A Friendly Introduction to Mathematical Logic

by Christopher C. Leary, Lars Kristiansen

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Genres: Philosophy, Mathematics, Logic, Nonfiction, Science, 21st Century, Textbooks

380 pages, Paperback

First published December 8, 1999

Reviews

[Adam · Rating 3 out of 5]

I wouldn't call this downright friendly. It is more friendly than Mendelson's Mathematical Logic text, and it has the occasional, conversational tone to the reader, like somehow in a nonfiction book the author is managing to break a fourth wall. But the text still won't be accessible to the absolute mathematical novice, or even the reader with some mathematical background who goes into it not already having a concept of syntax and semantics and how these tend to get treated in Mathematical Logic.

Still I can't think of a text that tries to address these topics at this level, which is more friendly. So it's a good book.

[Arya · Rating 4 out of 5]

Great book for learning about Mathematical Logic, even if you have no background in symbolic logic! You just need an open mind, a lot of time, and maybe a friend that's willing to break things down for you. I only gave it four stars since it is still a little intimidating, but I would find it extremely hard to introduce all these topics in a simpler manner.

[Kevin Doran · Rating 1 out of 5]

I didn't get far into the book before putting it down. The review reflects my experience with the first 50 or so pages only. I can only image that there must be a better book.

For a book that is supposed to lay the foundations of mathematics, it is not very rigorous, and it is disorganized in its presentation. The foundations are poorly laid out. There are many ideas that are presented, like functions and sets and relations, that, while familiar to the reader, should not be used to set the foundation of the theory without some sort of formulation and specific definition. For example, without any specification of an axiom or justification, we are told to accept the existence of structures containing universes of objects and functions that map to each symbol of a language. While I can certainly accept the existence of such an object, I do not trust a presentation that doesn't justify or state such a claim as being assumed as an axiom. How much of set theory do we need to create a theory that is supposed to make claims about set theory? Maybe there is simple answer to this and I'm over reacting; but if there is such an answer, the author should have included it.

[Lucille Nguyen · Rating 3 out of 5]

Rather poorly organized and presented, some presentations of material were more intuitive than others, but overall other books on logic and mathematics are both more "friendly" (ironic, given the title) and comprehensive than this text.