[FOM] Consequence of PA inconsistency

Timothy Y. Chow tchow at alum.mit.edu
Wed Apr 28 15:14:07 EDT 2010

Harvey Friedman wrote:
> I think that it is best, before we get into this standard technique,  
> to determine whether or not what I wrote is truly responsive to the  
> discussion that is going on about whether "an inconsistency in PA  
> refutes arithmetic Platonism". When I wrote this paragraph, I thought  
> it was responsive, but I would like to make sure.

Well, *I* think it is responsive.  The suggestion I made, roughly 
speaking, was to cope with an inconsistency in PA by questioning the 
meaningfulness of arbitrarily many alternations of quantifiers.  A natural 
objection to this proposal is to ask, "So how many is too many?"  If we 
can give an argument that any particular cut-off point is implausible, 
then that lends weight to the argument that if we give up on arbitrarily 
many alternations then we may have to give up on quantifiers altogether.

On the other hand, if by "making sure" you mean that you want to make sure 
that you'll change someone's mind or settle some philosophical issue 
definitively, or even that everyone involved in this discussion will 
regard your comment as responsive, then I think that may be too much to 
ask for.


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