Le 27-oct.-06, à 00:40, 1Z a écrit :

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>>> 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.
Exactly.
Bruno
http://iridia.ulb.ac.be/~marchal/
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