A Contemporary Introduction
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Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course.
The book explores the following questions. Are there quantificational idioms that cannot be expressed with the
familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'---and if not, what are the alternatives? Should logical consequence be understood in terms or models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like modus ponens or double-negation elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how?
Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding.
Table of Contents
1.1 Propositional logic
1.2 Predicate logic
1.4 Use and mention
2.1 Generalized quantifiers
2.2 Second-order quantifiers
2.3 Substitutional quantifiers
3 Modal Logic
3.1 Modal propositional logic
3.2 Modal predicate logic
3.3 The slingshot argument
3.4 Kripke’s defense of de re modality
4.1 The material conditional
4.2 No truth conditions?
4.3 Stalnaker’s semantics and pragmatics
4.4 Is Modus Ponens valid?
5 Logical Consequence via Models
5.1 Informal characterizations of consequence
5.2 Tarski’s account of logical consequence
5.3 Interpretational and representational semantics
6 Logical Consequence via Proofs
6.1 Introduction rules as self-justifying
6.2 Prawitz’s proof-theoretic account of consequence
6.3 Intuitionistic logic
6.4 Kripke semantics for intuitionistic logic
6.5 Fundamental logical disagreement
7 Relevance, Logic, and Reasoning
7.1 Motivations for relevance logic
7.2 The Lewis Argument
7.3 First-degree entailment
7.4 Logic and reasoning
7.5 Uses for relevance logic
8 Vagueness and the Sorites Paradox
8.1 What is vagueness?
8.2 Three-valued logics
8.3 Fuzzy logics
8.5 Vagueness in the world?
Appendix A: Greek Letters
Appendix B: Set-Theoretic Notation
Appendix C: Proving Unrepresentability
John MacFarlane is is Professor of Philosophy and a member of the Group in Logic and the Methodology of Science at the University of California, Berkeley, USA. He is the author of Assessment Sensitivity: Relative Truth and Its Applications (2014).