Mathematical Logic

By addebook • Jul 14th, 2008 • Category: Mathematics

Mathematical Logic

Mathematical Logic
By Stephen Cole Kleene

Publisher: Dover Publications
Number Of Pages: 416
Publication Date: 2002-12-18
ISBN-10 / ASIN: 0486425339
ISBN-13 / EAN: 9780486425337
Binding: Paperback

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.

Summary: Excellent introduction
Rating: 5

I have to agree with the more recent reviewer and disagree with the first one. I don’t even have college-level maths; in fact, I failed abysmally in my school-leaving maths exams (I think I got an F). I wanted to read this because, now in my mid-30s, I had got very interested in various mathematical topics (game theory, number theory, logic) and was sick of just reading popular scientific books about them that assumed that you didn’t know how to read the symbols. I ordered this to get me started on logic.

Kleene does an excellent job of introducing a novice like me to the first principles; it’s true that he doesn’t hang about, and he has a way of bullying his readers into making the effort to understand by dropping sarcastic little remarks like ‘Anyone who cannot follow this is clearly mentally sluggish’, years of teaching logic in Madison, WI clearly finding payback right there. Some readers may find that kind of thing overbearing, but I found it bracing. I admit that I’m only on page 14, but already I can find the scope of a propositional connective, and when I woke up this morning I had never heard of such a thing.

I thoroughly recommend this book; a brisk, clear, ruthlessly no-nonsense introduction to the subject. Maybe it’s not ‘Mathematical Logic for Dummies’, but Kleene would probably crack that dummies shouldn’t be attempting the subject in the first place.

Summary: Not for the autodidact
Rating: 3

Ten years ago, I took an undergraduate course in symbolic logic. Wishing recently to refresh my (extremely rusty) memories of the propositional calculus and the first-order predicate calculus, I picked up this meaty text and was extremely dismayed to find myself soundly defeated within the first few pages. Kleene does not even make a pretense of holding the reader’s hand: either you get it or you don’t. There is nothing even remotely “user-friendly” about this book’s presentation of its material.

If one were to read this book under the guidance of a teacher, I think it might be worthwhile. It may not be fair for me to blame the author for my inability to understand his writing. If you’re smarter than I am, you might breeze right through it.

I cannot recommend this book, though, good though it may be, for anyone who wishes to teach him/herself logic, nor for anyone who wishes to brush up on the subject. There are exercises for the reader to test his/her understanding of the material, but no answer key is provided. This is heavy-duty stuff, and not well-suited to the self-teacher.

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