[FOM] The unreasonable soundness of mathematics
Timothy Y. Chow
tchow at alum.mit.edu
Sun May 15 16:43:38 EDT 2016
On Sun, 15 May 2016, Daniel Mehkeri wrote:
> Ultrafinitism is about feasibility, addition and multiplication are
> feasible operations, while exponentiation isn't.
O.K., this is one definition of ultrafinitism. It isn't the definition of
ultrafinitism I had in mind, and I agree with you that my original
argument about "unreasonable soundness" doesn't directly apply to
ultrafinitism as you have defined it. Maybe, from your perspective, the
version of ultrafinitism I have in mind is a strawman; I'm O.K. with that.
Although I did say that I did not want to debate "what Nelson believed," I
will point out the following MathOverflow question:
http://mathoverflow.net/questions/142669/illustrating-edward-nelsons-worldview-with-nonstandard-models-of-arithmetic
Nelson himself answered the question and engaged in some back-and-forth in
the comments. Based on Nelson's remarks, I believe that Nelson did not
simply hold that "multiplication is feasible and exponentiation is not" or
some such. But let us not argue that point on FOM; I just wanted to let
you know of the existence of these comments by Nelson.
Tim
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