Re: Who believes/believed that set theory is/was inconsistent?



Keith Ramsay wrote:
> I wrote:
> |The most respected person I've heard of doubting the
> |consistency of PA is Ed Nelson. He expressed his doubt
> |in his book _Predicative Arithmetic_. He spent some time
> |trying to find an inconsistency.
> |
> |Now, saying that someone believes that set theory is
> |inconsistent is a different (and more remarkable) story.

You're completely wrong about that,
and DCU knows it. He was just either too a) charitable,
or b) sadistic, to just come right out and say so,
like I did. He was utterly taken aback that someone
of your caliber could make so basic an error, so rather
than just reflexively insult you, as I did, he offered
you an opportunity either a) charitably, to clarify what
you REALLY meant, or b) sadistically, to dig your own hole
deeper. Unfortunately you then got mutually lost around
who was mislabeling what. But the point in any case is
that ZFC *decides* the question of the consistency of PA.
In classical FOL, consistency is equivalent to model-
existence and ZFC (by virtue of having an axiom of infinity)
PROVES the existence of a model for PA as a theorem.
THOU MAYEST NOT doubt the consistency of PA IF thou hast
conceded the consistency of ZFC. ZFC IS INHERENTLY MORE
dubitable, NOT less, than PA. Thus it would NOT be more
remarkable, for Ed Nelson or anyone else, to doubt the
consistency of ZFC than to doubt the consistency of PA.
Unless he was looking for errors in the proof that the
set-from-ZFC's-axiom-of-infinity really is a domain for a
model of PA.

.

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