On 10/22/2013 6:19 AM, Bruno Marchal wrote:

"[]p -> p" is correctness. It is trivially true for the machine I consider, because they are correct by definition/choice.

Consistency is correctness on the f: []f -> f. It is a very particular case of 
There are machines which are not correct, yet consistent. For example Peano-Arithmetic + the axiom beweisbar('f').

Believing '0=1', does not make you inconsistent. Only non correct.

?? But in ordinary logic a false proposition allows you to prove anything. So if I prove '0=1' then I can prove any proposition - which is the definition of inconsistency.


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