 
coni. principle 59 b 35 ; )( one 
72 a 32 ; bodies 984* 6 ; concepts, 
substance 2; b 27, 4i b 9, 72 a 32 ; 
movement 53 a 8, 73 a 29; genera 
tion 69 b 10, 88 a 33. 
Snub Z. 5, 25 b 31. 
Socrates 987" 1-4, 78 b 17-31, 86 b 3. 
I Socrates the younger 36 b 25. 
Solon referred to 983 a 3. 
Sophistic 4 b 1 8 ; concerned with 
non-being 26 b 14 ; sophistical 
objections 32 a 6, 49 b 33- 
i Sophists 996 a 32, 4 b 17, 26 b 15. 
i Sophocles I5 a 3o. 
i Soul, partly falls within scope of 
physics 2o a 5 ; substance of living 




I, 42 b 9, 

35 b 22, 

things 35 b 14, 43 a 35 ; = its 
essence 36 a i, 43 b 2; )( soulless 
things 46 a 36 ; )( reason, not all 
soul can survive death 7o a 26. 

Species 998 b 7 ; indivisible 9gS b 29, j 
34 a 8 ; one in species 999 a 2, i6 b I 
31, i8 b 7, 49 b 18, 29, s8 a 18 ; part j 
of genus 999 a 4, 23 b 18. 25; other j 
in species I. 8, 9, i8 a 38, 54 b 28 ; I 
genus part of species 23 b 24 ; 
genus matter of species 24 b 8, 38 a 
6 ; species composed of genus | 
and differentiae 39 a 26, 57 b 7. 

Speusippus 28 b 2l, 72 b 3i ; referred 
to 69 a 36, 75 a 33, 36, b 37, 76 a 2i, 
8o b 14, 26, 84 a 13, 8s a 32, 86 a 2, j 
29, 87 b 6, 27, 9o a 7, 25, b 17, 9i a | 
34, b 23, 32, 92 a ii- b 8. 

Spheres of the stars A. 8. 

Spontaneity, coni. luck, )( nature, | 
art984 b 14, 3 2 a 13, b 23, 34 a 10, 
b 4, 7o a 7. 

Stars A. 8 ; their nature 73 a 34. 

State, v. Habit. 

Strife (Empedocles) o a 27. 

Styx 983 b 32. 

Substance Z and H passim ; its 
meanings A. 8, A. I ; = ultimate 
subject 983 b 10, 2 a 3, 7 a 31, I7 b 
13, I9 a 5, 29 a 8, 38 b 15, 42 a 26 ; 
)( modification, accident 983 b 10, j 
10, 7 a 31, 38 b 28, 7i a I ; 

44 a 15, 49 a 36, 77 a 35 ; are num 
bers substances? 987 a 19, i b 26, 

76 a 30; sensible substance 997 a | 

34, 42 a 25, 69 a 30, b 3 ; = form, I 

b 21, 993 a 18, 32 b I, ! 

29, 38 b 14, 4i b 9, so b [ 

2 ; are there non-sensible sub- ! 

stances ? 997 a 34, 59 a 39 ; uni- ! 

versals not substance Z. 13, 3 a 7, | 
53 16, 6o b 21, 87 a 2; primary 

being 28 a 14, 30 ; prior in defini- ! 

tion, knowledge, time 28 a 32 ; ! 

alone separable 28 a 34 ; four no- \ 

tions of it 28 b 33 ; whether mat- | 
ter is substance Z. 3 ; material 
substance 42 a 27, 49 a 36, 77 a 36 ; 

syn. individual 3o a 19; primary ! 

32 b 2 ; = matter, form, and con- j 

crete thing 35 a i, 7o b 13 ; )( con- j 

crete thing 35 b 22, 37 a 29; )( j 

genus 42 a 21, 53 b 21 ; being not j 
the substance of things 40 18 ; 

unity not the substance I. 2, 4o b ] 

1 8 ; a principle and cause 4i a 9, ] 

b 30, 43 a 2 ; generally recognized 
substances 42 a 6 ; natural 42* 8, 
7o a 5 ; mathematical objects as 
substances M. 1-3, 42 a 1 1, 69 a 35; 
coni. actuality, complete reality, 
42 b 10, 43 a 23, 35, 44 a 9, 5o b 2, 
72 a 25 ; prior in substantiality 
49 b n, 5o a 4, 77 b 2 ; incompo- 
site 5i b 27; concrete 54 b 4; 
eternal, unmovable substance A. 
6 ; why are there many sub 
stances? 89 b 31. 

