187 A ristotle on Intelligible Matter STEPHEN GAUKROGER In Metaphysics K, Aristotle talks of mathematical objects having matter: 6Xus 8' a?rop?a??? TLS av 'TTOLŒII ict-riv f'TTL<JT?f.Llll1 TO 6ta«opfiaat 'TTEPL Tfis ( 1 059b 14- 1 6). There can be only one kind of matter that he has in mind here. Sensible matter is ruled out because this is the proper object of physics whereas, as he points out (1059b20-21), the matter of mathematical objects is the proper subject of first philosophy. Nor can prime matter be at issue here, since this is a purely limiting notion in- troduced to account for changes between contraries in sensible matter, such as generation and corruption. This leaves us with what Aristotle calls noetic or 'intelligible' matter - and in Metaphysics Z we are told explicitly that intelligible matter is present in the objects of mathematics: bXr 61 fi a!.o6iiTT) £6T?V ? 8i VOllT1Í, plv olov Insofar as this claim relates to geometry it has occasionally caused puzzlement, but there is a relatively straightforward solution to the puzzle. Insofar as it relates to arithmetic it is acutely problematic, but Aristotle nowhere even suggests that it does not cover the whole of mathematics.
Phronesis – Brill
Published: Jan 1, 1980
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