Core Logic

by Neil Tennant

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 counterintuitiveirrelevancies. 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 deductiveprogress with potential logical strengthening by chaining proofs 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.

Genres: Logic

360 pages, Kindle Edition

Published September 1, 2017

About the author

Neil Tennant is an American philosopher. He is Arts & Humanities Distinguished Professor of Philosophy at the Ohio State University; and, before taking up his appointment at the Ohio State University he held positions at the University of Edinburgh, the University of Stirling, and the Australian National University.

Along with Michael Dummett, Crispin Wright, Tennant is one of the most notable figures who have attempted to extend the project of providing anti-realist semantics for empirical language. He has also written extensively on intuitionistic logic and other non-classical logics. [wikipedia]