Mathematical Logic (Dover Books on Mathematics)
by Mathematics, Stephen Cole Kleene
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Book Summary Information
Author: Mathematics, Stephen Cole KleeneEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 2002-12-18
ISBN: 0486425339
Number of pages: 416
Publisher: Dover Publications
Book Reviews of Mathematical Logic (Dover Books on Mathematics)
Book Review: Excellent Excellent Book
Summary: 5 Stars
This book was written by one of the great American mathematical minds of this century. I've read it cover to cover and it happens to be my favorite logic book for its scope, depth, and clarity. Kleene uses a combined model-theoretic and proof-theoretic approach, and derives many interesting results relating the two (he also gives mention to special axioms for Intuitionistic logic). Although his focus in the first part of the book is on a more or less mathematical treatment of standard first-order predicate logic (augmented later by functions and equality), he also spends considerable time discussing the ways in which formal logic can and should be used to analyze "ordinary language" statements and arguments. After setting the groundwork, he moves onto subjects such as set theory, formal axiomatic theories, turing machines and recursiveness, Godel's incompleteness theorem, Godel's completeness theorem, and just about every interesting subject relating to logic in the first half of the twentieth century.
For the mathematically inclined self-teacher, Kleene's exposition should not be difficult at all, in fact I found it remarkably clear compared to other mathematical treatments of the subject (which are necessary if one wants to understand the deeper results). I suppose less mathematically inclined readers could try Irving Copi's "Symbolic Logic" as a start, although even that requires some mathematical proficiency, and since it doesn't cover many of the things you will want to know about, you'll end up coming back to a book like Kleene's anyway. So to summarize, if you want to learn the hard stuff (from the first half of the twentieth century--which includes just about everything the layman/philosopher wants to know), there is no better or easier way.
Summary of Mathematical Logic (Dover Books on Mathematics)
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
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