[FOM] Are the proofs of con(PA) circular?

[Martin Davis]

Richard Heck wrote:
>On 05/18/2011 07:14 PM, Martin Davis wrote:
>>Discussion of Gödel's beliefs should take note 
>>of the fact that he himself offered another 
>>proof of con(PA) via the equivalent con(HA) - his "Dialecta" interpretation.
>Presumably Gödel thought, then, that we had some 
>other way of knowing that HA is consistent?

Maybe. But the Dilectica interpretation provides 
a proof that HA is consistent, and it was known 
that the consistency of HA implies that of PA by a simple argument.

Martin


Martin Davis
Professor Emeritus, Courant-NYU
Visiting Scholar, UC Berkeley
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