FOM: Friedman,fom,& Sheep's.Shop.

penelope maddy pmaddy at
Fri Feb 20 13:28:54 EST 1998

At 11:38 AM 2/20/98 -0500, Robert Tragesser wrote:
>        Those [algebraic constructs] are not only an impressive set of
>but in practice one can't do without them; & they are
>distinct from the set theoretic organon (tools).
>        This distinction is more than just psychological.
>        If the set-based is truly scientific and professional,
>mustn't they account for this profound difference and radically justify
>its suppression?

One can think that all mathematical objects are ultimately (modelled as)
sets without thinking that all effective mathematical methods are set
theoretic methods.  Compare:  one can think that everything studied in the
sciences is ultimately physical without thinking that the only effective
scientific methods are those of physics.  Who would expect botanists or
psychologists to use the same methods as physicists?  

Pen Maddy

Departments of Philosophy and Mathematics
UC Irvine

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