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This is actually wrong.. There's an old joke in logic: sound, complete, consistent -- pick two :) I think you're misunderstanding what soundness is. Soundness
by dvt 10y ago
This is actually wrong.. There's an old joke in logic: sound, complete, consistent -- pick two :)
I think you're misunderstanding what soundness is. Soundness means that a proof in that logic implies a (semantic) entailment in that logic. That is:
Γ ⊢ A ⇒ Γ ⊨ A
It's a very specific characteristic.
- mafribe 10y agoSorry, I mean inconsistent where I wrote sound.
- jsprogrammer 10y agoI'm still not sure it's true that an inconsistent logic can prove anything. Certainly an inconsistent logic contains contradictory proofs, but I don't think every inconsistent logic can be used to "prove" any arbitrary theorem.