Logic & Philosophy of Mathematics

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  1. First-Order Logic (Second Edition)

    John Heil

    "In his introduction to this most welcome republication (and second edition) of his logic text, Heil clarifies his aim in writing and revising this book: 'I believe that anyone unfamiliar with the subject who set out to learn formal logic could do so relying solely on [this] book. That, in any case, is what I set out to create in writing An Introduction to First-Order Logic.' Heil has certainly accomplished this with perhaps the most explanatorily thorough and pedagogically rich text I’ve personally come across.     "Heil's text stands out as being remarkably careful in its presentation and illuminating in its explanations—especially given its relatively short length when compared to the average logic textbook. It hits all of the necessary material that must be covered in an introductory deductive logic course, and then some. It also takes occasional excursions into side topics, successfully whetting the reader’s appetite for more advanced studies in logic. The book is clearly written by an expert who has put in the effort for his readers, bothering at every step to see the point and then explain it clearly to his readers. Heil has found some very clever, original ways to introduce, motivate, and otherwise teach this material. The author's own special expertise and perspective—especially when it comes to tying philosophy of mind, linguistics, and philosophy of language into the lessons of logic—make for a creative and fresh take on basic logic. With its unique presentation and illuminating explanations, this book comes about as close as a text can come to imitating the learning environment of an actual classroom. Indeed, working through its presentations carefully, the reader feels as though he or she has just attended an illuminating lecture on the relevant topics!" —Jonah Schupbach, University of Utah 

    Answer Key: Solutions to the even-numbered problems are included in the book. A PDF with solutions for all of the problems is available to instructors only, click here to request the solutions PDF.

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  2. Logic and Philosophy (13th Edition)

    Alan Hausman, Frank Boardman, Howard Kahane

    A comprehensive introduction to formal logic, Logic and Philosophy: A Modern Introduction is a rigorous yet accessible text, appropriate for students encountering the subject for the first time. Abundant, carefully crafted exercise sets accompanied by a clear, engaging exposition build to an exploration of sentential logic, first-order predicate logic, the theory of descriptions, identity, relations, set theory, modal logic, and Aristotelian logic. And as its title suggests, Logic and Philosophy is devoted not only to logic but also to the philosophical debates that led to the development of the field.

    Download the Table of Contents (PDF)

    Much new material has been added for the 13th edition. An introduction to set theory and its relationship to logic and mathematics, including philosophical issues, is now part of Chapter 13. Chapter 15 is an introduction to modal logic and Kripke semantics, concluding with a discussion of philosophical problems with any logical accommodation of modalities. Instructors who do not wish to present proof methods will find chapters on truth trees for both sentential and first-order logic, and a presentation of trees for modal logic.
     
    Special features of this text include presentations of the history of logic, alternatives to traditional methods of conditional and indirect proof, and a discussion of semantic problems with universal and existential instantiations. Throughout, the authors are sensitive to philosophical issues that arise from the relationship between ordinary language, symbolic logic, and justifications for the syntax and semantics of the various symbolic languages. Discussions range from the justification of the truth table for the sentential rendering of if . . . then statements to semantic and syntactic paradoxes, including some troubling paradoxes that arise in ordinary language (e.g., the so-called hangman or surprise quiz paradox). Answers to the even-numbered exercises are included in the back of the book.

    Logic and Philosophy includes ample material for a one-semester or two-semester course and provides a thorough preparation for more advanced logic courses.

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  3. Classical Logic and Its Rabbit-Holes

    Nelson P. Lande

    "Many students ask, 'What is the point of learning formal logic?' This book gives them the answer. Using the methods of deductive logic, Nelson Lande introduces each new element in exquisite detail, as he takes students through example after example, proof after proof, explaining the thinking behind each concept. Shaded areas and appendices throughout the book provide explanations and justifications that go beyond the main text, challenging those students who wish to delve deeper, and giving instructors the option of confining their course to the basics, or expanding it, when they wish, to more rigorous levels. Lande encourages students to think for themselves, while at the same time providing them with the level of explanation they need to succeed. It is a rigorous approach presented in a style that is informal, engaging, and accessible. Students will come away with a solid understanding of formal logic and why it is not only important, but also interesting and sometimes even fun. It is a text that brings the human element back into the teaching of logic."
         —Hans Halvorson, Princeton University

