Logic Primer

Overview

This text presents a self-contained introduction to logic suitable for majors and nonmajors, and can be covered entirely in a one-semester course. Natural deduction systems of sentential logic and of first-order logic, truth tables, and the basic ideas of model theory are presented without superfluous discussion. This allows the instructor to choose various ways of presenting the material. The text is organized into definitions, comments, examples, and exercises in a modern, visually helpful format. Comments are ...
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Overview

This text presents a self-contained introduction to logic suitable for majors and nonmajors, and can be covered entirely in a one-semester course. Natural deduction systems of sentential logic and of first-order logic, truth tables, and the basic ideas of model theory are presented without superfluous discussion. This allows the instructor to choose various ways of presenting the material. The text is organized into definitions, comments, examples, and exercises in a modern, visually helpful format. Comments are kept to a minimum so that definitions and examples are usually on the same page, making it easy for students to compare the two. In addition, there are over 500 exercises, with solutions to more than half of them provided in an appendix.

Logic Primer differs from existing texts in several important ways. The proofs are shorter and more elegant. The rules of proof are stated in terms of denials of sentences rather than negations; this results in more intuitive rules that students learn more quickly. Most important pedagogically, the authors' natural deduction systems explicitly track the assumptions on which each step in a proof depends.

Colin Allen is Assistant Professor of Philosophy and Michael Hand is Associate Professor of Philosophy, both at Texas A&M University.

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What People Are Saying

From the Publisher
"Logic Primer is an excellent textbook: wonderfully concise, clear, and rich. Irecommend it highly for introductory courses in formal logic. And the web-based software is state-of-the-art."—Torin Alter, Department of Philosophy, The University of Alabama

"By far the smoothest running natural deduction system that I have seen in 28 years of teaching logic. The proof checker website and the low cost of the text make Logic Primer the first choice!"—Jonathan Gold, West Liberty State College

"I am very pleased to see that Logic Primer is coming out in a second edition. I have used the first edition to great effect in turning my classes into learning communities of careful readers. The new material on identity, and the revisions to previous material, are well motivated and will be helpful. The key virtue of the book, however, is its clear, direct, and intelligibly sequenced presentation of logic. I look forward to being able to continue to build my course around the structure provided by Logic Primer."—William S. Robinson, Professor of Philosophy, Iowa StateUniversity

"What makes Logic Primer a uniquely valuable text is not that it contains everything you need for an introductory logic course (which, of course, it does), but that it contains nothing more. While providing students with a clear and comprehensive yet streamlined presentation of first-order logic, it allows instructors the freedom to tailor the structure and pace of the course to fit their own pedagogical goals. Moreover, the natural deduction system is elegant, intuitive,and free of various unnecessary procedures that, though common in other systems, tend to make derivations difficult for students to grasp."—Amy Kind, Department of Philosophy, Claremont McKennaCollegePlease note: Don't use; Amy Kind is thanked in the acknowledgments.

Torin Alter
Logic Primer is an excellent textbook: wonderfully concise, clear, and rich. I recommend it highly for introductory courses in formal logic. And the web-based software is state-of-the-art.
Jonathan Gold
By far the smoothest running natural deduction system that I have seen in 28 years of teaching logic. The proof checker website and the low cost of the text make Logic Primer the first choice!
William S. Robinson
I am very pleased to see that Logic Primer is coming out in a second edition. I have used the first edition to great effect in turning my classes into learning communities of careful readers. The new material on identity,and the revisions to previous material, are well motivated and will be helpful. The key virtue of the book, however, is its clear, direct, and intelligibly sequenced presentation of logic. I look forward to being able to continue to build my course around the structure provided by Logic Primer.
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Product Details

  • ISBN-13: 9780262510653
  • Publisher: MIT Press
  • Publication date: 8/12/1992
  • Series: Bradford Books Series
  • Edition description: Older Edition
  • Pages: 188
  • Product dimensions: 7.04 (w) x 9.01 (h) x 0.43 (d)

Meet the Author

Colin Allen is Professor of Philosophy at Texas A&M University. He is the coauthor of Nature's Purposes (MIT Press, 1998), Species of Mind (MIT Press, 1997), and The Cognitive Animal (MIT Press, 2001).

Michael Hand is Professor of Philosophy at Texas A&M University.

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Table of Contents

Preface
Acknowledgements
Ch. 1 Sentential Logic 1
1.1 Basic Logical Notions 1
1.2 A Formal Language for Sentential Logic 3
1.3 Translation of English to Sentential Wffs 10
1.4 Primitive Rules of Proof 17
1.5 Sequents and Derived Rules 28
1.6 Theorems 35
Ch. 2 Truth Tables 39
2.1 Truth Tables for Sentences 39
2.2 Truth Tables for Sequents 43
2.3 Tautologies 46
2.4 Indirect Truth Tables 49
2.5 English Counterexamples 53
Ch. 3 Predicate Logic 57
3.1 A Formal Language for Predicate Logic 57
3.2 Translation of English to Quantified Wffs 67
3.3 Primitive Rules of Proof 76
3.4 Sequents, Theorems, and Derived Rules of Proof 89
Ch. 4 Models 93
4.1 Finite Interpretations and Expansions with One-Place Predicates 93
4.2 Finite Countermodels for Arguments with One-Place Predicates 99
4.3 Finite Countermodles for Arguments with Many-Place Predicates 102
4.4 Finite Countermodels for Arguments with Identity 107
4.5ä Infinite Countermodels 110
Answers to Selected Exercises 113
Index 189
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