FOM: Re: Maddy on method
pmaddy at benfranklin.hnet.uci.edu
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.
More information about the FOM