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Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism

Philosophia Mathematica 22 (3):321-344 (2014)

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Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.details A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more (...) Download Export citation Bookmark 28 citations
The Relevance of Premises to Conclusions of Core Proofs.Neil Tennant - 2015 - Review of Symbolic Logic 8 (4):743-784.details The rules for Core Logic are stated, and various important results about the system are summarized. We describe its relationship to other systems, such as Classical Logic, Intuitionistic Logic, Minimal Logic, and the Anderson–Belnap relevance logicR. A precise, positive explication is offered of what it is for the premises of a proof to connect relevantly with its conclusion. This characterization exploits the notion of positive and negative occurrences of atoms in sentences. It is shown that all Core proofs are relevant (...) Download Export citation Bookmark 11 citations
On Some Mistaken Beliefs About Core Logic and Some Mistaken Core Beliefs About Logic.Neil Tennant - 2018 - Notre Dame Journal of Formal Logic 59 (4):559-578.details This is in part a reply to a recent work of Vidal-Rosset, which expresses various mistaken beliefs about Core Logic. Rebutting these leads us further to identify, and argue against, some mistaken core beliefs about logic. Download Export citation Bookmark 1 citation
Normalizability, cut eliminability and paradox.Neil Tennant - 2016 - Synthese 199 (Suppl 3):597-616.details This is a reply to the considerations advanced by Schroeder-Heister and Tranchini as prima facie problematic for the proof-theoretic criterion of paradoxicality, as originally presented in Tennant and subsequently amended in Tennant. Countering these considerations lends new importance to the parallelized forms of elimination rules in natural deduction. Download Export citation Bookmark 9 citations
An Expressivist Bilateral Meaning-is-Use Analysis of Classical Propositional Logic.John Cantwell - 2015 - Journal of Logic, Language and Information 24 (1):27-51.details The connectives of classical propositional logic are given an analysis in terms of necessary and sufficient conditions of acceptance and rejection, i.e. the connectives are analyzed within an expressivist bilateral meaning-is-use framework. It is explained how such a framework differs from standard inferentialist frameworks and it is argued that it is better suited to address the particular issues raised by the expressivist thesis that the meaning of a sentence is determined by the mental state that it is conventionally used to (...) Download Export citation Bookmark 1 citation

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