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

mareg_at_mimosa.csv.warwick.ac.uk
Date: 01/29/05 

Date: Sat, 29 Jan 2005 20:34:11 +0000 (UTC)

In article <3625maF4pqgpgU1@individual.net>,
        Mike Oliver <mike_lists@verizon.net> writes:
>mareg@mimosa.csv.warwick.ac.uk wrote:
>
>> 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!
>
>I'm not sure whom you would put in the category described. Most
>mathematicians who are realists about sets are convinced that AC
>is true.
>
>(I'm assuming that "ACC" was a typo for "AC"; if not, then I
>suppose my response could be a non-sequitur.)

Yes, I meant "AC". My impression is rather that most mathematicians prefer
to assume AC (rather than not AC), because it results in cleaner statements
of theorems, like every vector space has a basis. I generally assume and use
AC myself, but that is not the same thing as believing that it is any more
true than not AC. What I find surprising is that there are people who
believe that it is either true or false, but they don't know which.

Derek Holt.

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