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

On 19 Jul 2005 10:55:24 -0700, "george" <greeneg@xxxxxxxxxx> wrote:

>
>
>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.

While of course I appreciate your clarifying my intentions
(guffaw), actually no, giving him an opportunity to dig his
hole deeper was not what I had in mind.

I'll just point out that you can't decide whether my
motivation was "charitable" or "sadistic". Possibly
you should keep this in mind the next time you feel
the urge to explain someone's motivations to him?
I mean it's not like charity and sadism are sort of
subtle variations on the same theme, they're close
to complete opposites - when something looks to you
like charity or sadism, you can't decide which,
_maybe_ you should conclude that your intention
recognizer is not functioning all that well?

Maybe you should even decide that in fact you have
no idea what my intentions were here? It's hard to
see how you decided it had to be either charity
or sadism, couldn't be anything in between.

>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.


************************

David C. Ullrich
.

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