Cohabiting with the logical paradoxes: a negative assessment and a proposal

At the commonsensical level of the manifest image, we seem to take for granted logical laws of all sorts, including classical logic (CL) and naive principles of truth and predication (TP), which, however, generate logical paradoxes such as the liar, Russell’s paradox and Curry’s paradox. The formal logic of the scientific image comes to the rescue by proposing many competing formal systems that restore consistency, by sacrificing either principles of CL or principles of TP. We wish to explore a different path, which aims at saving both CL and TP, and deals with the paradoxes when they come to the fore, without swallowing contradictions or explosion. We consider the viability of Batens’ Inconsistency-Adaptive Logic (IAL) to pursue this goal and we end up with a negative assessment. We then sketch an alternative proposal that incorporates IAL’s distinction between provisional and final derivability.