The Basic Works of Aristotle (Modern Library Classics) (154 page)

10
     Let us now mention a point which presents a certain difficulty both to those who believe in the Ideas and to those who do not,
(15)
and which was stated before, at the beginning, among the problems.
⁶⁵
If we do not suppose substances to be separate, and in the way in which individual things are said to be separate, we shall destroy substance in the sense in which we understand ‘substance’; but if we conceive substances to be separable, how are we to conceive their elements and their principles?

If they are individual and not universal,
(20)
(
a
) real things will be just of the same number as the elements, and (
b
) the elements will not be knowable. For (
a
) let the syllables in speech be substances, and their elements elements of substances; then there must be only one
ba
and one of each of the syllables,
(25)
since they are not universal and the same in form but each is one in number and a ‘this’ and not
a kind possessed of a common name (and again they suppose that the ‘just what a thing is’
⁶⁶
is in each case one). And if the syllables are unique, so too are the parts of which they consist; there will not, then, be more
a
’s than one, nor more than one of any of the other elements, on the same principle on which an identical syllable cannot exist in the plural number.
(30)
But if this is so, there will not be other things existing besides the elements, but only the elements. (
b
) Again, the elements will not be even knowable; for they are not universal, and knowledge is of universals. This is clear from demonstrations and from definitions; for we do not conclude that this triangle has its angles equal to two right angles, unless every triangle has its angles equal to two right angles,
(35)
nor that this man is an animal, unless every man is an animal.

But if the principles
are
universal, either the substances composed of them are also universal, or non-substance will be prior to substance; for the universal is not a substance, but the element or principle is universal, and the element or principle is prior to the things of which it is the principle or element.
[1087a]

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,
(5)
a single separate entity. But if, e. g., in the case of the elements of speech, the
a
’s and the
b
’s may quite well be many and there need be no
a
-itself and
b
-itself besides the many, there may be, so far as this goes, an infinite number of similar syllables. The statement that all knowledge is universal,
(10)
so that the principles of things must also be universal and not separate substances, presents indeed, of all the points we have mentioned, the greatest difficulty, but yet the statement is in a sense true, although in a sense it is not. For knowledge, like the verb ‘to know’,
(15)
means two things, of which one is potential and one actual. The potency, being, as matter, universal and indefinite, deals with the universal and indefinite; but the actuality, being definite, deals with a definite object—being a ‘this’, it deals with a ‘this’. But
per accidens
sight sees universal colour, because this individual colour which it sees is colour; and this individual
a
which the grammarian investigates is an
a
.
(20)
For if the principles must be universal, what is derived from them must also be universal, as in demonstrations
⁶⁷
; and if this is so, there will be nothing capable of separate existence—i. e. no substance. But evidently in a sense knowledge is universal, and in a sense it is not.
(25)

¹
Phys
. i.

²
Met
. vii, viii, ix.

³
Plato, Xenocrates, and the Pythagoreans and Speusippus, respectively, are meant.

⁴
Cf. chs. 2, 3.

⁵
Cf. chs. 4, 5.

⁶
Cf. chs. 6–9.

⁷
Cf. iii. 998
^a
7–19.

⁸
Which nevertheless the theory in question represents as Ideas apart from sensible things.

⁹
iii. 997
^b
12–34.

¹⁰
Cf. 1076
^a
38–
^b
11.

¹¹
Cf. vi. 1026
^a
25, xiii. 1077
^a
9.

¹²
sc
. indivisibility and humanity.

¹³
The reference is apparently to Aristippus; Cf. iii. 996
^a
32.

¹⁴
Apparently an unfulfilled promise.

¹⁵
Chs. 2, 3.

¹⁶
1077
^a
17–20, 24–
^b
11.

¹⁷
Cf. vii. 1039
^a
2,
Soph. El.
178
^b
36–179
^a
10, and Plato,
Parmenides
, 132
AB
,
D
-133
A
.

¹⁸
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 vet is held to be absolute.

¹⁹
With 1078
^b
34–1079
^b
3 Cf. i. 990
^b
2–991
^a
8.

