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

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METAPHYSICS 321
between the Numbers and the units which compose
them: 1 But in this, as in other branches of the argument,
his main point is always that there is a fundamental
contradiction between the notion of a unit of
number and the fact of differences of kind. It is not,
of course, necessary here to recapitulate those of his
objections to Ideal Numbers which apply also to the
Ideal Theory in general. 2 But it is to be noticed that,
in Aristotle's view, if
Ideas and Ideal
once we assumed the existence of
Numbers, the ordinary mathematical
numbers would lose their status, for they could only
have the same component parts and therefore the same
nature as the Ideal Numbers themselves. 3 The position
of magnitudes would be equally dubious ; for qud
ideal they must go by ideal numbers, and qud mathematical
they must go by mathematical number
4
and
from the way in which the theory of magnitudes is
deduced, be considers that the further dilemma arises
that either it must be possible for a surface to exist
without line, and a solid without surface, or else all
three must be one and the same. 5
Finally, as concerns the ultimate principles of things,
in which Plato and the Platonists had sought to find
the ultimate basis and constituents of their Numbers
and Ideas, 6 Aristotle asserts that it is impossible to
know the constituent parts of all being, since that
1
MetajfJi. xiii. 6-8. * Mctaph. i. 9, 992, b, 13 ; xiv.
'
As in Metaplh. xiii. 9, 1085, a, 3, 1C90, b, 20.
23, and in xiv. 2, 1090, a, 7 sqq. 5 Ibid, i, 9, 992, a, 10 ; xiii. 9,
c. 3, 1090, a,25-b, 5, they are used 1085, a, 7, 31.
against Speusippns. 6 Cf. Zelleb,PA. d, Gr. pi. i.
3 Metajjli. i. 9, 991, b, 27 ; xiv, 628 sq., 805.
3, 1090, b, 32 sqq.
VOL. I.
y
322 ARISTOTLE
knowledge cannot be derived from any prior knowledge. 1
He doubts whether all being can have the same constituent
parts, 2 or whether out of the combination of the
same elements, at one time a number and at another
time a magnitude could arise. 3 He remarks that such
constituent parts can only be ascribed to substances, and
only to those substances which have some admixture of
materiality. 4 He further demonstrates that such constituent
parts could neither be thought as individual
nor as universal :
not as individual, because they would
not then be cognisable and could not be the constituents
of more things or Ideas than one ; not as
universal, because in that case they would not be of the
nature of substance. 5
In another connection, he takes
exception to the variance of the Platonic suggestions as
to the 'material element,' 6 and rejects altogether the
assumption of Speusippus that there are more than one
original but different frindfia? A closer inquiry into
the two Platonic ultimate principles, ' the One,' and
'
the Great and Little,' leads Aristotle to declare that
they are both misconceived.
He asks how the One can
be a thing existing by itself, when no universal is a
substance. The notion of unity expresses only a
1
Metwph. i. 9, 992, b, 24 ;
5
Metajih. xiii. 10, 1086, b, 19,
against which, indeed, his own 1087, a. 4.
distinction of demonstrative and 6 Metapli. xiv. 1, 1087, b, 4,
inductive knowledge might be 12,26, c. 2,1089,b,ll; cIZellee,
used. Ph.. d. Gr. pt. i. p. 628, 3.
2
This is suggested, without ' Of it the remark in Metapli.
mention of Plato,in Metapli. xii. 4, xiv. 3, 1090, b, 13 sqq. is true, that
1070, a, 33 sqq. ; cf. what was ad- Nature is not Eirei