[FOM] truth and consistency
T.Forster at dpmms.cam.ac.uk
Mon Jun 2 04:53:48 EDT 2003
On Sun, 1 Jun 2003, Charles Parsons wrote:
> Surely we have
> additional reason for accepting ZFC, namely that the reasonings it
> embodies have been used in mathematics for over a hundred years (i.e.
> from some time before ZFC was formulated)
This sounds a bit swift. Let's face it, if that were true, then the
universal reaction to the announcement of the axioms of FZ would have
been `Ah, yes, that's what we've been doing all along'.
Of course, i have a special take on this, being an NF-iste. I derive
a certain amount of wry amusement from my practice of taking slabs of
ZF-is-jolly-natural discourse and replacing `ZF' by `NF' throughout, and
noticing how little the mathematical content changes, but how greatly the
apparent plausibility changes. Mathematics is mathematics, plausibility
is - at least in part - socially constructed.
ZF derives a lot of plausibility simply by having become the default.
Marco Forti says from time to time that it is pure accident that ZF was
set up with foundation instead of his antifoundation axiom, and i think he
makes an interesting case. ZF is certainly plausible, and it is plausible
beco's it does what we want, and no-one has yet found a contradiction in
it. The null hypothesis, which i commend to my readers for thei attention,
is that anything beyond that is hindsight.
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