Logical Methods

An accessible introduction to philosophical logic, suitable for undergraduate courses and above.

Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed.
 
Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic’s development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy.
 
This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs.
 
Features:

An accessible introduction to proof theory for readers with no background in logic

Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics

Provides tools and techniques of particular interest to philosophers and philosophical logicians

Features short summaries of key concepts and skills at the end of each chapter

Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students’ understanding and developing skills in new directions

How to Read This Book xi
I Propositional Logic
1 Introduction 3
2 Connectives: and & if 19
3 More Connectives: not & or 35
4 Facts about Proofs & Provability 49
5 Models & Counterexamples 75
6 Soundness & Completeness 91
II Modal Logic
7 Necessity & Possibility 117
8 Actuality & 2D Logic 153
9 Modal Natural Deduction 167
III Predicate Logic
10 Proofs for Predicate Logic 189
11 Models for Predicate Logic 217
12 Coda 245
Glossary 255
References 261
Symbol Index 267
Subject Index 269“The book can be recommended not only to students and teachers of mathematics and philosophy, but also to a wider circle of readers interested in all aspects of applications of modern symbolic logic in linguistics, computer science, and philosophy and methodology of science. The authors’ style, way of presentation and choice of topics add to the real
pleasure of reading this book.”
—MathSciNet

"[A]n innovative and rigorous textbook that will challenge both instructors and students. Its novel structure and balanced approach to proof and model theory distinguish it from more conventional introductory logic texts.... offers substantial rewards for those who invest the effort to navigate its complexities."
—Philosophy in Review

“[N]ot your typical textbook in formal logic....As a pedagogical tool, Restall and Standefer’s Logical Methods fares well with other, relatively recent, logic textbooks out in the market....an excellent textbook for intermediate logic and other graduate-level logic courses.”
—Teaching PhilosophyGreg Restall is Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. He is the author of Logic: An Introduction and coauthor of Logical Pluralism. Shawn Standefer is Assistant Professor of Philosophy at National Taiwan University.