Wisdom

If position and relation Post Date: Tue, 5 Aug 2008 18:18:24 +0000
What should we think of a blind man who should laugh at those who see, if he heard them speak of the relations of objects as seen ? Yet we present the same spectacle to a pure spirit when we talk of the impossibility of an order different from what our senses perceive. 205 The principles of physical science are in great part conditional ; for they are true only on the supposition of the reality of the data furnished by experience. If position and relation to place are not essential to bodies, distance and motion are conditional facts true only under certain suppositions.

Autor of the post: Undefined

A further explanation Post Date: Tue, 5 Aug 2008 18:31:38 +0000
All the natural sciences, as we have seen, are reduced to the calculation of extension and motion ; they do not reach the essence of things, but are limited to one aspect, that presented by experience. In these sciences there is consequently nothing strictly absolute ; in this re spect, they are far below metaphysics, which knows things that are absolutely necessary. A further explanation of this doctrine is required, and will be given in the follow ing chapters, 206 MUST not the theory which supposes the relations of bodies to be variable, put an end to all the natural sciences? Can there be science without a necessary object and can there be a necessity which is compatible with vari ability ? The natural sciences have two parts : one physical, and the other geometrical.

Autor of the post: Undefined

The difficulty thus disappears Post Date: Tue, 5 Aug 2008 18:44:51 +0000
The first supposes the data fur nished by experience ; the second forms its calculations relative to these data. Change the relations of external beings, and the data will be different, you will have a new experience producing a new physical science : the calcula tion will be the same, only new results will be obtained from the new data. The difficulty thus disappears.

Autor of the post: Undefined

In mechanics, the problems Post Date: Tue, 5 Aug 2008 19:00:28 +0000
All the physical sciences are based on observation, all their combinations are made from data furnished by experience ; therefore the physical sciences are not wholly absolute, but they have a part which is conditional. The theory of uni versal gravitation is developed as a body of geometrical science, but it starts from the data furnished by experience Destroy these data and from a body of physical science it becomes a body of pure geometry. In mechanics, the problems of the composition and decomposition of forces have a physical signification, inasmuch as they presuppose the data of experience ; suppress these data and there re mains only a composition of lines which mean nothing when we call them forces.

Autor of the post: Undefined

If the relations of bodies Post Date: Tue, 5 Aug 2008 19:17:45 +0000
Therefore mechanics is only a system of geometrical applications. 207 Here another difficulty arises which is apparently more serious than the other. If the relations of bodies are not essential, but are subject to variation ; if our calcula tions upon them are not founded upon data which are in trinsically necessary, it seems that geometry is destroyed, or limited in such a way to the ideal order, that it can not be sure that on descending to the field of experience it will not find that false which it regarded as true, and that true which it reputed false.

Autor of the post: Undefined

I said this difficulty was Post Date: Tue, 5 Aug 2008 19:31:12 +0000
For example, the dis tances of bodies are calculated by considerations of geo metry : if the relation of distance is variable, and a body may be in many places at the same time, geometry turns out false. Such a supposition is no more than the appli cation of the foregoing theory ; for, if the relations are variable, this variation may affect distance, which is only a relation. I said this difficulty was more serious than the other, because it leaves the field of experience, and attacks the order of our ideas, an order which we must hold to be indestructible, unless we wish to give up our reason.

Autor of the post: Undefined

But if the relations Post Date: Tue, 5 Aug 2008 19:41:17 +0000
What would become of our reason if geometry were contradicted by the reality ? what would become of an order of ideas in contradiction to facts? Still I repeat that the force of this difficulty is only apparent, and if analyzed will be found of no more weight than the objection which we have already answered. A body which is a hundred yards distant from another, cannot be only one yard distant; geometry would be opposed to it. But if the relations of bodies are variable this proposition can mean nothing with respect to the reality.

Autor of the post: Undefined

If you alter or destroy Post Date: Tue, 5 Aug 2008 19:57:19 +0000
Therefore geometry is false. I admit the conse quence ; but the principle on which it is based involves a supposition contrary to my theory. If you alter or destroy the relations of bodies, you destroy distance, which is a re lation, consequently you cannot have a distance of one hundred yards, nor of one yard, nor any distance at all, and if there is no distance there is no contradiction.

Autor of the post: Undefined

Geometrical truth is true Post Date: Tue, 5 Aug 2008 20:13:37 +0000
If, then, you ask how great is the distance between them, your ques tion is absurd ; for it supposes a distance, whereas there is no distance at all. 208 This solution rests on a fundamental principle which we ought never to lose sight of. Geometrical truth is true in reality when the conditions of geometry exist in reality; if these conditions do.

Autor of the post: Undefined

This is a true proposition Post Date: Tue, 5 Aug 2008 20:28:12 +0000
not exist, there is no real geometry! There is nothing strange in this : in fact, the same occurs in the purely ideal order ; even there, geometry rests on cer tain postulates, without which it is impossible. Two tri angles with the same base and altitude are equivalent to each other. This is a true proposition, but only on the supposition that there are those orders of points which are called lines, and that the lines form angles, and are united at three points.

Autor of the post: Undefined

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