Most philosophy departments, and many maths departments too, teach little or no serious logic, despite the centrality of the subject. Many students will therefore need to teach themselves, either solo or by organizing study groups.

But what to read? Students need annotated reading lists for self-study, giving advice about the available texts. The *Teach Yourself Logic *Study Guide, linked below,* *aims to provide the needed advice by suggesting some stand-out books on various areas of mathematical logic. NB: *mathematical* logic — so we are working a step up from the kind of ‘baby logic’ that philosophers may encounter in their first year courses. You can also find here some supplements and further *Book Notes* of various kinds.

The main Guide and its Appendix are in PDF form, designed for on-screen reading. Learning mathematical logic involves a serious time commitment, and different people have different backgrounds/requirements, so you’ll want detailed advice from which you can work out which books might work for you. That’s why the full Guide *is* rather long. But it is (I hope) approachable written and informative. Try it out here:

**Teach Yourself Logic 2105: A Study Guide**(PDF, iv + 94 pp.) Last updated 1 Jan 2015.**Appendix: Some Big Books on Mathematical Logic**(PDF, 39pp.) Comments on a number of the more general, multi-area, textbooks on mathematical logic. Last updated 2 August 2014.

If the Guide’s length makes it sound daunting, there are also some supplementary webpages which might help ease your way in:

**About the Guide**Is the Guide for you? A short excerpt on the general aim of the Guide and what it covers.**The Very Short Teach Yourself Logic Guide**A summary of the headline recommendations on the core mathematical logic curriculum.

And here are some additional webpages:

**Serious Set Theory**The final section of the Guide in stand-alone form.**Category Theory**A supplementary page linking to a reading list, my work-in-progress Notes on Category Theory, and other on-line resources**Book Notes**Links to separate webpages on the books covered in the Appendix and also to various other books on logic and the philosophy of mathematics. Latest new page added 28 Sept. 2104.

It goes without saying, of course, that all constructive comments and suggestions continue to be most warmly welcomed. Many thanks, in particular, to those who have earlier sent comments which are now deleted because I’ve taken up (or plan to take up) the suggestions in newer versions of the Guide.

I would like to know what you think of Katalin Bimbó’s new book “Proof Theory: Sequent Calculi and Related Formalisms” (2014, Taylor and Francis). It’s a textbook aimed at advanced undergraduates focusing ‘on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic.’

Do you think it would be suitable for learning more about sequent calculi in general, and proof theory in specific?

Thanks for alerting me to this book, which I didn’t know of before. I can’t give you a view, then, though preview pages look pretty encouraging.

I’ve noticed a new category theory book that takes a different sort of approach:

Category Theory for the Sciencesby David I. Spivak (MIT Press). It’s not quite out in the UK but is available from US Amazon. It focuses on ideas and examples, rather than proofs for theorems, and it looks like it aims to show how category theory can be useful outside mathematics.There is a version online at the author’s website, here: http://math.mit.edu/~dspivak/teaching/sp13/CT4S–static.pdf

I’ll take a look, and thanks for the info!

I’d be interested in hearing what you think of Johan van Benthem’s “Modal logic for open minds”. I just got it in the mail today and I like what I see on a quick flip-trough. Of the other books I’ve used (Hughes & Cresswell, Sider, Girle…) this seems by far most similar to Girle’s book—not just in content but also in being written in a readable and engaging style. However, it’s more than 100 pages bigger than Girle’s, and I believe a bit wider in scope.

There was a brief comment in version 10 of the Teach Yourself Logic Guide. It said:

Some would say that Johan van Benthem’s Modal Logic for Open Minds (CSLI 2010) belongs much earlier in this Guide. But, though developed from a course intended to give ‘a modern introduction to modal logic’, it is not really routine enough in coverage and approach to serve at an elementary level. It takes up some themes relevant to computer science: worth having a look at to get an idea of how modal logic fares in the wider world.

I would like to know what you think of Paul Tomassi’s ‘Logic’? One difficulty I found with this book, is that there are no solutions therein, and the webpage for access to the solutions has, since Paul Tomassi’s passing, taken them offline.

Tomato’s book is OK — but I’d say counts as baby logic, which isn’t really the topic of the Guide, and there are better books at that level.

Yeah, after I reread the introduction to your book, I realized that you might not include it for that reason. Thanks for the great resource, I am especcially pleased that you introduced the books that deal,with mathematical topics that might be missing from an introductory Logic course like More Precisley by Steinhart, very useful.

As the guide is made towards people studying logics for the purposes of both mathematics and philosophy, why not suggest Susan Haack’s Philosophy of Logics? I am a mathematics student with interest in logics and lately bought this book. It’s an amazing read, and it talks a lot about why we need logic and how to build a logic.

Well, I’m remember Haack’s old book as indeed being good of its kind, and I’m glad that you found it helpful. I’ll have to take another look at it and consider whether this (and some similar books) might be mentioned in what is, basically, a guide to mathematical logic.

Pingback: Reading list | Axiomatized Intuition

I used J L Bell & M Machover’s ‘A Course in Mathematical Logic” (1977) when it first appeared as a friendlier alternative to Schoenfield. At the time this was in conjunction with Bell & Slomson’s “Models and Ultraproducts”. Bell & Machover’s book is still in print and not particularly expensive.