FOM: a question re. completeness

Arnon Avron aa at
Tue Feb 3 19:24:20 EST 1998

> It is rather just what I said: for s unprovable in PA, is it always the
> case that PA would be inconsistent if s were provable in PA. If you say
> that is not precise or meaningless, then you must also say that it is
> meaningless to say that if G (or not G) were provable in PA, then PA would
> be inconsistent. I don't think that this is meaningless ... and I don't see
> any reason to do so. In some sense of the term 'precision', it may lack the
> precision that the question 'Is 'Prov_T(neg ConT)-->neg ConT' provable in
> T?' has ... but that doesn't mean that the one should be substituted for
> the other.

I miss something here. As I understand it, the question is trivial,
because "if s is unprovable in PA then (if s were provable in PA then
PA would be inconsistent)" is an instance of a tautology. You surely
meant something different. Can you define it more precisely?

Arnon Avron

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