²⁰
sc
. in the essence of man.

²¹
100
D
.

²²
With 1079
^b
12–1080
^a
8 Cf. i. 991
^a
8–
^b
9.

²³
ll. 15–20.

²⁴
ll. 23–35.

²⁵
Cf. 1076
^a
38–
^b
11.

²⁶
Plato is meant.

²⁷
i. e. in which the numbers differ in kind.

²⁸
Speusippus is meant.

²⁹
Some unknown Platonist.

³⁰
Xenocrates is meant.

³¹
This refers to Plato; Cf. i. 992
^b
13–18.

³²
Speusippus is meant.

³³
Xenocrates is meant.

³⁴
l. 19.

³⁵
Cf. 1080
^a
18–20, 23–35.

³⁶
Plato.

³⁷
The theory of ideal number holds that 2 comes next after the original 1, 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 1. Similarly between 2 and 3 there will be the first unit in 3, and so on.

³⁸
i. e. if there is a difference of kind between the numbers.

³⁹
1081
^a
5–17.

⁴⁰
Cf. 1080
^a
18–20, 23–35.

⁴¹
Cf. 1080
^b
37–1083
^a
17.

⁴²
That of Xenocrates; Cf. 1080
^b
22.

⁴³
1080
^a
15–
^b
36.

⁴⁴
This includes Plato (Cf.
Phys
. 206
^b
32) and probably Speusippus.

⁴⁵
i. e. to account for the oddness of odd numbers they identify the odd with the 1, which is a principle present in all numbers, not with the 3, which on their theory is not present in other numbers.

⁴⁶
Cf. i. 992
^a
22.

⁴⁷
Cf. xiv. 1090
^b
21–24. 1 answers to the point (the ‘indivisible line’), 2 to the line, 3 to the plane, 4 to the solid, and 1 + 2 + 3 + 4 = 10.

⁴⁸
sc
. the Atomists.

⁴⁹
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.

⁵⁰
This probably includes Plato himself.

⁵¹
i. e. that which is to the geometrical forms as the primary 1 is (according to the Platonic theory) to numbers.

⁵²
With 1085
^a
7–19 Cf. i. 992
^a
10–19.

⁵³
Cf. i. 992
^b
1–7, xiv. 1088
^a
15–21.

⁵⁴
Speusippus is probably meant.

⁵⁵
i. e. probably Plato and Xenocrates.

⁵⁶
Cf. 1083
^b
36.

⁵⁷
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.

⁵⁸
Speusippus is meant.

⁵⁹
Xenocrates is meant.

⁶⁰
Plato.

⁶¹
Phys
. i. 4–6;
De Caelo
, iii. 3–4;
De Gen. et Corr.
i. 1.

⁶²
Speusippus is meant; Cf. N. 1090
^a
7–15, 20–
^b
20.

⁶³
iii. 1003
^a
7–17.

⁶⁴
1078
^b
17–30.

⁶⁵
iii. 999
^b
24–1000
^a
4, 1003
^a
5–17.

⁶⁶
i. e. the Idea; Cf, 1079
^b
6.

⁶⁷
sc
. universal premisses do not give singular conclusions.

1
     Regarding this kind of substance, what we have said must be taken as sufficient. All philosophers make the first principles contraries: as in natural things,
(30)
so also in the case of unchangeable substances. But since there cannot be anything prior to the first principle of all things, the principle cannot be the principle and yet be an attribute of something else. To suggest this is like saying that the white is a first principle, not
qua
anything else but
qua
white, but yet that it is predicable of a subject, i. e. that its being white presupposes its being something else; this is absurd,
(35)
for then that subject will be prior. But all things which are generated from their contraries involve an underlying subject; a subject, then, must be present in the case of contraries, if anywhere.
[1087b]
All contraries, then, are always predicable of a subject, and none can exist apart, but just as appearances suggest that there is nothing contrary to substance, argument confirms this. No contrary, then, is the first principle of all things in the full sense; the first principle is something different.

