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Aristotle - index for METAPHYSICA Book 13 Part 9

How number can consist of the one and plurality

  
Paragraph 1 Since there is not contact in numbers, but succession, viz. between the units between which there is nothing, e.g. between those in 2 or in 3 one might ask whether these succeed the 1-itself or not, and whether, of the terms that succeed it, 2 or either of the units in 2 is prior.
Paragraph 2 Similar difficulties occur with regard to the classes of things posterior to number, - the line, the plane, and the solid.
Paragraph 3 (All these views share a difficulty which occurs with regard to species-of-a-genus, when one posits the universals, viz. whether it is animal-itself or something other than animal-itself that is in the particular animal.
Paragraph 4 Some, then, generate spatial magnitudes from matter of this sort, others from the point - and the point is thought by them to be not 1 but something like 1-and from other matter like plurality, but not identical with it;
Paragraph 5 Again, how number can consist of the one and plurality, they make no attempt to explain;
Paragraph 6 All these objections, then, and others of the sort make it evident that number and spatial magnitudes cannot exist apart from things.
Paragraph 7 But regarding numbers the questions we have raised and the conclusions we have reached are sufficient (for while he who is already convinced might be further convinced by a longer discussion, one not yet convinced would not come any nearer to conviction);
Paragraph 8 Those who posit numbers only, and these mathematical, must be considered later;


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