[FOM] V = WF costs nothing

James Hirschorn James.Hirschorn at univie.ac.at
Thu Feb 7 15:00:26 EST 2008

On Wednesday 06 February 2008 16:23, Timothy Y. Chow wrote:
> But if one is interested in which axioms are *true* [...]
> then V = WF is no longer "costless." 

I will mention my own view on V=WF. I think it may be "inherently vague". It 
does not seem very meaningful when, for example, one can take the ordinal 
omega and "turn it upside down" to obtain a counterexample to V=WF. Thus I 
think it may be "indefinite", meaning that is has no truth value in the 
Platonistic sense.

This seems compatible with (my understanding of) what Kunen meant in his 
introduction to the chapter on the well-founded sets: E.g. "... our adopting 
the Axiom of Foundation does not comment on whether there are really ... x 
such that x = {x}."

James Hirschorn

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