FOM: formalism
Matthew Frank
mfrank at math.uchicago.edu
Mon May 29 19:29:12 EDT 2000
On Mon, 29 May 2000, Robert Black wrote:
> Consider now a pi_1 claim like 'PA is consistent'. What is the 'formalist'
> going to say about this claim? He can of course announce that it's
> provable, in, say, ZF (a sigma_1 fact), or that it's disprovable in, say,
> PA+not-Con(PA) (another sigma_1 fact)
As for me, this is all that I do.
> but what about the claim itself's being true or false?
I do not answer this question. I am not interested in it (for now--if
someone exhibits an inconsistency in PA I will be very interested). And,
for the moment, I do not think it something worth worrying about.
As for my claim that "for *much of* modern mathematics the only
meaningful notion of truth (if it is a notion of truth at all) is
provability in some formal system)". The "much of" was intended to
capture the following: I believe that 17+18=35 is true in that, if you
count out 17 things, and then count out 18 things, put them together and
count them, you will generally count up to 35. I don't think that this
goes very far.
--Matt
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