FOM: ultrafinitism; objective vs. subjective

[Todd Wilson]

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.

-- 
Todd Wilson
Computer Science Department
California State University, Fresno