FOM: wider cultural significance: polylogism

Vladimir Sazonov sazonov at
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
>       calculus?)
>   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
>       logic?)

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's) logic:

Man: If A => B and A then B.

Woman: If A => B and she likes B then A.

Vladimir Sazonov

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