[FOM] Provability of Consistency

Anton Freund freund at mathematik.tu-darmstadt.de
Tue Mar 26 15:33:54 EDT 2019

> In summary, Anton Freund's post is mathematically correct, but not quite
> relevant.

I still think that the results that I have mentioned are relevant, so let
me try to condense my point into a single question:

(*) What do we gain by establishing that PA is consistent in your sense?

For the usual formalization of consistency there is a clear answer (which
I sketched in my previous post): If we are convinced that PA is consistent
in the usual sense, then we have reason to believe that any
\Pi^0_1-statement that is provable in PA (such as Fermat's Last Theorem)
is actually true (even if we were not convinced that PA is sound). I would
be genuinely interested whether your formalization of consistency has
similar significance for the foundation of mathematics.

Best wishes,

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