FOM: Re: Maddy on method

penelope maddy pmaddy at
Fri Feb 20 19:07:52 EST 1998

>	we can prove every mathematical theorem, upon appropriate 
>	definitional reductions, entirely within the apparatus 
>	of set theory.

We can think that a particular theorem of algebra is provable from the
axioms of set theory (via definitions of the appropriate algebraic notions)
without thinking that we would ever have discovered that algebraic theorem
-- that is, without thinking that we would ever have thought of looking at
these particular sets in this particular way -- without thinking
'algebraically'.  That's what I mean when I deny that the methods of algebra
are the methods of set theory.  


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