FOM: ultrafinitism; objective vs. subjective

Vladimir Sazonov sazonov at
Thu Mar 19 23:25:25 EST 1998

Todd Wilson wrote:
> Vladimir Sazonov writes:
> > Then, we are using some ideas, abstract notions like the natural
> > numbers.  These ideas are also subjective in the sense that they
> > are our creations (with the roots in reality, of course) and
> > often vague. What is not vague, is any concrete tool we use (a
> > formal system with explicitly fixed rules and axioms).
> But isn't a "concrete" formal system with axioms and rules at least as
> vague as the natural numbers?  The formulas being manipulated by such
> formal systems, as well as the proofs themselves, are defined by
> structural induction and can grow to arbitrary size, just as the
> natural numbers can.

Yeas, you are right. But when we prove a concrete theorem, 
everything is OK. 

Vladimir Sazonov
Program Systems Institute,  	| Tel. +7-08535-98945 (Inst.), 
Russian Acad. of Sci.		| Fax. +7-08535-20566
Pereslavl-Zalessky,		| e-mail: sazonov at 
152140, RUSSIA			|

More information about the FOM mailing list