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It is possible to prove consistency but to do so requires using a more powerful system of axioms which in turn might be inconsistent. What Goedel showed is that
by koyanisqatsi 4y ago
It is possible to prove consistency but to do so requires using a more powerful system of axioms which in turn might be inconsistent. What Goedel showed is that in any system that can encode arithmetic (and consequently some notion of computation, e.g. lambda calculus) can not be complete if it is consistent.
- V__ 4y agoAh, thank you, that makes more sense. Maybe a weird follow-up question: Is it possible (or does it make sense) to find a proof in an inconsistent system and to try to "transform" it into a consistent one?
- koyanisqatsi 4y agoYes, paraconsistent logic could be considered an instance of such a system: https://en.wikipedia.org/wiki/Paraconsistent_logic https://en.wikipedia.org/wiki/Paraconsistent_logic.