FOM: wider cultural significance: polylogism
sazonov at logic.botik.ru
Sat Mar 6 03:23:20 EST 1999
Stephen G Simpson wrote:
> In f.o.m., we can try to clarify and sort out the merits of several
> possible positions vis a vis polylogism. The extreme forms of these
> positions might be caricatured as follows:
> 1m. there is only one appropriate logic for f.o.m. (predicate
> 2m. there are many different logics appropriate for different
> aspects of mathematics (second-order logic? dynamic logic?
> temporal logic?) or different f.o.m. programs (intuitionistic
My opinion: However classical logic seems most preferable for
contemporary mathematics, we should not think that this is the
only reasonable *mathematical* logic forever. It is possible
that, unlike intuitionistic logic, we will need something new
irreducible to classic logic (via Kripke models or the like).
> For example, some mathematicians and math
> educators in the United States are now pushing the idea of
> ethnomathematics -- different mathematics for different ethnic groups.
Is it serious? By the way, I listened that Kolmogorov gave
the following joke definition of woman's (in contrast to
Man: If A => B and A then B.
Woman: If A => B and she likes B then A.
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