Neil Tennant presents an original logical system with unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. Core Logic, which lies deep inside Classical Logic, best formalizes rigorous mathematical reasoning. It captures constructive relevant reasoning. And the classical extension of Core Logic handles non-constructive reasoning. These core systems fix all the mistakes that make standard systems harbor counterintuitive irrelevancies. Conclusions reached by means of core proof are relevant to the premises used. These are the first systems that ensure both relevance and adequacy for the formalization of all mathematical and scientific reasoning. They are also the first systems to ensure that one can make deductive progress with potential logical strengthening by chaining proofs together: one will prove, if not the conclusion sought, then (even better!) the inconsistency of one's accumulated premises. So Core Logic provides transitivity of deduction with potential epistemic gain.
Because of its clarity about the true internal structure of proofs, Core Logic affords advantages also for the automation of deduction and our appreciation of the paradoxes.
Neil Tennant isArts & Humanities Distinguished Professor of Philosophy and Distinguished University Scholar at the Ohio State University. He has taught at the Universities of Edinburgh and Stirling and at the Australian National University. His books include Anti-Realism and Logic (OUP 1987), The Taming of the True (OUP 1997), Changes of Mind (OUP 2012), and Introducing Philosophy: God, Mind, World, and Logic (Routledge 2015).