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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