wrong; for their view is very destructive,Mulberry Femmes Totes Pas cher, since they will admit that this question itself affords some difficulty-whether, when we count and say — 1,2,3-we count by addition or by separate portions. But we do both; and so it is absurd to reason back from this problem to so great a difference of essence.
Book XIII Chapter 8
First of all it is well to determine what is the differentia of a number-and of a unit, if it has a differentia. Units must differ either in quantity or in quality; and neither of these seems to be possible. But number qua number differs in quantity. And if the units also did differ in quantity, number would differ from number, though equal in number of units. Again, are the first units greater or smaller, and do the later ones increase or diminish? All these are irrational suppositions. But neither can they differ in quality. For no attribute can attach to them; for even to numbers quality is said to belong after quantity. Again, quality could not come to them either from the 1 or the dyad; for the former has no quality, and the latter gives quantity; for this entity is what makes things to be many. If the facts are really otherwise, they should state this quite at the beginning and determine if possible,Camisetas Polonia Baratas, regarding the differentia of the unit, why it must exist, and, failing this, what differentia they mean.
Evidently then, if the Ideas are numbers, the units cannot all be associable,Camisetas Racing Club Baratas, nor can they be inassociable in either of the two ways. But neither is the way in which some others speak about numbers correct. These are those who do not think there are Ideas, either without qualification or as identified with certain numbers, but think the objects of mathematics exist and the numbers are the first of existing things, and the 1-itself is the starting-point of them. It is paradoxical that there should be a 1 which is first of 1’s, as they say, but not a 2 which is first of 2’s,Doudoune Moncler Femme Longue Pas cher, nor a 3 of 3’s; for the same reasoning applies to all. If, then, the facts with regard to number are so, and one supposes mathematical number alone to exist,Fitflop New sequins Pas cher, the 1 is not the starting-point (for this sort of 1 must differ from the-other units; and if this is so,Camisetas Sporting Gijon Baratas, there must also be a 2 which is first of 2’s, and similarly with the other successive numbers). But if the 1 is the starting-point, the truth about the numbers must rather be what Plato used to say, and there must be a first 2 and 3 and numbers must not be associable with one another. But if on the other hand one supposes this,Goedkope Aston Villa Voetbalshirts, many impossible results, as we have said, follow. But either this or the other must be the case, so that if neither is, number cannot exist separately.
It is evident, also,Moncler Huivi Ja Korkit, from this that the third version is the worst,-the view ideal and mathematical number is the same. For two mistakes must then meet in the one opinion. (1) Mathematical number cannot be of this sort,Parajumpers Miehet Californian New Port, but the holder of this view has to spin it out by making suppositions peculiar to himself. And (2) he must also admit all the consequences that confront thoselinks:
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