### On the separable existence of numbers

 Paragraph 1 First of all it is well to determine what is the differentia of a number - and of a unit, if it has a differentia. Paragraph 2 Evidently then, if the Ideas are numbers, the units cannot all be associable, nor can they be inassociable in either of the two ways. Paragraph 3 It is evident, also, from this that the third version is the worst, - the view ideal and mathematical number is the same. Paragraph 4 The Pythagorean version in one way affords fewer difficulties than those before named, but in another way has others peculiar to itself. Paragraph 5 If, then, it is necessary, if number is a self-subsistent real thing, that it should exist in one of these ways which have been mentioned, and if it cannot exist in any of these, evidently number has no such nature as those who make it separable set up for it. Paragraph 6 Again, does each unit come from the great and the small, equalized, or one from the small, another from the great? Paragraph 7 Again, number must be either infinite or finite; Paragraph 8 But if number is finite, how far does it go? Paragraph 9 Again, if number can exist separately, one might ask which is prior - 1, or 3 or 2? Paragraph 10 If the 1-itself must be unitary (for it differs in nothing from other 1's except that it is the starting-point), and the 2 is divisible but the unit is not, the unit must be liker the 1-itself than the 2 is.

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