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This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.
"Goldfarb produces a modern classic. One of the kindest, most avuncular logic books I have ever seen. Every page is evidence of the author's warmth toward his students and his dedication to conveying logic to them in a way that respects them as mature persons. His thorough mastery of the subject and its philosophy is another feature that distinguishes this book from the mountain of logic texts written by . . . persons for whom logic is . . . not a professional specialty as it is with Goldfarb, an accomplished and respected logician who has been teaching this material for over twenty years. No logic book I know of conveys kind warmth toward readers or deeply modest non-dogmatic competence in the field more than Goldfarb's 2003 Deductive Logic. The usual scientistic hocus-pocus, formalistic pedantry, and breezy dogmatism are nowhere to be found in this book. Its examples are chosen to appeal to the intelligent humanities student, not merely to the mathematical science or computer engineering student. They are carefully and tastefully crafted to avoid irrelevant linguistic complexities, both logical and sociological.
" . . . A form of Quine's distinctive . . . philosophy and organization of logic has been meticulously and creatively implemented. Accordingly, . . . deduction in the sense of step-by-step inferring of conclusions implied by given premises is substantially deferred until Section 33 of the books 44 Sections. The 44 sections averaging six pages in length are unequally divided into four Parts titled respectively: Truth-functional Logic, Monadic Quantification Theory, Polyadic Quantification Theory, and Identity and Names. The material in this book has been thoroughly classroom-tested. Most first-edition logic texts are loaded with errors that are exasperating to students and instructors alike. My reading has turned only one (non-exasperating) error: on pages 18, 69, and 289 the space in Augustus De Morgan's last name is omitted. Despite an honest effort to detect further errors typographical and otherwise, the reviewer, to his amazement, has found none.
"If a college instructor wants to present a Quinean form of modern first-order logic with identity and names but without functions in a competent, accurate and thoughtful way while avoiding patronizing spoon-feeding, this might be the best text. No other book I know comes close."
—John Corcoran, State University of New York at Buffalo
"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
"This is the finest introduction to logic available."
—John Symons, University of Texas, El Paso
PART I: TRUTH-FUNCTIONAL LOGIC
A. Analysis: §1 Statements; §2 Conjunction; §3 Negation; §4 Disjunction; §5 Grouping; §6 Truth-functions; §7 Conditional; §8 Logical Paraphrase.
B. Logical Assessment: §9 Schemata and Interpretation; §10 Validity and Satisfiability; §11 Implication; §12 Use and Mention; §13 Equivalence.
C. Reflection: §14 General Laws; §15 Disjunctive Normal Form; §16 Expressive Adequacy; §17 Formal Systems.
PART II: MONADIC QUANTIFICATION THEORY
A. Analysis: §18 Monadic Predicates and Open Sentences; §19 The Existential Quantifier; §20 The Universal Quantifier; §21 Further Notes on Paraphrase; §22 Universe of Discourse.
B. Logical Assessment: §23 Schemata and Interpretation; §24 Validity, Implication, and Equivalence; §25 Testing Monadic Schemata.
C. Reflection: §26 Monadic Satisfiability; §27 General Laws.
PART III: POLYADIC QUANTIFICATION THEORY
A. Analysis: §28 Polyadic Predicates; §29 Paraphrase.
B. Logical Assessment: §30 Schemata and Interpretation; §31 Validity, Implication, and Equivalence; §32 Instances; §33 Deduction; §34 Deduction Extended.
C. Reflection: §35 Soundness; §36 Other Laws; §37 Prenex Form; §38 Completeness; §39 Further Consequences; §40 Decidability.
PART IV: IDENTITY AND NAMES
§41 Identity; §42 Inferences with Names; §43 Descriptions; §44 Elimination of Descriptions.
Colleges and Universities that have adopted Deductive Logic include:
University of Alberta
University of California, Berkeley
University of Illinois, Chicago
University of Illinois, Urbana-Champaign
University of Miami
University of Pennsylvania
University of Toronto (Missasauga campus)
University of Viriginia
About the Author:
Warren Goldfarb is Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic, and Professor of Philosophy, at Harvard University.