[FOM] Platonism, and Nik Weaver's take on ZFC

[Tom Dunion]

It seems to me, in the ongoing “Falsifying Platonism” thread
there is somewhat of a consensus that we have more confidence
that the system PA captures our unshakeable beliefs about the
natural numbers than we have about ZFC capturing our more
tentative intuitions about the universe of sets -- if indeed there
even is one canonical universe.)

(Putting it another way: An inconsistency arising from PA
would be much more unsettling to the general mathematics
community than one arising from ZFC.)

In this connection, but going a bit further, I note Nik Weaver’s
“liar paradox” post of April 14 has a pointer to his website,
where in item 4 he raises the concern that even if ZFC is
consistent, there are “good reasons to suspect that some
number-theoretic assertions provable in ZFC may be false."

I’d be interested if he (or anyone) would wish to say more
either in agreement or disagreement with that assessment.
(I acknowledge Weaver does present some reasons for his
suspicions in the article, and that I am an agnostic on this
matter.)

-- Tom Dunion