Core Logic 1st Edition by Neil Tennant (PDF)

Description

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 transitivityof 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.

User’s Reviews

Editorial Reviews: Review “Due to the author’s clear and approachable style this book may be interesting to a large circle of logicians, mathematicians and philosophers.” — Branislav Boricic”Although the author’s approach is purely logical and philosophical, rather than mathematical, it seems likely that the book would be extremely interesting to mathematicians specializing in logic and the foundations of mathematics. Due to the author’s clear and approachable style this book may be interesting to a large circle of logicians, mathematicians and philosophers. Students with a basic understanding of classical, intuitionistic and relevant logic principles will find this book an invaluable introduction to an area of central importance in logic, philosophy, computer science and, generally, methodology and philosophy of science.” — Branislav Boricic, mathSciNet About the Author Neil Tennant, Arts & Humanities Distinguished Professor of Philosophy, Ohio State UniversityNeil Tennant is Arts & 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).

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The “core logic” project sounds very interesting and, from my non-specialist position, a very welcome refreshing look at foundations of logic. Unfortunately I found the presentation in the book a bit on the disorganized side and unevenly paced. My background is probably matching “advanced undergraduate”, but I’ve had little exposure to natural deduction systems — generally speaking this is no big deal, they are “natural” enough, but for example “diamond == vacuous discharge of assumptions is allowed” vs. “box == … prohibited” on page 20 with no further definition or elaboration (I am maybe a quarter of the way through the book, flipping over some pages; maybe I missed it…?) is critical but not entirely clear to me — is it a standard convention? The system is also presented in some articles by Prof. Tennant and I think those might be almost as useful sources as this book.

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