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Re: Cantor's absurdity, once again, why not?
Posted:
Mar 14, 2013 6:43 AM
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On Thursday, March 14, 2013 3:17:06 AM UTC-7, fom wrote:
> For example, Wittgenstein understood perfectly
> well how to apply Cantor's argument and he
> certainly is not thought of as believing in
> a completed infinity.
Here's an "acceptable" use of the diagonal argument: Given a provably well-defined list of provably well-defined real numbers (so that every digit of every number on the list can provably be computed), the diagonal argument gives us a new provably well-defined real number not on the list.
Notice that that argument doesn't require the use of an actual infinite.
> However, he also did not attack the mathematicians
> who conducted investigations along those lines.
He most certainly did mock them.
FWIW, I was motivated to start this thread after reading an article you wrote about problems you had in your encounters with mathematicians who didn't accept your ideas. I'd like to know a little more about that, although I admit you really have no obligation to tell us more if you don't want to.
The mathematics community has simply lost touch with reality.
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