Substratum, def. 28 b 36 ; two mean 
ings 38 b 5, 49 a 28 ; syn. matter 
983* 30, 985 b 10, 992 b i, 22 a 1 8, 
7o a ii ; proximate, ultimate i6 a 
20, 23, I7 b 24, 24 b 10 ; )( matter 
44 b 9. 

Successive, def. 68 b 31 ; succession 
)( common reference 5 a n ; suc 
cession in numbers 85 a 4. 

Syllogism, starts from the what* 
34 a 31, 78 b 24; primary syllo 
gisms I4 b 2. 

Ten, limit of the number-series 
986 a 8, 73 a 20, 84 a 12 ; ten prin 
ciples (Pythagoreans) 986 a 22. 

Tethys 983 b 30. 

Thales 983 b 20, 984 a 2 ; referred to 

984*27,996*91 39 a 12 (?). 

Thargelia 23 b n. 

Thaten 33 a 7, 49 a 19,21. 

Theology 26 a 19, 64 b 3. 

Theoretical knowledge E. i, 993 b 

Thinking, thought (v6r)(ris) )( mak 
ing 32 b 15 ; coni. definition 52 a 
29> b i> 75 a 3 5 )( faculty of 
thought A. 7, 9; )( desire 72 a 26; 
its primary object 72 a 27. 

Third man 99o b 17, 39 a 2, 59 b 8, 
79 a 13. 

This I7 b 25, 30 a 4, 7o a 10. v. 

Thought (four), v. Reason. 

Time, incidentally quantitative 2O a 
29 ; prior in 28 a 32, 38 b 27, 49 b 
ii ; eternal 7i b 7. 

Timotheus 993 b 15. 

Total (irav) )( whole, all 24 a I, 8. 

Trojan war i8 b 16. 

Truth 993 a 30, b 20, 9 a I, b 2 ; def. 
0. 10, n b 25 ; absolute, relative 
n b 3 ; being as truth E. 4, 0. 10, 
65 a 2i. 

Two, v. Dyad. 


Unequal, the 8; b 5, 88 b 32, 89 b ] 
615, 9i b 35 ; inequality i b 23. 

Unit, def. i6 b 25, 89 b 35 ; point 
without position 84 b 26 ; specific- ! 
ally the same, associable M. 6-8, \ 
99i b 24; specifically different, \ 
inassociable M. 6-8, 992 a 3 ; 
differentia of 83 a 2 ; unitary num 
bers 8o b 19, 30, 82 b 6. 

Universal 42 a 15, 6g a 26, 86 a 32 ; 
def. 23 b 29, 38 b II ; not sub- | 
stance Z. 13, 3 a 7, 53 b i6,6o b 21, j 
87 a 2 ; whether the first princi- j 
pies are M. 10, 3 a 7, 6o b 19, 7i a j 
20; object of knowledge 3 a 14, 
36 a 28, 59 b 26, 6o b 20, 87 a 16 ; 
essential (naff avrd) I7 b 35 ; prior ! 
in definition i8 b 32 ; )( genus 
28 b 34. 

Universe, not episodic 76 a I. 

Unlike, its meanings i8 a 19. 

Void 48 b 9 ; (Democritus) 
9 a 28. 


What 25 b 31, 26 a 36, 28 a i7, 3o a 17; 
parts of the22 a 27; starting-point 
of syllogism 34 a 3i, 78 b 24. 

Whole I3 b 22, 52 a 22 ; its mean 
ings A. 26 ; )( total 24*1. 

Wisdom, philosophy (o-o</>i a) A. I ; 
with what principles it deals A. 2, 
K. i, 2, 995 b 12, 996 b 9 ; with 
first causes 98i b 28. 

Xenocrates referred to 28 b 24, 69 a 
35, 76 a 20, 8o b 22, 28, 83 b 2, 85 b 
7, 86 a 5, 8b b 28, 9o b 20-32, 9i b 

Xenophanes 986 b 21-27, Ioa 6. 

Zeno i b 7. 
Zeus 9i b 6. 


B 407 .36 1910 v.8 SMC 


The works of Aristotle