Wisdom

Others assert that it Post Date: Sat, 2 Aug 2008 4:23:59 +0000
Philosophers have adopted different opinions as to the divisibility of matter. Some maintain that there are unex- tended points in which the division ends, and that all com posite bodies are formed of these. Others assert that it is not possible to arrive at simple elements, but the division may continue ad infinitum continually approaching the limit of composition, but never reaching it.

Autor of the post: Undefined

They are the limit Post Date: Sat, 2 Aug 2008 4:42:12 +0000
The first of these opinions is equivalent to the admission of geometrical points realized in nature; the second, though apparently less favorable to this realization, must come to it at last. Unextended molecules are the realization of the geo metrical point, in all its exactness. They are the limit of dimension, because division ends with them.

Autor of the post: Undefined

Therefore, from this opinion held Post Date: Sat, 2 Aug 2008 4:56:43 +0000
They are the generative elements of dimension, because they form ex tension. They occupy a determinate position in space, be cause bodies with all their conditions and determinations in space are formed of them. Therefore, from this opinion held by eminent philosophers like Leibnitz and Boscowich, it follows that the geometrical point exists in nature 11: all the purity and exactness of the scientific order.

Autor of the post: Undefined

I remarked above that, although Post Date: Sat, 2 Aug 2008 5:12:19 +0000
The opinion which denies the existence of unextended points, admits, as it necessarily must admit, infinite divisi bility. Extension has parts, and therefore is divisible; these parts, in their turn, are either extended or not ex tended; if unextended, the supposition fails, and the opin ion of unextended points is admitted; if extended, they are divisible, and we must either come at last to unextended points, or continue the division ad infmitum. I remarked above that, although less favorable to the real existence of geometrical points, this opinion as well as the other does acknowledge their realization.

Autor of the post: Undefined

This opinion therefore, does not Post Date: Sat, 2 Aug 2008 5:24:12 +0000
The parts into which the composite is divided are not created by the division, but exist before the division, and without them the division would be impossible. They do not exist be cause they may be divided, but they may be divided because they exist. This opinion therefore, does not ex pressly admit the existence of unextended points, but it, admits the possibility of eternally coming nearer to them, and this not only in the ideal, but also in the real order; because the divisibility is not affirmed of the ideas, but of the matter itself.

Autor of the post: Undefined

Our ability to divide Post Date: Sat, 2 Aug 2008 5:36:57 +0000
Although our experience of division is limited, divi sibility itself is unlimited-. A being endowed with greater powers than we possess, might carry the division further than we are able to do. Our ability to divide is limited, but God, by his infinite power, can push the division ad infinitum, and His infinite intelligence sees in an instant all the parts into which the composite may be divided.

Autor of the post: Undefined

If the geometrical point exists Post Date: Sat, 2 Aug 2008 5:47:30 +0000
Omitting the difficulties which attend an opinion which seems to suppose the existence of what it denies, I will ask if geometry can require more rigorous exactness than is found in the points to which infinite power can come, ii we suppose it to exercise its eternal action in dividing the composite ; or, in other words, can there be any more strictly geometrical points than those seen by an infinite intelligence in an infinitely divisible being ? This not only satisfies our imagination and our ideas of exactness, but goes even beyond. Experience teaches us that to imagine an unextended point is not impossible ; and to think it in the purely intellectual order, is only to conceive the pos sibility of this infinite divisibility, and to be suddenly placed at the last limit, a limit which must still be far distant from that to which, not abstraction, but the sight of infinite intelligence can reach. If the geometrical point exists, the geometrical line also exists ; for it is only a series of unextended points ; or, if we are unwilling to acknowledge these, a series of extremes to which division infinitely continued at last arrives.

Autor of the post: Undefined

It is an error Post Date: Sat, 2 Aug 2008 5:59:28 +0000
A series of geometrical lines forms a surface ; and a union of surfaces forms a solid, the ideal order agreeing with reality in its formation as in its nature. 34 This theory of the realization of geometry extends equally to all the natural sciences. It is an error to say, for example, that the reality does not correspond to the theories of mechanics.

Autor of the post: Undefined

Mechanics supposes this point Post Date: Sat, 2 Aug 2008 6:16:22 +0000
It should rather be said that it is not the reality that is at fault, but the means of exper imenting ; the blame should not be imputed to the reality, but rather to the limitation of our experience. The centre of gravity in a body, is the point where all the forces of gravitation in the body unite. Mechanics supposes this point to be indivisible, and in accordance with this supposition, establishes and demonstrates its theorems, and solves its problems.

Autor of the post: Undefined

Is this because the centre Post Date: Sat, 2 Aug 2008 6:27:28 +0000
Here stops the me chanician, and the machinist begins, who can never dis cover the strict centre of gravity supposed in the theory. Experience disagrees with the principles, and we ought to correct the former by adhering to that which is determined by the latter. Is this because the centre of gravitydoes not exist in nature with all the exactness which science supposes ? No ; the centre exists, but the means of find ing it are wanting.

Autor of the post: Undefined

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