Paraconsistent and Multivalued logics vs Gödel's Theorem: A Question

[aoanla]

As people reading this may know, Gödel's Theorem, which places limits on the consistency/strength of axiomatic systems like mathematics, is based upon demonstrating the existence of a necessary contradiction in any sufficiently powerful such system

Comments

[mcmartin]

There's apparently a number of logics of provability. I picked up a monograph on the subject while in Ithaca a few months back and haven't yet studied it in detail. I will look into it.