[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.
Tim
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