[FOM] Formalization Thesis vs Formal nature of mathematics

Alex Blum blumal at mail.biu.ac.il
Fri Jan 4 04:51:57 EST 2008

Vladimir Sazonov wrote:

 > For me, abstractness of mathematical objects appears to be 
consequence of its rigorous (formal) character.

Rigour whether formal or otherwsise can't be enough. Chess has rigourous 
rules. The pieces are  concrete  and  they may all be taken as 
inerpetations of formal terms.  Is there any subject that cannot be 
formalized? In fact given Godel's incompleteness theorem, arithmetic may 
be weakest in the area of formalization. I think without demarking the 
subject area of mathematics, you won't succeed in isolating the subject.

Alex Blum


More information about the FOM mailing list