[FOM] Brief Reply to Comments on my Opinion 57

William Tait 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.

Bill Tait

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