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That they exist in reality Post Date: Mon, 4 Aug 2008 22:43:36 +0000 What then are these relations ? I know not. But I know that they exist and that these necessary laws exist. That they exist in reality I know by experience, which gives testimony of their existence ; that they are possible, I know on the authority of my ideas, the connection of which forces my assent to their intrinsical evidence. Autor of the post: Undefined Geometry plays an important part Post Date: Mon, 4 Aug 2008 22:53:55 +0000 160 That this evidence touches but one aspect of the object, is true ; that there are many things in the object which we do not know, is likewise true ; but this only proves that our science is incomplete, not that it is illusory or false. 161 It is difficult for us to conceive the pure intelligi bility of the sensible world, both because our ideas are always accompanied by representations of the imagination, and because we try to explain it by simple addition and subtraction of parts, as though all the problems of the uni verse could be reduced to expressions of lines, surfaces, and solids. Geometry plays an important part in all that re gards the appreciation of the phenomena of nature; but when we want to penetrate to the essence of things, we must lay aside geometry and take up metaphysics. Autor of the post: Undefined For, though the imagination Post Date: Mon, 4 Aug 2008 23:05:08 +0000 There is no more seductive philosophy than that which reduces the world to motions and figures, but at the same time there is none more superficial. A slight reflection on the reality of things shows the insufficiency of such a sys tem. For, though the imagination be satisfied with it, the understanding is not, and it takes a noble revenge on its unfaithful companion, when, forcing the imagination to fix itself upon objects, the understanding sinks it in an ocean of darkness and contradiction. Autor of the post: Undefined The best proof Post Date: Mon, 4 Aug 2008 23:20:32 +0000 Those who laugh at the forms, the acts, the forces, and other such expressions used with more or less exactness in different schools, ought to reflect that even in the physical world there is something more than is perceived by the senses ; and that even sen sible phenomena cannot be explained by mere sensible re presentations. Physical science is not complete until it calls to its aid metaphysics. The best proof of this will be found in the next chapter, where we shall see the imagination entangled in its own representations. Autor of the post: Undefined These parts are extended Post Date: Mon, 4 Aug 2008 23:33:56 +0000 162 THE divisibility of matter is a question that tor ments philosophers. Matter is divisible because it is ex tended, and there is no extension without parts. These parts are extended or are not : if they are, they are again divisible ; if they are not, they are simple, and in the divi sion of matter we must come to unextended points. Autor of the post: Undefined Division does not make Post Date: Mon, 4 Aug 2008 23:44:32 +0000 This last consequence can be avoided only by recourse to the infinite divisibility of matter, and even this is a means of escaping the difficulty rather than a true solution. I in timated elsewhere that infinite divisibility seems to sup pose the very thing which it denies. Division does not make the parts, it supposes them ; that which is simple can not be divided ; therefore, the parts which may be divided pre-exist in the infinitely divisible composition. Autor of the post: Undefined If you answer Post Date: Mon, 4 Aug 2008 23:59:33 +0000 Let us imagine God to exert his infinite power in divid ing, will he exhaust divisibility ? If you say no, you seem to place limits to his omnipotence; if you say yes, we shall have arrived at simple points, as otherwise the divisi bility would not be exhausted. Even supposing that God does not make this division, his infinite intelligence certainly sees all the parts into which the composite is divisible ; these parts must be simple, or else the infinite intelligence would not see the limit of divisibility. If you answer that this limit does not exist, and therefore cannot be seen, I reply that we must then admit an infinite number -of parts in each portion of matter ; there would, in this case, be no limit of divisibility, because the number of parts would be inexhaustible ; but this infinite number would be seen by the infinite intelli gence, as it is, and all these parts would be known as they are. Autor of the post: Undefined It does not mend Post Date: Tue, 5 Aug 2008 0:17:13 +0000 The difficulty still remains ; these parts are simple or composite ; if simple, the opinion which we are opposing does, at least, admit unextended points ; if composite, the same argument may be repeated ; they are again divisible. "We shall then have a new infinite number in each one of the parts of the first infinite number ; but as this series of infinities must be always known to the infinite intelligence, we must come to simple points, or else say that the infinite intelligence does not know all that there is in matter. It does not mend the matter to say that the parts are not actual but only possible. Autor of the post: Undefined 163 Some say Post Date: Tue, 5 Aug 2008 0:31:12 +0000 In the first place, possible parts are existing parts, because, if the parts are not real, there must be real simplicity, and consequently, indivisibility. Secondly, if they are possible, they may be made to exist by the intervention of an infinite power ; and then what are these parts ? they are either extended or unextended, and the matter returns to where it was before. 163 Some say that a mathematical quantity, or a body mathematically considered, is infinitely divisible, but that natural bodies are not bt-cunse their natural form requires a determinate quantity. Autor of the post: Undefined Besides, when we reach Post Date: Tue, 5 Aug 2008 0:42:07 +0000 This is the explanation which was given in the schools ; but it is very clear that there is no grouni for affirming that these natural bodies require a cer tain quantity, beyond which division is impossible. This cannot be proved either a priori or a posteriori: not a priori, because we do not know the essence of bodies, and cannot say that there is a point where the natural form re quires the limit of divisibility ; neither can it be proved a posteriori, because the means of observation at our disposal are so coarse, that it is impossible for us to reach the last limit of division and discover a part which cannot be di vided. Besides, when we reach this quantity beyond which division cannot go, we have a true quantity, by the suppo sition ; if it is quantity it is extended ; if it is extended it has parts ; if it has parts it is divisible. 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