Bruno Marchal wrote:
> Le 27-oct.-06, à 16:51, 1Z a écrit :
> > Bruno Marchal wrote:
> >> Le 26-oct.-06, à 18:02, 1Z a écrit :
> >>> Measure is a lot more difficult in MMW. It has to be
> >>> deprived by apriori necessity. Do you have
> >>> a solution?
> >> A good candidate for apriori necessity (and possibility) is
> >> provability
> >> (and conssitency) by a lobian machine.
> >> http://iridia.ulb.ac.be/~marchal/
> > Are Lobian machines apriori necessary themselves ?.
> Lobian machines are apriori themselves in the same sense than numbers
> and their effective relations are a priori themselves.
That's in the sense of abstract truth, not in the sense
of real existence, then. (Remember: anti-Platonists
agree that "2+2=4" is a necessary apriori truth,
they just disagree that "2" exists).
> So a strict
> answer is NO. Since Dedekind-Godel we know that we cannot prove the
> existence of numbers from pure logic. That is why such things as Peano
> Arithmetic exists.
Questions about real, ontological existence, beyond mathematical
are separate. Anti-Platonists
can and do accept Godel.
> But the answer is "YES" once we postulated the existence of numbers,
> like Peano Arithmetic does.
> Note that all self-referentially correct classical machine are lobian.
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