Metalogic: An Introduction to the Metatheory of Standard First Order Logic [Paperback]

Geoffrey Hunter (Author)

Book Description

Publication Date: June 26, 1996 | ISBN-10: 0520023560 | ISBN-13: 978-0520023567

This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Included is a complete proof, accessible to non-mathematicians, of the undecidability of first order logic, the most important fact about logic to emerge from the work of the last half-century.
Hunter explains concepts of mathematics and set theory along the way for the benefit of non-mathematicians. He also provides ample exercises with comprehensive answers.

Editorial Reviews

Review

"A remarkable book, in a class by itself among logic books. It has the ideal combination of readability, thoroughness, and preciseness. . . . Recommended not only as a first course text, but also as painless, indeed pleasurable reading." -- Computing Reviews

About the Author

Geoffrey Hunter, now retired, has taught in the Department of Logic and Metaphysics at the University of St. Andrews, Scotland, and has also taught in Canada, England, the United States, and Wales.

Product Details

• Paperback: 302 pages
• Publisher: University of California Press (June 26, 1996)
• Language: English
• ISBN-10: 0520023560
• ISBN-13: 978-0520023567
• Product Dimensions: 8 x 5.5 x 0.8 inches
• Shipping Weight: 11.2 ounces (View shipping rates and policies)
• Average Customer Review: 3.6 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #881,509 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

13 of 13 people found the following review helpful:

5.0 out of 5 stars A Good Introduction to a Difficult Subject, January 2, 2007

By 

a philosopher - See all my reviews

This review is from: Metalogic: An Introduction to the Metatheory of Standard First Order Logic (Paperback)

I must respectfully disagree with many of the negative things said in the previous reviews about this book. I find it to be by far and away the easiest to understand text on metalogic that I have come across. I am, however, a professional philosopher with a good deal of training in logic. So the material is not new to me, which surely makes the book much easier for me to understand. That said, I think that some of the previous reviewers have unfairly judged this book owing to the complexity of the material it covers. One should remember that Hunter's aim is not to present rigorous arguments but to INTRODUCE metalogic. I am sure he would be satisfied if his reader is inspired to look into any of the proofs in more detail elsewhere. As far as the claim that the book contains errors, I have yet to read a logic text that didn't!

16 of 17 people found the following review helpful:

5.0 out of 5 stars Forget "Godel Escher Bach", read "Metalogic"!, August 20, 2001

By A Customer

This review is from: Metalogic: An Introduction to the Metatheory of Standard First Order Logic (Paperback)

I feel compelled to write this review because I disagree utterly with the previous reviewer. This is a fantastic book! I have no specialist training in logic, but I found "Metalogic" to be a clear, interesting, well-written and definitely "painless" text. I highly recommend this book as an introduction to metalogic; in fact, I would recommend it in preference to the other popular text on metalogic, the brilliant "Godel Escher Bach". Whereas "Godel Escher Bach" introduces the field of metalogic using allegories, parables, illustrations and copious references to turtles, "Metalogic" introduces it using clear, simple arguments and gentle, step-by-step explanations.

A quote from the preface: "Many elementary logic books stop just where the subject gets interesting. This book starts at that point and goes through the interesting parts...." Many of us who have struggled through the dry and boring foundations of elementary logic have become aware that not all logic is as tedious as the foundations. Beyond elementary logic lies a fascinating world inhabited by the paradoxes of Bertrand Russell, the counterintuitive proofs of Turing, Church and Godel, and the mindboggling infinite sets of Cantor. The problem is, just where logic becomes interesting, it also becomes unattainable to the average Joe. "Metalogic" undertakes to introduces this field to those without the specialist training that is normally required, and it succeeds admirably.

2 of 2 people found the following review helpful:

5.0 out of 5 stars My foundation book for mathematical logic, October 1, 2009

By 

Gary R. Lomp, Ph.D. "SignalDoc" (Long Island, New York) - See all my reviews

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This review is from: Metalogic: An Introduction to the Metatheory of Standard First Order Logic (Paperback)

I have a dozen books on Foundations, some specifically on Logic, some Logic with Set Theory (e.g., Tourlakis), some pure Set Theory. This one is one of my favorites. I am an accomplished mathematics reader, and more than occasional doer, even though not a mathematician per se (Electrical Engineering is my field). My experience with the subject of this book has not been that of the professional philosopher or logician, but I have endeavored to read and absorb the material in all of my sources. This book is easily the one that opens the door most cordially, assuming little (which I appreciate since I am not getting a professor's help with subtleties nor that priceless mnemonic support that comes from classroom gestalts induced by a great expositor). The read somehow seems more perspicuous than the others, allowing the reader to feel more confident. The fact that Hunter takes the reader from first principles through decidability without holes or hand-waving is remarkable, and one suffers a minimal amount of that nagging feeling that something wasn't fully understood. (Of course, that feeling is normal when breaking in new ideas, but it's nice when you can go pages between bouts.) I recommend the book highly. When I thought I had lost it (I have almost 1000 books) I was ready to buy a replacement. As in all studies, the reader does well to use multiple sources, so he need not make this the "one and only". But I'd surely start with it.