[FOM] Platonism and Formalism
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.
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