Core Logic

Synopsis

Neil Tennant Presents An Original Logical System With Unusual Philosophical, Proof-theoretic, Metalogical, Computational, And Revision-theoretic Virtues. Core Logic Is The First System That Ensures Both Relevance And Adequacy For The Formalization Of All Mathematical And Scientific Reasoning. Cover; Core Logic; Copyright; Dedication; Preface; Acknowledgments; Contents; Chapter 1: Introduction And Overview; Abstract; 1.1 The Aim Of This Book; 1.2 Inference And Proof As Primary In Logic; 1.3 The Debate Over Logical Reform; 1.3.1 Debate Over Rules Governing Logical Operators; 1.3.2 Debate Over Efq And Relevance; 1.3.3 The Two Main Lines Of Reform Of Classical Logic; 1.3.4 Structural Rules In The Sequent Calculi; 1.3.5 On Inductive De Nition Of Proof-in-system-s; 1.3.6 Reexive Stability; 1.4 On Pluralism About Logic, And The Explication Of Deductive Validity 2.3.1 Comments On The Rules Of Core Logic2.3.2 Comments On Discharge Rules In Core Logic; 2.3.3 The Admissibility Of Cut For Core Logic; 2.3.4 Special Features Of Core Logic That Ensure Relevance; 2.3.5 Core Logic Provides Enough Transitivity Of Deduction For All Scienti C Purposes; 2.3.6 Philosophical Arguments For Core Logic; 2.3.7 Other Important Advantages Of Core Logic; 2.3.8 Core Logic's Eschewal Of Thinning And Cut As Rules Of The Proof System; 2.3.9 Core Logic's Shedding Of Other Old Saws; 2.4 Why `core'?; Chapter 3: The Logic Of Evaluation; Abstract; 3.1 The Logical Operators 3.2 Our Inferentialism Delivers The Truth Tables3.3 Atomic Determinations; 3.3.1 Using The Simplest Kind Of Atomic Basis; 3.3.2 Co-inductive Definition Of -relative Verifications And Falsifications; 3.3.3 Rules Of Verification And Falsification, In Graphic Form; 3.4 Extension To First Order: Saturated Terms And Formulae; 3.4.1 Rules Of Verification And Of Falsification At First Order; 3.4.2 Further Features Of First-order Verifications And Falsifications Relative To The Simplest Kind Of Atomic Basis; 3.4.3 On The Soundness Of The Evaluation Rules; 3.4.4 A Note On Nomenclature 3.5 More General Atomic Bases3.5.1 Inclusions And Contrarieties; 3.5.2 The Notion Of A Determination Relative To An Atomic Basis; 3.5.3 Broadening The Atomic Basis Affords Us A New Way Toverify Conditionals; 3.5.4 Rules Of Determination Relative To An Atomic Basis; Chapter 4: From The Logic Of Evaluation To The Logic Of Deduction; Abstract; 4.1 From Evaluation To Deduction; 4.2 Graphic Rules Of Core Logic C; 4.3 Reasons For Preferring Parallelized To Serial Forms Of Elimination Rules; 4.4 Absurdity And Contrarieties; 4.4.1 Conclusion Occurrences Of Absurdity (?) Neil Tennant. Includes Bibliographical References (pages 338-345) And Index.