Can infinite be comprised of finite parts in nature

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Borisu
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Can infinite be comprised of finite parts in nature

Post by Borisu » November 2nd, 2017, 9:07 am

I find myself learning the Chovot HaLevavot (Hebrew: חובות הלבבות‎‎ Duties of the Heart) book. In the first chapter of the book the author deals in general with the of the finity of the world. The second author's tenant, on which he builds his subsequent proofs is goes like this:-
"...Furthermore, it is evident that anything which has parts must have a whole, since a whole is merely the sum of its parts. Therefore, it is not possible for something infinite to be comprised of parts, because a part, by definition, is an amount separated from another amount, and through the part the whole is measured, as Euclides mentioned in the fifth treatise of his book of measures.

If we consider in our thoughts something which is infinite in actuality, and we take a part from it, the remainder will undoubtedly be less than what it was before. And if the remainder is also infinite, then one infinite will be greater than another infinite, which is impossible.

Alternatively, if the remainder (of the whole) is now finite, and we put back the part that we took away - then the whole will be finite, but it was originally infinite, if so the same thing is finite and infinite which is a contradiction and impossible. And therefore, it is impossible to take out a part from something which is infinite, since whatever is comprised of parts is undoubtedly finite..."
I have some difficulty with the proof. Let alone that that there are sets like natural numbers which are infinite but defined by "sum of its" parts. Also what comes to mind, is the mathematical definition of infinite group sizes e.g. cardinality numbers. Which suggests that group can still be equal in "size" even if some members are taken away from them. For example the group of all natural numbers and the group of all naturals number excluding number one are actually "equal" in sizes in cardinlaity terms. On first sight this seems to be in contradiction to authors logical proof. However I feel uncomfortable for taking abstract mathematical definition of groups and applying them directly to material world, certainly what the author had in mind. I mean can we treat the set of naturals numbers the same way as universe with infinite mass (measured in actual units like kilograms). Does erasing "number one" is the same as taking one kilogram of material from the mass of Universe for the sake of author's argument. I feel that it is not. But I just cannot put my finger in what the actual difference between two.

In summary, the question is, does the cardinality number argument, destroys the author's attempt to prove the impossibility of infinite being comprised of finite parts. BTW any references to historical or modern philosophical essay dealing with the issue is warmly welcome.

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Albert Tatlock
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Re: Can infinite be comprised of finite parts in nature

Post by Albert Tatlock » November 2nd, 2017, 5:38 pm

Borisu wrote:is the same as taking one kilogram of material from the mass of Universe
You can't do that. Where would you put the kilogram of Universe so it wasn't still in the Universe?

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Atreyu
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Re: Can infinite be comprised of finite parts in nature

Post by Atreyu » November 6th, 2017, 7:56 pm

I'm not sure how to exactly answer your post, but answer me this:

Why cannot something infinite be composed of an infinite number of finite parts?

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