Re: Godel Contradiction

MoeBlee <jazzmobe@xxxxxxxxxxx> writes:

Then what do you mean by 'finitistically provable'? PRA doesn't prove
the consistency of Robinson arithmetic does it?

Why do you think the consistency of Robinson arithmetic is not provable
in PRA? Recall that Robinson arithmetic is very weak and in particular
does not include any form of induction. (A finitistic consistency proof
is given by Shoenfield.)

Robinson arithmetic is included, per second incompleteness, in the
theories whose consistency is not provable by themselves or weaker
theories, right?

It is included among such theories but not by the second incompleteness
theorem: the theory is too weak to prove the derivability conditions and
so the theorem does not apply.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxx)

"Wovon mann nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

Relevant Pages