[FOM] Sazonov on intuitive and formal mathematics

Gabriel Stolzenberg gstolzen at math.bu.edu
Sun Jul 29 13:49:36 EDT 2007

  Quoting Vladimir Sazonov in "Re: [FOM] re 'understanding Putnam on
understanding mathematics,'" Sat, 28 Jul 2007:

>   Without intuition formalization is not interesting. Without
>  formalizability intuition is too poor and vague to be considered
>  as mathematical.

   I'm sympathetic to this view.

> >   [Hilbert] succeeded in saving classical mathematics by a
> >   radical reinterpretation of its meaning without reducing
> >   its inventory, namely, by formalizing it, thus transforming
> >   it in principle from a system of intuitive results into a
> >   game with formulas that proceeds according to fixed rules.

> "Game with formulas" assumes "meaningless". But that is wrong.
> Interplay of intuition with formalism is not a meaningless game.
> Who said that formalization excludes or removes the intuition?

   I think you did because formalization excludes the part of the
intuition with which there is the interplay about which you speak.

   Finally, perhaps you could also explain how Hilbert's remark
that "[the logical laws] that Aristotle taught do not hold" fits
with your point of view.

   Gabriel Stolzenberg

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