But these thinkers make one of the contraries matter, some
¹
making the unequal—which they take to be the essence of plurality—matter for the One,
(5)
and others
²
making plurality matter for the One. (The former generate numbers out of the dyad of the unequal, i. e. of the great and small, and the other thinker we have referred to generates them out of plurality, while according to both it is generated
by
the essence of the One.) For even the philosopher who says the unequal and the One are the elements,
(10)
and the unequal is a dyad composed of the great and small, treats the unequal, or the great and the small, as being one, and does not draw the distinction that they are one in definition, but not in number. But they do not describe rightly even the principles which they call elements, for some
³
name the great and the small with the One and treat these three as elements of numbers,
(15)
two being matter, one the form; while others
⁴
name the many and few, because the great and the small are more appropriate in their nature to magnitude than to number; and others
⁵
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,
(20)
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 universal than the great and the small. But as it is,
(25)
they say one of these things but do not say the other. Others oppose the different and the other to the One,
⁶
and others oppose plurality to the One.
⁷
But if, as they claim, things consist of contraries, and to the One either there is nothing contrary, or if there is to be anything it is plurality, and the unequal is contrary to the equal, and the different to the same, and the other to the thing itself,
(30)
those who oppose the One to plurality have most claim to plausibility, but even their view is inadequate, for the One would on their view be a few; for plurality is opposed to fewness, and the many to the few.

‘The one’ evidently means a measure. And in every case there is some underlying thing with a distinct nature of its own,
(35)
e. g. in the scale a quarter-tone, in spatial magnitude a finger or a foot or something of the sort, in rhythms a beat or a syllable; and similarly in gravity it is a definite weight; and in the same way in all cases, in qualities a quality, in quantities a quantity (and the measure is indivisible, in the former case in kind, and in the latter to the sense); which implies that the one is not in itself the substance of anything.
[1088a]
And this is reasonable; for ‘the one’ means the measure of some plurality, and ‘number’ means a measured plurality and a plurality of measures.
(5)
(Thus it is natural that one is not a number; for the measure is not measures, but both the measure and the one are starting-points.) The measure must always be some identical thing predicable of all the things it measures, e. g. if the things are horses, the measure is ‘horse’, and if they are men, ‘man’. If they are a man, a horse, and a god, the measure is perhaps ‘living being’,
(10)
and the number of them will be a number of living beings. If the things are ‘man’ and ‘pale’ and ‘walking’, these will scarcely have a number, because all belong to a subject which is one and the same in number, yet the number of these will be a number of ‘kinds’ or of some such term.

Those who treat the unequal as one thing, and the dyad as an indefinite compound of great and small,
(15)
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,
(20)
smooth and rough, straight and curved. Again, (
b
) apart from this mistake, the great and the small, and so on, must be relative to something; but what is relative is least of all things a kind of entity or substance, and is posterior to quality and quantity; and the relative is an accident of quantity,
(25)
as was said, not its matter, since something with a distinct nature of its own must serve as matter both to the relative in general and to its parts and kinds. For there is nothing either great or small, many or few, or, in general, relative to something else, which without having a nature of its own is many or few, great or small, or relative to something else. A sign that the relative is least of all a substance and a real thing is the fact that it alone has no proper generation or destruction or movement,
(30)
as in respect of quantity there is increase and diminution, in respect of quality alteration, in respect of place locomotion, in respect of substance simple generation and destruction. In respect of relation there is no proper change; for, without changing, a thing will be now greater and now less or equal, if that with which it is compared has changed in quantity.
(35)
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.
[1088b]
It is strange, then, or rather impossible, to make not-substance an element in, and prior to, substance; for all the categories are posterior to substance. Again, (
d
) elements are not predicated of the things of which they are elements,
(5)
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,
(10)
1 would be few), there must be also one which is absolutely many, e. g. 10 is many (if there is no number which is greater than 10), or 10,000. How then, in view of this, can number consist of few and many? Either both ought to be predicated of it, or neither; but in fact only the one
or
the other is predicated.