On 17 Dec 2012, at 22:31, meekerdb wrote:

On 12/17/2012 1:15 PM, Quentin Anciaux wrote:
ISTM that consistency is the fact that you can't have contradiction.

In some logics you're allowed to have contradictions, but the rules of inference don't permit you to prove everything from a contradiction. I think they are then called 'para-consistent'.

But that can have some uses in natural language studies, but be misleading in the ideal case needed fro physics.

In particular it is important to understand that PA + "PA is inconsistent" is a consistent theory.

Indeed if from PA + "PA is inconsistent" you can get a contradiction in PA, then you have prove correctly, by absurdum, the consistency of PA in PA, violating the second incompleteness theorem.

Dt -> ~BDt is equivalent with Dt -> DBf.

Bruno



Incompletness that you can't prove every proposition.

No, incompleteness is you can't prove every true proposition. Which implies there is some measure of 'true' other than 'provable'.

Brent

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