[FOM] Mathematics and rigour

[Vladimir Sazonov]

Quoting "Timothy Y. Chow" <tchow at alum.mit.edu> Thu, 08 Mar 2007:

>> Also it is not a precision what distinguishes various views on the
>> foundation of mathematics (Intuitionism, Predicativism, etc.)
>
> Although it is true that precise formal versions of intuitionism,
> predicativism, etc., have been proposed and gained widespread acceptance,
> the point I am making is that typically these philosophies are *motivated*
> by some sort of argument like this: The law of the excluded middle, or
> impredicativity, or what have you, is dubiously unclear, and therefore
> should not be admitted into the realm of mathematics.  They fall afoul of
> some threshold of precision.
>
> As I constructed that last paragraph, I found myself wondering whether
> *clarity* is a better word than precision.  It might be.


 From my subjective point of view (I belive, confirmed by the 
overwhelming majority of mathematicians) classical mathematics in the 
form of ZFC is much more clear than any complications related with 
Intuitionism, etc. It does not mean that Intuitionism does not have 
some specific interest and does not deserve to be studied. No doubts, 
it is a graet idea. But it does not replace mathematics in general, as 
ZFC (and what can be done in it) is not the whole mathematics, but only 
some current version of so called classical mathematics.


Vladimir

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