can be divided.
But, again, it is not possible that such entities should exist separately. For if besides the sensible solids there are to be other solids which are separate from them and prior Nike Free TR Fit 3 to the sensible solids, it is plain that besides the planes also there must be other and separate planes and points and lines; for consistency requires this. But if these exist, again besides the planes and lines and points of the mathematical solid there must be others which are separate. (For incomposites are prior to compounds; and if there are, prior to the sensible bodies, bodies which are not sensible, by the same argument the planes which exist by themselves must be prior to those which are in the motionless solids. Therefore these will be planes and lines other than those that exist along with the mathematical solids to which these Peony Short Czyścibut 5801 thinkers assign separate existence; for the latter exist along with the mathematical Naiset Nike Free Run 3 solids, while the others are prior to the mathematical solids.) Again, therefore, there will be, belonging to Naiset Parajumpers Denali these planes, lines, and prior to them Naiset Nike Free Run 3 there will Sebastian Aho Jersey have to be, by the same argument, other lines and points; and prior to these Alexander Ovechkin Jersey points in the prior lines there will have to be other points, though there will be no others prior to these. Now (1) the accumulation becomes absurd; for we find ourselves with one set of solids Jordan Shoes apart from the sensible solids; three sets of planes apart from the sensible planes-those which exist apart from the sensible planes, and those in the mathematical solids, and those which exist apart from those in the mathematical solids; four Neal Broten Jersey sets of lines, and five sets of points. With which Vancouver Canucks Jersey of these, then, will the mathematical sciences deal? Certainly not with the planes and lines and points in the motionless solid; for science always deals with what is prior. And (the same account will apply also to numbers; for there will be a different set of units apart from each set of points, and also apart from each set of realities, from the objects of sense and again from those of thought; so that there will be various classes of mathematical numbers.
Again, how is it possible to solve the questions which we have already enumerated in our discussion of difficulties? For the objects of astronomy will exist apart from sensible things just as the objects of geometry will; but how is it possible that a heaven and its parts-or anything else which has movement-should exist apart? Similarly also the objects of optics and of harmonics will exist apart; for there will be both voice and sight besides the sensible or individual voices and sights. Therefore it is plain that the other senses as well, and the other objects of sense, will exist apart; Brandon Tanev Jersey for why should one set of them do so and another not? And if this is so, there will Canada Goose Camp Hooded also be animals existing apart, since there will be senses.
Again, there are certain mathematical theorems that are universal, extending beyond these substances. Here then we shall have another intermediate substance separate both from the Ideas and from the intermlinks:
http://www13.plala.or.jp/gakuki3/cgi_bin/aska/aska.cgi
http://www13.plala.or.jp/gakuki3/cgi_bin/aska/aska.cgi
http://www13.plala.or.jp/gakuki3/cgi_bin/aska/aska.cgi |
