Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: LordBeotian (pokipsy76_at_CANCELLAMIyahoo.it)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 08:43:51 GMT

"LordBeotian" <pokipsy76@CANCELLAMIyahoo.it> ha scritto

> > Hmmm! Well I think of myself as a platonist, but I don't consider that
> > it is meaningful to say that the axiom of choice, which is a meaningful
> > statement about sets, is either true or false in any absolute sense.
> > So perhaps I am being inconsistent? I find it strange that there are
> > some mathematicians who do claim to believe that ACC is true or false,
> > although they do not generally expect ever to find out which!
>
> Is there any statement about set that you consider true or false in some
> absolute sense?

What I wanted to point out is this:

There are 2 possibilities:

1) you think that statements about sets in general cannot be considered true
or false (in any absolute sense).
In this case I think it is not clear in which sense you could be "platonist"
because you would find that "there exists the empty set" or "there exist the
set of natural number" are not true (nor false) statements (in any absolutse
sense), while platonism is (usually) characterized by belief in existence of
mathematical objects.

2) you think that some statements about sets are true or false and some are
not (i.a.a.s.), so it is not clear why AC is a special case, what makes the
case of AC different from (for example) the axiom of infinity so thet the
former has not an (absolute) truth value while the latter does have?

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