[FOM] Arithmetical soundness of ZFC

Thomas Forster T.Forster at dpmms.cam.ac.uk
Sun May 24 04:14:08 EDT 2009

Isn't this easy?  Don't most (if not all) ZF-istes believe that (i) ZF(C) 
is not only consistent but sound *as a theory of (wellfounded) sets*? 
And (ii) isn't the obvious interpretation of arithmetic into ZF (natural 
numbners are cardinals of finite sets) sufficiently faithful to ensure 
that ZFC's theory of natural numbers is sound too?

   I know this is only a sketch, but surely something like this must be 
what is going on at the back of the mind of anyone who thinks ZF(C) is 
arithmetically sound.   It might be worth thinking which of (i) and (ii) 
is questionable.


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