[FOM] RE: FOM New Axioms

Jeremy Clark jclark at noos.fr
Tue Jul 1 17:16:08 EDT 2003

Matt Insall wrote:

> [Bill Tait]
> just as it does now, to most mathies;
> the only thing that's really changed since is that it is now in 
> text-books
> and undergraduate courses.
> True, there *were* doubters back then, but there are also doubters now,
> (including me).
> [Matt Insall]
> Among mathematicians, there are doubters of many things, but when 
> pinned
> down,
> I seems to me that just about every mathematician would agree with the
> axioms
> of ZF.

Is this true? Since one or two of the axioms of ZF, taken with the 
rules of
intuitionistic logic, imply forms of the law of excluded middle, you are
immediately ruling out anyone with even the slightest leanings towards
intuitionism or constructivism. Also, I would hazard a guess that there 
many mathematicians who doubt that it even makes any sense to say
that the axioms of ZF are 'true'. Perhaps the statement "most 
believe in ZF" should be added to ZF as an axiom, to lend credibility...

Jeremy Clark

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