[FOM] Brief Reply to Comments on my Opinion 57
wwtx at earthlink.net
Thu Nov 13 22:00:22 EST 2003
On Nov 11, 2003, at 7:48 PM, Doron Zeilberger wrote:
> human mathematics is also finite, but humans
> pretend that it is infinite, and that's a fiction
That human mathematics is finite is certainly true: it was the basis of
Hilbert's fin itist proof theory.
That humans pretend that it is not finite, I doubt very much. What lots
of humans believe is that mathematics is about infinite things. For
example omega is infinite. That is a different matter completely.
One of the traditional arguments against the actual infinite was that,
being finite, we could not comprehend it. It was one of the arguments
that Bolzano in _Paradoxes of the Infinite_ and (I think) Cantor in his
_Grundlagen_ took on.
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