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Logic & Philosophy of Mathematics

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  1. A Philosophical Companion To First-Order Logic

    Edited by R. I. G. Hughes

    A Philosophical Companion To First-Order Logic

    This volume of recent writings, some previously unpublished, follows the sequence of a typical intermediate or upper-level logic course and allows teachers to enrich their presentations of formal methods and results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

  2. An Introduction to Logic

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

    An Introduction to Logic

    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.

  3. Beginning Logic

    E. J. Lemmon

    Beginning Logic

    “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.

  4. Classical Logic and Its Rabbit-Holes

    Nelson P. Lande

    Classical Logic and Its Rabbit-Holes

    "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

  5. Companion To Lemmon's Beginning Logic

    Prepared by George Schumm

    Companion To Lemmon's Beginning Logic

    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.

  6. PNG

    Warren Goldfarb

    Deductive Logic

    "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

  7. Formal Logic (Fourth Edition)

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

    Formal Logic (Fourth Edition)

    This new edition provides additional problems, solutions to selected problems, and two new Supplements: “Truth-Functional Equivalence” reinstates material on that topic from the second edition that was omitted in the third, and “Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification—once contemplated by Jeffrey—can result in a dramatic speed-up of certain proofs.

  8. Logic, Semantics, Metamathematics (Second Edition)

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

    Logic, Semantics, Metamathematics (Second Edition)

    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.

  9. Prior Analytics

    Aristotle
    Translated by Robin Smith

    Prior Analytics

    “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

  10. Truth, Vagueness, and Paradox

    Vann McGee

    Truth, Vagueness, and Paradox

    “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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