Methods of Logic: Fourth Edition

by Willard Van Orman Quine

Book Overview

This widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

• Format: Paperback
• Language: English
• ISBN: 0674571762
• ISBN13: 9780674571761
• Release Date: November 1982
• Publisher: Harvard University Press
• Length: 344 Pages
• Weight: 1.12 lbs.
• Dimensions: 1.1" x 6.1" x 9.0"

Customer Reviews

Start Here

This is the best place to start if you want to learn first-order logic: truth functions and quantification theory. Here is why. Quine is an acknowledge master of symbolic logic. Quine is the clearest and most coherent writer on logic. Quine's logic is the most careful and conservative. By the last I mean the following. Propositional logic, quantification theory, set theory, and mathematics are all different animals. Drawing the line between first-order logic (quantification theory) and set theory allows one to treat the former without the antinomies and other issues plaguing set theory. First order logic has been proven complete, while set theory is not complete. And first-order logic alone is a fascinating and useful tool. One can then tack on set theory as another layer if desired. Yet all other authors I've read fail to make this distinction. I've even read one popular book on "first-order logic" that begins with defining "true" and "false" as members of a set. Why? This book includes nothing about modal logic, deontic logic, etc. This is a good thing. Begin at the beginning, the foundation. Then if you want to go off onto one of these tangents you'll have a solid base upon which to evaluate these other logics. Besides all this you'll learn some useful techniques developed by Quine himself such as his Main Method for proving the validity of valid quantificational schema. He'll also teach you alternative methods developed by others. If you don't understand any of the terms above, don't worry. You will by the time you're done with this book. It is easy to follow for the moderately motivated beginner and rich enough to be of great value to anyone else. And it is a terrific reference. If you really need something super-basic to get started try Elementary Logic: Revised Edition.

Masterpiece

I don't think you get this in a lot of other books. Just look at the Historical Notes; In themselves a guided direction to the most important work on logics. This is truly time saving instead of go wondering what books to read, up to the date of Quine's book of course.In the end it also contains bibliography, but also a note to a whole other index covering literature up to 1935, this is truly at great value.I find this book helpful in analysis concerning ideas; Whatever they are, since language usage is the tool for thought, even if not written down.It's simply a MIND-SPEAKER.Also more newer books, in for instance computer science, in my personal opinion, skip important questions already asked by scientists which then have been elaborated on.People who read logic for the first time, like me, ask fundamental questions in order to understand, following Quine's reasoning is surely educational.

A good start

Like any great book, this one could be a bit, though not too much, better. By far and away the most useful element of Quine's book is his treatment of translating ordinary English into logical schemata. I have never seen such a lucid and effective presentation of the task, and I recommend the book very highly to anybody on that account. His presentation of truth-functional and quantificational schemata are solid are simply excellent. The book, however, is not without its defects of which I should caution prospective buyers about. First, there are many treatments in the book of historical interest, but to a student of first-order logic they may seem to be a bit excessive. His incorporation of Polish notation, while fascinating in its own right, is not in accorance with Quine's drive for efficiency and conciseness. A similar account goes for his treatment of Boolean algebra. It is in that treatment that Quine introduces many ideas indispensible to quantificational logic, yet it is tempting to skip over those chapters when one can sufficiently delve into quantification theory. Secondly, his notation is, as another reviewer points out, unorthodox. It is very effective and in my opinion superior to the conventional formality, but this could be difficult to deal with, and one wonders if Quine should have been more cautious about varying his symbols from the norm. Finally, Quine's treatment of the Completeness Proof and the Lowenheim Theorem, while quite solid in their own right, could be more effective. Quine seems to be keen on applying a constructivist approach to the proof, and spends many pages on definitions and lemmas that can be avoided. One can provide a proof by contradiction in order to sufficiently demonstrate most of his treatment of the matter, as so much of it is spent proving the "law of infinite conjunction," which is really only an 8 step proof. I won't go into the details here, but keep that in mind when studying the chapter. Nevertheless, Quine's work is as entertaining as it is rigorous.

a great introduction to first-order logic ...

Quine is well-known in this century for being one of the premier analytic philosophers in the Anglo-American tradition. He probably used this book for his upper-division course in logic for philosophy majors. After reading this book, I can see his reputation is well-justified.This book is more than just a textbook in logic. In his own way, Quine shows in his examples just how difficult it is to break down ordinary language into symbolic logic, and in the process (hopefully), one should learn both rigorous thinking and charity. These are rare commodities today.Quine has the rather idiosyncratic position that modal logic only confuses matters. However, I would rather read a complete introduction to modal logic, than to receive only a chapter's worth of treatment. Hence, I can deal with his excluding modal logic from this book.I do wish there was a short chapter or glossary on informal logic, since many other treatments do continue to use those terms (e.g. Copi). Knowing the terminology does help one to communicate in prose one's analysis of an argument. It does help to know all those latin distinctions (e.g. ad hominem, ad nominem, ad populii, petitio principii, etc.).That being said, I'm a much clearer thinker for having worked through this book, and I would heartily recommend this for anybody.

Quine is a master of logic

I've taught college level logic courses, and I return, from time to time, to classics. No one who is serious about contemporary logic can afford to not read Quine. His explanations are clear, although the symbols used are a bit unorthodox. I recommend this to anyone who is already familiar with elementary symbolic logic. Additionally, an awareness of modal or quantificational logic would be helpful.