Proof and Consequence
An Introduction to Classical Logic with SIMON and SIMON SAYS
  • Publication Date: June 29, 2006
  • ISBN: 9781551115474 / 1551115476
  • 328 pages; 7" x 9"

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Proof and Consequence

An Introduction to Classical Logic with SIMON and SIMON SAYS

  • Publication Date: June 29, 2006
  • ISBN: 9781551115474 / 1551115476
  • 328 pages; 7" x 9"

Proof and Consequence is a rigorous, elegant introduction to classical first-order natural deductive logic; it provides an accurate and accessible first course in the study of formal systems. The text covers all the topics necessary for learning logic at the beginner and intermediate levels: this includes propositional and quantificational logic (using Suppes-style proofs) and extensive metatheory, as well as over 800 exercises.

Proof and Consequence provides exclusive access to the software application Simon, an easily downloadable program designed to facilitate an intuitive understanding of classical logic through the generation and analysis of proofs. It also aids with the representation of natural language sentences in the formal language. Equipped with nearly all the exercises found in the text, Simon helps students work efficiently and effectively by detecting and explaining errors in solutions as they proceed. Students can also submit assignments, view their own records, and check their standing in the class.

The complete logic package includes:

  • The logic textbook, Proof and Consequence
  • A very helpful study guide to the textbook, containing extra exercises, Simple Simon
  • Access, through Simon, to the grading software, Simon Says, that allows students to submit assignments and track their grades


Proof and Consequence is a thorough introduction to classical logic, including propositional and first order logic. An excellent choice for an introductory or middle-level logic student, it is well (and often charmingly) written, clear on points that are often fuzzy in other books, and follows a well-laid path through the material. It's a very nice book.” — Bryson Brown, University of Lethbridge

Chapter 1: General Introduction

1.1 Where Logic Comes From
1.2 The Nature of the Subject
1.3 The Aims of this Book

Chapter 2: Classical Propositional Logic 1

2.1 From Arguments to Proofs
2.2 The Rules of L

Chapter 3: Propositional Logic 2

3.1 Formal Systems
3.2 Theorems
3.3 Uniform Substitution
3.4 Theorem and Sequent Introduction
3.5 Effectiveness
3.6 Validity
3.7 The Strong Soundness of L
3.8 The Strong Completeness of L

Chapter 4: Quantificational Logic 1

4.1 The Inadequacy of Propositional Forms
4.2 Quantificational Rules

Chapter 5: Quantificational Logic 2

5.1 The Formal System Lq
5.2 The Rules of Lq
5.3 Lq-theoremhood Preserving Operations
5.4 Models for Quantificational Logic
5.5 Determining Validity
5.6 First-Order Theories
5.7 First-Order Theories of Relations
5.8 Experimenting With First-Order Theories

5.9 Quantificational Models Revisited

5.10 Quantificational Models: The Details

5.11 The Soundness of Lq

5.12 The Completeness of Lq

Appendix A: Normal Forms

Appendix B: The Connectives of Natural Language

Glossary of Terms

Table of Symbols

Index of Exercises

Index of Names

Index of Subjects

Ray Jennings is Professor of Philosophy at Simon Fraser University. He is the author of The Geneology of Disjunction (Oxford University Press, 1994).

Nicole Friedrich is a researcher in philosophy and computer science. She is also the curator of Simon Fraser’s Laboratory for Logic and Experimental Philosophy.