Customer Reviews

Logic for Mathematicians

5 star:		(0)
4 star:		(1)
3 star:		(2)
2 star:		(0)
1 star:		(0)

 

 

I bought this book as a self-study guide for mathemetical logic. It contains a thorough treatment of propositional and predicate calculus, and briefly covers related subjects such as set theory and Goedel's incompleteness theorem. Overall it is fairly good, presenting the topic in a clear concise manner. The low (for a math textbook at least) price and the fact that it contains answers to selected exercises make this a decent choice for a self-study guide. The only problem I had was the fact that this book contains many typographical errors (I have the 1988 revised edition), which can be somewhat confusing in the the early sections of the book and extremely confusing in later chapters, which are difficult enough.

"Logic for Mathematicians" starts well, giving clear and formal explanations of formal logical systems and the predicate calculus. There are plenty of examples in the book, many of which clarified difficult or poorly worded definitions. I have been using this book recently to help me understand concepts that are much more tersely introduced in Elliott Mendelson's "Introduction to Mathematical Logic". This latter book may be better for it's later proofs (e.g., Godel's incompleteness theorem), but the early explanations of how the formal systems work is more easily understood from "Logic for Mathematicians". I gave it only four stars, though, because it becomes a bit less readable later on.

The proof of Godel's theorem is incomplete; instead, the author uses convincing examples to demonstrate the generality of recursive functions and from there shows Godel's results.

This is a fairly useful work for beginners in mathematical logic. However, one gets the idea that Hamilton himself is a bit muddled, as that's how it comes across in places. I wonder whether there is a text on mathematical logic that isn't a bit muddled now I come to think of it.