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

METAPHYSICS 325
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oversight he involves himself in this contradiction, that
matter tends to its own annihilation, that the evil
tends to the good and must of necessity assume it into
itself. 1 Further contradictions arise in the considerations
that the Great and Little (as was above remarked
of the ' Unlimited ' of the Pythagoreans) must be a thing
existing for itself, • a substance ; whereas at the same
time as a determination of number and magnitude it
cannot possibly be so, and that the same principle would
of necessity have to be given in actuality as unlimited,
which is a position in fact unthinkable. 2 If, finally, we
ask the Platonists in what way the numbers can be
deduced from their ultimate principles, distinct statements
are entirely wanting. We ask if they arise by a
mixture, or ky a composition, or by a generation, and
there is no answer. 3 We are not told how out of the
One and the Many could be produced those units of
which numbers are composed, 4 or whether number be
itself limited or unlimited. 5 There is no deductiqn of
the first uneven number or of any of the rest except
the first ten. 6 We are not shown from whence those
unities arise out of which is made up the indefinite
duality which, by its combination with the One, is to
7
generate the remaining units : and we are not shown
how the duality of the Great and Little can, with the
aid of the One, bring forth any numbers which could
1
Phys.i. 9, 192, a, 19.; Metaph. i
Metaph. xiii. 9, 1085, b, 12
xiv. 4, 1092, a, 1. sqq. an argument immediately
'*
Phys. iii. 5, 204, a, 8-34, cf. directed against Speusippus.
c. 4, 203, a, 1 sqq. 5 Ibid. 1085, b, 23, c. 8, 1083,
xiv. 5, 1092, a, 21 b, 36 sqq. ; xii. 8, 1073, a, 18.
sqq. ; xiii. R, 1085, b, 4 sqq.; cf. c. Zbllbk, ibid. p. 591, 3.
7, 1082, a, 20. ' Netapli. i. 9, 991, b, 31.
326 ARISTOTLE
not arise by the doubling of the One. 1 There are a
multitude of similar objections to be found in Aristotle,
but these will be more than sufficient.
These criticisms of the Platonic theory are not all
of equal value.
Not a few of them, at least in the form
in which Aristotle directly states them, rest undeniably
upon a misunderstanding of Plato. 2 Nevertheless, it
cannot be gainsaid that Aristotle has noted the weak
points of Plato's theory with a keen insight, and has
conclusively exposed its defects.
Not only has he completely
exhibited the obscurities and dilemmas of the
theory of Ideal Numbers, but he has also refuted once
for all the Ideal Theory and the assertions of Plato as
to the original basis of things. Among the arguments
which he uses in his
attack, there are two, which stand
out as decisive, and to which all the others mediately
or immediately return : first, that all universal concepts
(such as those of the One, of Being, of the Great and
Little, of the Unlimited, and in fact all the concepts
involved in the Ideas) are in no sense substantial, and
that they denote only certain qualities and relations,
and at the most only the genera and species
and not the things themselves ;
devoid
of things,
second, that the Ideas are
of motive power, and not only cannot explain,
but would actually make impossible the changes of
phenomena, the coming to be and ceasing to be of
things, change and movement, with all the natural
properties of things that rest thereon. 3
In the direction
1
Metapli. xiv. 3, 1091, a, 9. on the importance which he him-
" Cf. Zbllhr, Platon. Stud, self attached to this objection ;
257 sqq. cf., for example, Metaph. i. 9,
3 Aristotle frequently insists 991, a, 8 : iriyTuv St fiixarra