ARISTOTLE AND THE EARLIER PERIPATETICS vol.I by Eduard Zeller, B.F.C.Costelloe 1897

320 ARISTOTLE
METAPHYSICS 319
•
between the Ideas and the things of sense the whole
less untenable, Aristotle would still say that it could by
science of Mathematics. The difficulties which would
no means fulfil the task of a true Philosophy, which is
thus arise were set out by Aristotle with a painstaking
to exhibit the basis and principles of the world of
thoroughness most tiresome to the modern mind, though
appearances. As the Ideas are not in things, they
in his day it may possibly have been needful in order
cannot make up the essence of things, and they cannot
to cut off all ways of escape for the Pythagorising
contribute anything to the being of things. Even 1
the
school, led by such men as Xenocrates and Speusippus.
relation of the one to the other cannot be stated clearly,
He asks how we are to think to ourselves the causality
for Plato's own references to some kind of copying and
of numbers, 1
or how they can contribute to the existence
participation are always unintelligible metaphors. 2 The
of things. 2 He shows how capricious and contradictory
is the application of these numbers to natural
principle of motive power, without which no process of
becoming and no explanation of nature is conceivable,
objects. 3 He points out the difference in character
is wholly wanting. 3 So also is the principle of final
between conceptual determinations, which are qualitative,
and numerical determinations, which are quanti-
cause. 4 Even in regard to the theory of Knowledge,
the Ideas cannot render us that service which Plato
tative, remarking that two numbers make up one
expected from them, for if they are outside of things,
number, but two Ideas do not make one Idea, and that
then they are not truly the essence of things, and therefore
the knowledge of the Idea leads to no sure con-
among the numbers which make up numbers no qualitative
differences can be posited, whereas there must
clusion as to the thing itself. 5 And how, on the other
be units qualitatively different if there were Ideal
hand, could we arrive, asks Aristotle, at any knowledge
of the Ideal, since innate Ideas are not to be
Numbers. 4 With minute and careful thoroughness, 5
he controverts the various suggestions as to the relations
assumed ? s All these difficulties will be vastly increased
if we are to follow Plato and his school in
of mathematics to the Ideal Numbers which were
thrown out by Plato and his school and the devices they
translating the Ideas into Numbers, and so interposing
resorted to in order to maintain a conceivable difference
1
Metaph. i. 9, 991, a, 12 (xiii. 335, b, 7 sqq. of. Eth. End. i 8,
5, init.). 1217, b, 23.
1
2
Metaph. i. 9, 991, a, 20, 992,
4
Metaph. i. 9, 991, b, 9, with apii/iois nyiv (tiiroiceifi.ciiziv).
Metaph. i. 7, 988, b, 6, o. 9,
the answer : if things are likewise 2
Metaph. xiv. 6 init., ibid.
a, 28 (xiii. 5, 1079, b. 24), i. 6, 992, a, 29 (where, instead of 5A,
numbers, one does not see of what 1093, b, 21 cf. c. 2, 1090, a, 7 sqq
987, b, 13, viii. 6, 1045, b. 7, xii. Si' 8 should be read).
10, 1075, b, 34. 5
use the ideal numbers are to them; 3
Loo. cit. from 1092, b, 29; cf
Metaph. i. 9, 991, a, 12 (xiii.
if, 3
on the other hand, things are the commentaries on this passage
Metaph. i. 9, 991, a, 8. 19 sqq. 5, 10 79, b, 15), vii. 6, 1031, a, 30
only arranged according to num- *
Cf. Zbll. Ph. d. Gr. pt. i. p.
b, 3 sqq. (xiii. 5) 992, a, 24 sqq. sqq. cf. Anal. Post. i. 22, 83, a,
ber, the same would be true of 568 sq. 854, 867 sq. 884.
b, 7, O. 7, 988, b, 3, vii. 8, 1033, 32: -ret yap etSri x^pera- reperlb,
26, xii. 6, 1071, b, 14, u. 10, opivrA. re yap eVti,
the ideas of them, which would 5 Loc. cit. i. 9, 991, b, 21 sqq.
:
ice.
not be numbers, but \6~)Oi iv 992, a, 2.
1075, b, 16, 27 ; Gen. et Curr. ii. 9, Vide supra, p. 202, &c.