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| 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; |