Aristotle on Metaphysics(2004) - Bibotu.com

88 ARISTOTLE’S METHOD IN METAPHYSICSside: essences are primary beings only because other things (e.g. this rose) arebeings in virtue of having essences. We will take up this aporia below, inChapter 7§5v.Twelfth Aporia (1001 b 26–1002 b 11)Are numbers, solids, surfaces and points themselves the primary beings or are theyprimary beings only because other things (e.g. this horse) have such geometricaland in general mathematical properties?See the comment on the precious aporia: the question here is whetherthings are literally constituted by mathematical properties, so that suchproperties are themselves the primary beings, or whether mathematicalproperties are primary beings only in the sense of explaining the being ofother things.Thirteenth Aporia (1002 b 12–32)Are there kinds (eidē) in addition to or besides (para) both sense-perceptiblethings and the entities postulated by mathematics?See the comment on the fifth aporia. But here the question is not simplywhether there are non-sense-perceptible and changeless things, butwhether these include only the entities postulated by mathematics, orwhether they include also other, non-mathematical entities. In general,<strong>Aristotle</strong> argues that mathematical entities, although non-sense-perceptibleand changeless, must apparently be repeatable. For example, if addition isto be possible (e.g. 1+1=2), apparently the mathematical unit (the number1) must be repeatable (for in the addition 1+1=2 it occurs twice). So thequestion is whether, in addition to changing things and changeless thingsthat are repeatable, there must also be changeless things that are strictlynon-repeatable.Fourteenth Aporia (1002 b 32–1003 a 5)Are the elements of things potentialities and capacities for causing andgenerating those things or are they what actually causes and generates thosethings?The elements of a thing are the ultimate causes of the thing. The aporiaarises because, on the one hand, the capacity to cause something appears tobe more basic than actually causing something; but, on the other hand, ifelements are simply capacities, they may not actually cause anything tobe.