Le 29-août-07, à 02:59, [EMAIL PROTECTED] a écrit :

> I *don't* think that mathematical
> properties are properties of our *descriptions* of the things.  I
> think they are properties *of the thing itself*.


I agree with you. If you identify "mathematical theories" with 
"descriptions", then the study of the description themselves is 
metamathematics or mathematical logic, and that is just a tiny part of 
mathematics.
After Godel, even formalists are obliged to take that distinction into 
account. We know for sure, today, that arithmetical truth cannot be 
described by a complete theory, only tiny parts of it can, and this 
despite the fact that we can have a pretty good intuition of what 
arithmetical truth is.

Bruno




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


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