[FOM] Platonism and Formalism

Torkel Franzen torkel at sm.luth.se
Tue Sep 30 06:40:43 EDT 2003

Karlis Podnieks says:

 >In formal theories, we cannot even formulate directly the "fact" that each
 >natural number can be generated by iterating the successor function.

  Certainly we can. For example, we can introduce a predicate
can_be_generated_by_iterating_the_successor_function, and formulate
directly the axiom (x)(x_is_a_natural_number -> x
can_be_generated_by_iterating_the_successor_function). Naturally, as with
any formal theory, any further use we make of the theory depends on what
axioms and rules of inference we introduce.

Torkel Franzen

More information about the FOM mailing list