[FOM] Choice of new axioms 1

Andrej Bauer Andrej.Bauer at andrej.com
Tue Feb 14 11:41:02 EST 2006

On Tuesday 14 February 2006 13:43, you wrote:
> Quoting Andrej Bauer <Andrej.Bauer at andrej.com>:
> > As an innocent onlooker to the current discussion about
> > "choice of new axioms", I have been wondering all along
> > why there needs to be one set of standard axioms that
> > "normal" mathematicians use?
> Because otherwise one can derive e.g. both MC and not-MC, and consequently,
> everything. (MC = there exists a measurable cardinal)

If you derive MC with one set of axioms and not-MC with another, you may _not_ 
conclude everything.

Perhaps I was not clear. It seems to me entirely possible, and quite likely 
useful, that e.g. measure theorists adopt ZFC+X while graph theorists adopt 
ZFC+Y, where X and Y cannot consistently coexist. My question is, why would 
this be such a bad idea? In fact, if professor Friedman proves enough results 
of his kind, he might cause mathematicians to do precisely that.

>> Is this something that is good for mathematics, or are we all in search
>> of aboslute truth, or what?
> Yes. Yes.

I had a housemate once who answered disjunctions with "yes". It was very 
annoying. It might be the real reason why I flirt with constructivism.


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