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Topic: Objections against Cantor
Replies: 4   Last Post: Nov 19, 2012 7:13 PM

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Posts: 3,810
Registered: 12/6/04
Re: Objections against Cantor
Posted: Nov 19, 2012 11:18 AM
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On Nov 19, 11:47 am, Zuhair <> wrote:
> (4) Ultrafinistism: Those restrict human mathematical reasoning to
> only feasible length descriptions, so it is more consistent than
> finitism, but yet it is too restrictive that most mathematicians see
> no clear justification for it to be true.
> The mere justification of what is available around us, and the finite
> nature of our abilities, is not a clear evidence of why should the
> universe abide by such inabilities. That's besides the fact that
> actual infinity through set construction is intelligible, so why
> commit ourselves to such a restriction based on some inability that
> the universe and reality around us might not necessarily copy and yet
> at the same time this non copying can still be touched by some of our
> descriptive apparatus though not in full as with ultra-finite matters.

You should have a look at the first chapter of Edward Nelson's
"Predicative Arithmetic", titled "The impredicativity of induction".

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