[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 

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.


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