consider what is said by others,Mężczyźni Barbour Quilted Kurtka, so that, if there is anything which they say wrongly, we may not be liable to the same objections,Malaga Pas Cher, while, if there is any opinion common to them and us, we shall have no private grievance against ourselves on that account; for one must be content to state some points better than one’s predecessors,Ralph Lauren Hoodies, and others no worse.
Two opinions are held on this subject; it is said that the objects of mathematics-i.e. numbers and lines and the like-are substances, and again that the Ideas are substances. And (1) since some recognize these as two different classes-the Ideas and the mathematical numbers, and (2) some recognize both as having one nature, while (3) some others say that the mathematical substances are the only substances, we must consider first the objects of mathematics, not qualifying them by any other characteristic-not asking, for instance, whether they are in fact Ideas or not, or whether they are the principles and substances of existing things or not, but only whether as objects of mathematics they exist or not, and if they exist, how they exist. Then after this we must separately consider the Ideas themselves in a general way, and only as far as the accepted mode of treatment demands; for most of the points have been repeatedly made even by the discussions outside our school, and,Lyon Pas Cher, further, the greater part of our account must finish by throwing light on that inquiry, viz. when we examine whether the substances and the principles of existing things are numbers and Ideas; for after the discussion of the Ideas this remans as a third inquiry.
If the objects of mathematics exist, they must exist either in sensible objects, as some say, or separate from sensible objects (and this also is said by some); or if they exist in neither of these ways, either they do not exist,Chaussures Nike Lunar Femme, or they exist only in some special sense. So that the subject of our discussion will be not whether they exist but how they exist.
Book XIII Chapter 2
That it is impossible for mathematical objects to exist in sensible things, and at the same time that the doctrine in question is an artificial one,arctic parka, has been said already in our discussion of difficulties we have pointed out that it is impossible for two solids to be in the same place, and also that according to the same argument the other powers and characteristics also should exist in sensible things and none of them separately. This we have said already. But, further, it is obvious that on this theory it is impossible for any body whatever to be divided; for it would have to be divided at a plane,Maillot Firmino Pas Cher, and the plane at a line,Portugal Pas Cher, and the line at a point, so that if the point cannot be divided,Uruguay Pas Cher, neither can the line, and if the line cannot, neither can the plane nor the solid. What difference, then, does it make whether sensible things are such indivisible entities,Chaussures New Balance 595, or,Ralph Lauren Långärmat Tee, without being so themselves,Män International Jackets, have indivisible entities in them? The result will be the same; if the sensible entities are divided the others will be divided too, or else not even the sensible entities
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