Le 18-août-06, à 17:38, 1Z a écrit :

> That is an explanation of mind-independence, not of  existence.
> The anti-Platonist (e.g. the formalist) can claim that
> the truth of mathematical statments is mind-independent,
> but their existence isn't.


"Their" existence ? Mathematical statements needs "chatty" machines. 
Mathematical truth, a priori doesn't (although "free structures" can 
feature some chatty aspects many times).

Let us make the following convention. When I will say "I believe there 
exist a perfect number", it is a shorter expression for, I believe the 
proposition "There is a perfect number" is true (satisfied in (N,+,*)) 
independently of me, or of any theory of cognition. (A good thing, 
giving that a theory of cognition is build *from* digital machine, that 
is from number theoretical relations).

Bruno


http://iridia.ulb.ac.be/~marchal/


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