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  4. Deductive Logic

    Warren Goldfarb

    "Warren Goldfarb's long-awaited Deductive Logic is an unusually perspicuous and effective logic textbook. It succeeds in achieving great precision without seeming pedantic and great depth without compromising accessibility. One main advantage of this book relative to its competitors is the lucidity with which it explains, in ways that even beginners can fully appreciate, the rapport between semantic and syntactic captures of logical consequence. Another marked advantage is the book's emphasis on deduction and its insistence on motivating the various clauses of the rules of deduction by showing, for example, what would ensue had these clauses been flouted. In this, Deductive Logic fills a real lacuna in logic-instruction and avoids the common pedagogical pitfalls of instruction via the tree method, where students find it rather mysterious why and how the method really works. The book is written in a clear and lively style and contains numerous exercises of varying degrees of difficulty. It is ideally suited for students in philosophy and computer science."
         —Ori Simchen, University of British Columbia

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  5. Formal Logic (Fourth Edition)

    Richard Jeffrey
    Edited, with a New Supplement, by John P. Burgess

    "Jeffrey’s text is a landmark in the history of logic textbooks. It covers elementary material (using tree rather than natural deduction) yet manages to also cover central material for an advanced undergraduate logic class, and it does so compactly and with finesse in barley over 150 pages. It is unique." —Paul McNamara, University of New Hampshire

     

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  6. Beginning Logic

    E. J. Lemmon

    “One of the most careful and intensive among the introductory texts that can be used with a wide range of students. It builds remarkably sophisticated technical skills, a good sense of the nature of a formal system, and a solid and extensive background for more advanced work in logic. . . . The emphasis throughout is on natural deduction derivations, and the text’s deductive systems are its greatest strength. Lemmon’s unusual procedure of presenting derivations before truth tables is very effective.”
         —Sarah Stebbins, The Journal of Symbolic Logic

    Published by Van Nostrand Reinhold in the U.K. Available from Hackett in the U.S. only.

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  7. An Introduction to Logic

    Morris R. Cohen & Ernest Nagel
    Edited, with a new Introduction, by John Corcoran

    Written for independent study and suitable for an introductory course in logic, this classic text combines a sound presentation of logic with effective pedagogy and illustrates the role of logic in many areas of humanistic and scientific thought. Cohen and Nagel’s elegant integration of the history of philosophy, natural science, and mathematics helps earn this work its distinguished reputation.

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  8. Truth, Vagueness, and Paradox

    Vann McGee

    “It is the only real treatise on truth in existence that takes full account of the liar paradox and other ‘semantical’ paradoxes and treats the sophisticated theories that have been developed in the last fifteen years. . . . The view of truth it expresses, the technical results obtained in working it out, and the general, self-contained treatment of the logical problems concerning truth combine to make this work a very important one.”
         —Charles Parsons, Harvard University

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  9. A Philosophical Companion To First-Order Logic

    Edited by R. I. G. Hughes

    This volume of recent writings, some previously unpublished, follows the sequence of a typical intermediate or upper-level logic course and allows teachers to enrich their presentations of formal methods and results with readings on corresponding questions in philosophical logic.

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  10. Prior Analytics

    Aristotle
    Translated by Robin Smith

    “This volume is an impressive tour de force. It is state-of-the-art Aristotle: it employs the most recent philological, philosophical, and logical advances which since the 1970’s at least have rendered previous translations and commentaries obsolete. The translation is the first to take account of the recent epistemically orientated natural-deduction approach, which restores Aristotle’s reputation as a consummate logician and reveals much more of Aristotle’s method than previous approaches. Every page of Robin Smith’s commentary shows extensive learning, taste, imagination, and skill. . . . An important and lasting contribution, not only to Aristotle scholarship and to the history of logic, but also to the history of philosophy itself.”
        —John Corcoran, SUNY Buffalo

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  11. Logic, Semantics, Metamathematics (Second Edition)

    Alfred Tarski
    Translated by J. H. Woodger
    Edited, with Introduction and Index, by John Corcoran

    Contains the only complete English-language text of “The Concept of Truth in Formalized Languages.” Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.

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  12. Companion To Lemmon's Beginning Logic

    Prepared by George Schumm

    This brief volume supplements Lemmon’s classic introductory logic text with almost 200 new exercises, many of them solved, solutions to selected exercises in Beginning Logic itself, a helpful commentary on Lemmon’s use of key technical terms, alternative formulations, and advice to students.

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