Teach Yourself Logic: A Study Guide, and other book notes

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:

This Guide currently has two supplements

  • Appendix: Some Big Books on Mathematical Logic (comments on a number — 17, at the moment — of the more general, multi-area, textbooks on mathematical logic: last updated 2 August 2014)
  • Serious Set Theory (more advanced readings on set theory, going beyond the recommendations in the core Guide: new page 28 July 2014)

And for those who don’t want to wade through the Guide and its Appendix, overlapping with their content but with links to other reviews of books, etc., there is also an additional webpage

  • Book Notes (on logic texts but also some philosophy of mathematics books: last update of content 2 August 2104)

NB The Guide and its Appendix are PDF documents designed for reading on screen. Ideally, read them 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 either 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.

12 Responses to Teach Yourself Logic: A Study Guide, and other book notes

  1. Appy says:

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

  2. Appy says:

    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!

    • David Auerbach says:

      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.

      • Peter Smith says:

        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!

        • Trismegistos says:

          He did. I one of his books he states the recipe: if you can prove that for any day n you will be alive for next day n + 1, you will live forever. So probably he just found the proof.

    • Rowsety Moid says:

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


      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

  3. Jason says:

    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


    • Peter Smith says:

      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.

  4. Alic says:

    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?

  5. Mige says:

    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.

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