[FOM] Platonism and Formalism

[Torkel Franzen]

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.

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Torkel Franzen