Many philosophy departments, and many maths departments too, teach little or no serious logic, despite the centrality of the subject. It seems then that many beginning graduate students in philosophy and maths will need to teach themselves from books, either solo or by organising study groups. But what to read? Students need a Guide, i.e. an annotated reading list for self-study, giving some advice about the available books. So here is my (on-going) attempt to provide one:

**Teach Yourself Logic: A Study Guide**(Version 11.0, 29 July 2014)

This Guide currently has two supplements

**Book Notes**(comments on a number — 17, at the moment — of the more general, multi-area, textbooks on mathematical logic: last updated 29 July 2014)**Serious Set Theory**(more advanced readings on set theory, going beyond the recommendations in the core Guide: new page 28 July 2014)

NB The Guide is a PDF document (78pp.) designed for reading on screen. Ideally, read it either (i) on an iPad (download in Safari, open e.g. in iBooks), or (ii) on a laptop (e.g. read two pages side-by-side using Adobe Reader in full-screen mode). If you do really want to print out the Guide in dead-tree form, then again the side-by-side format should work well.

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.

Wow. This guide is unusually thorough. But no love for lambda calculi/ combinatory logic? Too computer sciency?

I’ve pencilled in adding a section on lambda calculi, but I don’t seem to have got round to it. Not enough love, obviously!

Apparently Smullyan has a new book called Introduction to Mathematical Logic coming out in a few months. I’ll be interested to see what that covers. I’m hoping it’ll be more than just another puzzle book.

Just something to mention for future revisions!

Smullyan has a logic text out: Logical Labyrinths. It’s his First-order Logic book rewritten to intersperse puzzle, problems , more prose and typos. Also just out is The Gödelian puzzle book.

Heavens! Has Smullyan discovered the secret, if not of eternal youth, then at least eternal authorship ….? I guess I should indeed look at these three books though!

He did. I one of his books he states the recipe: if you can prove that for any day

nyou will be alive for next dayn + 1, you will live forever. So probably he just found the proof.Smullyan’s

A Beginner’s Guide to Mathematical Logicis now out in the US but not yet the UK. It’s an original publication from Dover. 288 pages.Contents:

Part I General Background

1. Genesis

2. Infinite Sets

3. Some problems arise!

4. Further Background

Part II Propositional Logic

5. Beginning Propositional Logic

6. Propositional Tableaux

7. Axiomatic Propositional Logic

Part III First-Order logic

8. Beginning First-Order Logic

9. First-Order Logic: Main Topics

Part IV The Incompleteness Phenomenon

10. Incompleteness in a General Setting

11. Elementary Arithmetic

12. Formal Systems

13. Peano Arithmetic

14. Further Topics

What are your thoughts on Quine’s “Set Theory and Its Logic” book? Is that a good treatment of basic set theory? How advanced would you say it is? Thanks much

Jason

The set theorists I know tend to be a bit harsh about Quine’s book (I’m not sure how fairly, but I’m no set theorist). I still think it is worth looking at for the different perspectives it provides, though I wouldn’t recommend starting there. As for difficulty, it is about on a par with e.g. Enderton’s set theory book, I’d have thought.

Thanks so much for this guide, I’m finding it immensely useful. I’ve worked through IFL and am now looking to go further.

I have a question which I thought you might be in a position to answer. I have very little maths background (I stopped at GCSE at school!) but am really interested in the foundations of maths (logic and set theory) for philosophical reasons. Realistically, how far am I likely to get without knowing much maths? And if the answer is ‘not far’, then what maths should I try to learn in order to get further?

Perhaps my answer to a related question on math.stackexchange might help http://math.stackexchange.com/questions/556147/how-much-math-does-one-need-to-know-to-do-philosophy-of-math/556170#556170

I really appreciate your guide; I have it bookmarked and return to it regularly. I asked you about Sider’s book a while back so I appreciate your comments on that!

Maybe you feel that this falls outside the intended scope of the guide, but I think it would be nice with a little section on the philosophy of logic. I found A. C. Grayling’s “An Introduction to Philosophical Logic” to be quite lucid and immensely informative, and for philosophers I think books like that can be helpful. Both for fleshing out the understanding of how the formal stuff relates to philosophical topics and for shedding some light on issues in logic itself in ways not usually covered by logic textbooks.