[FOM] Numbers vs writhmetic.
dmehkeri at gmail.com
Sat Jul 16 14:11:23 EDT 2011
> Two philosophers in whose philosophy mathematical truth is
> divorced from metaphysics are Hilbert and Carnap.
> In Hilbert we have the idea that mathematical concepts
> should be defined exclusively by a formal axiomatisation, and
> that the only requirement for the existence of entities thus
> defined is the logical consistency of the definitions.
To apply this to the natural numbers, obviously there will arise the
question of what logical consistency means. It was not my understanding
that Hilbert intended merely the absence of a "practically realisable"
contradiction. Rather he took at least Pi_1 sentences at face value,
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