on 2 July 2011
I've been looking for something like this for ages. I'm a PhD student who works with logic a lot (my thesis is formal semantics/philosophy of language etc) but I'm not a logician and I'm certainly not a mathematician. There are lots of introductory logic texts out there which cater to non-mathematicians (I like Paul Tomassi's) but I've always lamented the fact that doing any further logic meant reading books written for people with a maths background. This book is written with people like me in mind. It's not patronizing; it's sometimes slow going, but where it is hard work, it's hard because the material is tough, not because you have to learn to "speak maths" before you can read it.
It covers metalogic including soundness and completeness proofs; It'll teach you the basics of model theory and set theory; and it's great for semantics of predicate logic. It also includes a detailed section on modal logics. Then it covers non-classical logics (including Graham Priest's paraconsistent system).
If I had to come up with a criticism, it would be that the set theory section could be more detailed. It doesn't go into any axiom systems, for example. It does give you a nice version of Cantor's diagonalization proof though. Still, this isn't a set theory text; it just gives you what you need to handle the set theoretic notation that comes up through the rest of the book and on that score, it is excellent. Halmos's "Naive Set Theory" is already really accessible so if you're looking for more on set theory go there (although that doesn't cover axiom systems either, as the name suggests).
In short, this book is an accessible way to teach yourself all the logic you need for post-grad work in metaphysics or any area of philosophy where you need some technical knowledge without needing to be an all-out logician. It has exercises and answers and walks you through the construction of the various proofs in clear and concise English. Thank you Theodore Sider!