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

On 16 Jul 2005 11:07:26 -0700, "Keith Ramsay" <kramsay@xxxxxxx> wrote:

>
>Jim Spriggs wrote:
>|25 years ago (it might have been) I think I heard John Mayberry say
>that
>|someone believed that set theory was inconsistent and was trying to
>|prove it. Indeed, he said that the same person doubted the
>consistency
>|of PA. He named the person, but I cannot remember the name.
>|
>|To whom was Mayberry referring?
>|
>|The set theory may have been ZF but I don't recall precisely.
>
>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.

My first reading of this was that saying someone believes
that set theory is inconsistent is more remarkable than
saying that someone believes that PA is inconsistent.
That seemed like a remarkable thing for you to say...

You actually meant that saying that someone believes that
set theory is consistent is more remarkable than saying
that someone has doubts about the consistency of set theory, right?

>I don't believe I've ever heard that he actually believed
>ZF or the like is inconsistent. I seem to remember seeing
>a paper of his on set theory, although writing a paper on
>a theory doesn't necessarily say anything about one's
>expectations concerning its consistency.
>
>Keith Ramsay


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

David C. Ullrich
.

Relevant Pages

  • Re: Who believes/believed that set theory is/was inconsistent?
    ... Keith Ramsay wrote: ... > |25 years ago I think I heard John Mayberry say ... > |The set theory may have been ZF but I don't recall precisely. ... > inconsistent is a different story. ...
    (sci.logic)
  • Re: infinity
    ... were inconsistent, then it is only because ZF itself is inconsistent. ... Well, there can only be one proper class, ... such as von Neumann-Bernays-Godel Set Theory. ... What is the probability that A will win? ...
    (sci.math)
  • Re: Who believes/believed that set theory is/was inconsistent?
    ... |inconsistent is a different story. ... |My first reading of this was that saying someone believes ... |that set theory is inconsistent is more remarkable than ... This was taking "doubting the consistency of PA" to mean ...
    (sci.logic)
  • Re: Hans startling new set theory.
    ... All within Euclidian Geometry, of course. ... > also mean that you have evidence that ZF itself is _inconsistent_. ... there is NO PARADOX in ZF. ... Such a Set Theory IS consistent. ...
    (sci.math)
  • Re: Hans startling new set theory.
    ... and still all the main theories are inconsistent ... > A little bit of Physics would be NO Idleness in Mathematics. ... is a THEOREM that any sufficiently powerful axiom system is unable to ... > on Set Theory as its foundation par excellence, ...
    (sci.math)