[FOM] V = WF costs nothing
Timothy Y. Chow
tchow at alum.mit.edu
Wed Feb 6 16:23:41 EST 2008
Colin McLarty wrote:
> So V=WF changes nothing about ordinary mathematics, all of which is done
> up to isomorphism. V=L does change things up to isomorphism.
This argument makes sense if one regards the only "purpose" of set theory
as providing a foundation for mathematics, in the sense that sets are
there only to provide raw material for building arbitrary mathematical
structures.
But if one is interested in which axioms are *true*, or if one wants to
apply set theory to contexts (other than f.o.m.) in which it is natural to
consider non-well-founded sets, then V = WF is no longer "costless."
Therefore it still seems to me that V = WF demonstrates the critical role
that fashionability plays in the process of choosing axioms.
Tim
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