FOM: formalism

[Matthew Frank]

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