"Gödel's second incompleteness theorem states no consistent axiomatic system which includes Peano arithmetic can prove its own consistency. Stated more colloqui

"Gödel's second incompleteness theorem states no consistent axiomatic system which includes Peano arithmetic can prove its own consistency. Stated more colloquially, any formal system that is interesting enough to formulate its own consistency can prove its own consistency iff it is inconsistent." [1] I believe your position is that "sufficiently complex" == "able to formulate and prove its own consistency"; my position is that such a system would be worthless as a logic, because in such a system you can prove anything. Your second paragraph is inscrutable to me. Are you trying to claim that you can't prove everything with a known inconsistent logic? Are you referring to paraconsistent logics? [1] http://mathworld.wolfram.com/GoedelsSecondIncompletenessTheorem.html http://mathworld.wolfram.com/GoedelsSecondIncompletenessTheo...