Le 27-oct.-06, à 00:40, 1Z a écrit :

>>> Tom Caylor:
>>> Mathematical logic is richer than that.  This is what Bruno is 
>>> saying,
>>> that the math path points toward Rome.  And it is no more scary (a la
>>> possible spirits lurking under/in every rock) than the matter path.
>>> Limiting math as you are doing, and as Brent Meeker does in his
>>> response to my (X and not-X) note, is ignoring such evidence as the
>>> proofs of Godel and Tarski's Indefinability Theorem.
>>> Tom
>> Brent Meeker: But as I understand it, Bruno wants to identify 
>> "mathematical existence" with true existence statements about 
>> mathematical objects.
>>  Some of these are unprovable.  They can be consistently added to the 
>> axioms.  But also their negation can be consistently added to the 
>> axioms.  But not both.  So there are disjoint realms of consistent 
>> mathematics - some are Rome, some are Athens, some are Tuva, most are 
>> Harry Potter's home town.
> 1Z (Peter Jones): I suppose that is why he wants to base his case on 
> the
> subset of arithmetic everyone agrees on.




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