Wisdom

In the multiplication Post Date: Tue, 5 Aug 2008 3:35:02 +0000
It is evident that, multiplication being only addition shortened, if an infinite addition of zeros can give only zero ; multiplication can give no other result, although the other factor be infinite. Why then do mathematical results say the contrary ? This contradiction is not true, but only apparent. In the multiplication of the infinitesimal by the infinite we may obtain a finite quantity for product, because the infinitesimal is not regarded as a true zero, but as a quantity less than all imaginable quantities, but still it is something.

Autor of the post: Undefined

But as geometricians only consider Post Date: Tue, 5 Aug 2008 3:54:10 +0000
If this condition were wanting, all the opera tions would be absurd, because they would turn upon a pure nothing. Shall we therefore say that the equation, relation of the limit of the decrement, which is equal to B only when the differentials are equal to zero. But as geometricians only consider the limit in itself, they pass ovei all the intervals of the decrement, and place them selves at once at the point of true exactness.

Autor of the post: Undefined

The un extended, as such Post Date: Tue, 5 Aug 2008 4:06:08 +0000
Why then operate on these quantities ? Because the operations are a sort of algebraic language, and mark the course that has been followed in the calculations, and recall the connection of the limit with the quantity to which it refers. 170 Unity which is not number produces number ; why then cannot points without extension produce extension ? There is a great disparity between the two cases. The un extended, as such, involves only the negative idea of ex tension ; but in unity, although number is denied, this ne gation does not constitute its nature.

Autor of the post: Undefined

It belongs to the essence Post Date: Tue, 5 Aug 2008 4:24:48 +0000
No one ever defined unity to be the negation of number, yet we always define the unextended to be that which has no extension. Unity is any being taken in general, without considering its divi sibility ; number is a collection of unities ; therefore the idea of number involves the idea of unity, of an undivided being, number being nothing more than the repetition of this unity. It belongs to the essence of all number that it can be resolved into unity ; it contains unity in a determi nate manner.

Autor of the post: Undefined

The understanding is afraid Post Date: Tue, 5 Aug 2008 4:35:59 +0000
But the extended can not be resolved into the unextended, unless by proceeding ad infinitum, or else by some process of decomposition which we know nothing of. 171 THE arguments for or against unextended points, for or against the infinite divisibility of matter seem equally conclusive. The understanding is afraid that it has met with contradictory demonstrations ; it thinks it discovers absurdities in infinite divisibility, and absurdities in limit- irig it ; absurdities in denying unextended points, arid ab surdities in admitting them.

Autor of the post: Undefined

But who shall flatter himself Post Date: Tue, 5 Aug 2008 4:50:51 +0000
It is invincible attacking an opinion, but its strength is turned into weakness as soon as it attempts to establish or defend any thing of its own. Yet reason can never contradict itself; two contradictory de monstrations would be the contradiction of reason, and would produce its ruin ; the contradiction can, there fore, only be apparent. But who shall flatter himself that he can untie the knot ? Excessive confidence on this point is a sure proof that one has not understood the true state of the question, and such vanity would be punished by the conviction of ignorance.

Autor of the post: Undefined

You wish to know whether Post Date: Tue, 5 Aug 2008 5:04:55 +0000
With all these reserves I now proceed to make a few observations on this mysterious subject. 172 I am inclined to believe that in all investigations on the first elements of matter, there is an error which renders any result impossible. You wish to know whether extension may be produced from unextended points, and the method which you employ consists in imagining them already approached, and then trying to see if any part of space can be filled by them.

Autor of the post: Undefined

Our imagination makes us presuppose Post Date: Tue, 5 Aug 2008 5:15:51 +0000
This seems to me like trying to make a denial correspond to an affirmation. The unex tended point represents nothing determinate to us except the denial of extension; when, therefore, we ask if this point joined with others like it can occupy space, we ask if the unextended can be extended. Our imagination makes us presuppose extension in the very act in which we wish to examine its primitive generation.

Autor of the post: Undefined

173 In order to know Post Date: Tue, 5 Aug 2008 5:35:41 +0000
Space, such as we conceive it, is a true extension ; and, as has been shown, is the idea of extension in general ; to imagine, therefore, that the unextended can fill space, is to change non-exten sion into extension. It is true that this is precisely what is required, and in this consists the whole difficulty ; but the error is in attempting to solve it by a juxtaposition which makes these points both unextended and extended, an evi dent contradiction. 173 In order to know how extension is generated, it would be necessary to free ourselves from all sensible representations, and from all ideas which are in the least degree affected by the phenomenon, and co contemplate it with an eye as simple, a look as penetrating, as that of a pure spirit.

Autor of the post: Undefined

It would, in fine Post Date: Tue, 5 Aug 2008 5:53:03 +0000
It would be necessary to take from all geo metrical ideas all phenomenal forms, all representations of the imagination, and present them to the imagination puri fied from all mixture with the sensible order. It would be necessary to know how far extension, real continuity, agrees with the phenomenal. It would, in fine, be necessary to eliminate from the object perceived, all that relates to the subject which perceives it.

Autor of the post: Undefined

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