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:

Version 10.1 (20 April 2014)Teach Yourself Logic: A Study Guide,

The Guide is still a PDF, but it is now 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 using the two pages side-by-side format with Adobe Reader works well. (Printing from other readers, you may need to change the page set-up of the printer to recognise the reduced paper size, approximately A5.)

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 the suggestions in newer versions of the Guide.

I wonder how it is possible that a book like Ebbinghaus et al, which is very accessible and quite comprehensive in the (5th edition of the) German original, consistently gets so devastating reviews, for the (2nd edition) of the English translation. You write

> Ch. 11 is by some way the longest in the book, on ‘Free Models and Logic Programming’. This is material we haven’t covered in this Guide. But again it doesn’t strike me as a particular attractive introduction (we will perhaps mention some better alternatives in a future section to be added to Chapter 3).

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> *Summary verdict* The core material in Part A of the book is covered better (more accessibly, more elegantly) elsewhere.

Even so chapter 11 is really the hardest chapter of the entire book, dismissing it as inaccessible and inelegant without giving a better alternative indicates that the book must strike some really negative chords for philosophically oriented English readers. Or perhaps it is running completely against the flow of thought of the reviewers???

I wonder a bit what would happen if the books “Grenzen der Mathematik” and “Die Gödel’schen Unvollständigkeitssätze” of Prof. Dr. Dirk W. Hoffmann: () would prove so “good” and popular that they would be translated into English. Both books probably have strong and weak parts, but at least the book “Grenzen der Mathematik” is interesting and rewarding to read in the German original. (I haven’t read “Die Gödel’schen Unvollständigkeitssätze”, so I can’t say anything about it.) Would the books attract negative reviews criticizing the weaker parts of the book without mentioning the strong parts, because the text and the flow of thought just wouldn’t be quite right?

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

Hey. Thanks for sharing the guide.

I got a little bit confused around the baby logic section, say I buy your IFL book, will it be sufficient enough for me not to study Quine’s Elementary Logic book? I’m asking this because I’m buying a bunch of books and I can’t make up my minds about these two…

On a side note, just finished reading a book on Critical Thinking.

Regards,

Ahmad.

IFL is about three times the length of Quine’s little book, so (as you’d expect) goes quite a bit further in various ways. But his is a lovely classic, still worth reading too to reinforce some basic ideas, and give you a somewhat different perspective on some 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

Every time I have tried to download Teach Yourself Logic, my computer goes crazy. Does this location have malware?

Thanks for the alert, but I have not had previous report of problems (the file has been there three months), and running an initial scan on the LogicMatters site doesn’t reveal any problems either …. But I will double-check.

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.