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 2016: A Study Guide**(PDF, iii + 89 pp.) Last updated 1 Jan 2016.**Appendix: Some Big Books on Mathematical Logic**(PDF, 40pp.) Comments on a number of the more general, multi-area, textbooks on mathematical logic. Last updated 14 December 2015.

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:

**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.

Tomassi’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.

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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.

Bell and Machover is indeed pretty good — it’s on my list of books to comment on one day!

First off, thank you for providing this great resource. Having a guide is great for allowing more time to admire the scenery, rather than focusing wholly on not falling over cliffs, so to speak. Second, what are your thoughts on “The development of Logic”, by W. & M. Kneale?

I think the Kneale’s book was a remarkable achievement in its time, and it does stand up remarkably well 50 years on. But obviously a lot more, some very good indeed, has been written on the history of logic since then!

Thank you for your work in laying out a path to follow for self-study.

I am a little sad there isn’t more in the way of free books as the price can be very much like a closed door to so many of us who do not have access to large universities, and getting worse these days with the crunch in fund to public libraries. All the same, it look like you have done a very good service to people – I hope to prove that in coming days!!

I very much appreciate the point about the expense of logic books (even libraries in not-so-rich universities have problems keeping up). I do mark in the Guide some particularly good-value books and even a few freely available resources: but I realise that isn’t enough for those who have no access to major libraries (though you might find that such public libraries which you do have access to have an interlibrary load system.

Obviously, I can’t link to the well-known PDF repositories which break copyright (even when the copied books are old ones and even out-of-print).

I do think there are various good reasons for maintaining traditional book publishing (though I’m open to persuasion on the point). But I do think that it should be default that academic publishers — especially those that are university presses — put a significant amount of their back catalogue into the public domain e.g. a decade after publication. By that point sales will usually be low, so neither press nor author will lose much, but the book can gain a new lease of life.

Thank you very much for your guide. I have found it very useful in preparing for graduate school. I was wondering what you thought about “Introduction to Mathematical Logic” by Alonzo Church.

Church’s book was, in its time, a wonderful achievement and an immensely influential classic. It is, however, ages since I have looked at it. I ought to do so again one day!

What do you think about Schaum’s Outline of Logic, Second Edition of Nolt, Rohatyn and Varzi. I think it is the best for ‘baby logic’.

I don’t know the book, so can’t comment, sorry!

Thank you for putting this together. I stopped the guide where it says its not for elementary logic. I don’t have any experience with logic. Are there any free resources you recommend to learn elementary logic?

Well, in the Guide I do recommend Paul Teller’s introductory book which is freely available online.

I found your Guide really helpful for up-skilling in logic, sufficient to TA a class in Intermediate Logic—thank you.

I’m wondering if you’re aware of anything comparable in other areas of mathematics, particularly probability and statistics?

Thanks for the nice words about the Guide. But no, I don’t know of anything comparable in the probability area — I’d be reduced to googling, like you!

I think that in the latest version of Appendix there are references to other sections which has been removed (see page 6,8, 33 and 36). Please take a look at them.