Peter Smith, retired professor of Philosophy at Cambridge. He wrote the following on his blog, Logic Matters.
It is an odd phenomenon. Serious logic is taught less and less, at least in UK philosophy departments. Yet the amount of formally-informed work in philosophy is ever greater. It seems then that many beginning graduate students (if they are not to cut themselves off from working in some of the most exciting areas) will need to teach themselves, solo and by organising reading groups. But what to read?
Here then is the first of a planned series of posts covering different areas of logic of interest to philosophers. This instalment covers the basics, up to a good grasp of classical first-order logic. I’ll assume that you’ve already done a smidgin of logic of some kind (utter beginners innocent of all logic and worried by symbols might find Guttenplan’s book a useful preliminary).
Two general points I’ve made before. (a) Mathematics (and that’s what we are talking about here, to be honest!) is not a spectator sport: you should try some of the exercises in the books as you read along to check and reinforce comprehension. (b) It is much the best to proceed by reading a series of books which overlap in level, with the next one covering some of the same ground and then pushing on from the previous one, rather than to try to proceed by big leaps. Again this will help reinforce and deepen understanding as you re-encounter the same material from different angles.
- My Introduction to Formal Logic (2003, 2009) is intended for beginners (and has been the first year text in Cambridge): but it in fact already goes further than seems to be covered in whole undergraduate courses in some good UK universities. It was written as a teach-yourself book. It covers proposition and predicate logic ‘by trees’. It even has a completeness proof for predicate logic, though for a beginning book that’s very much an optional extra!
- Paul Teller’s A Modern Formal Logic Primer (1989) predates my book, is now out of print, but is freely available online. It is excellent, and had I known about it at the time (or listened to Paul’s good advice when I got to know him), I’m not sure that I’d have written my own book. Unlike my book, as well as introducing trees this also covers a (user-friendly) version of natural deduction. It is notably user-friendly.
- David Bostock’s Intermediate Logic (1997) goes only slightly further than either Paul’s book or my own, and is rather discursive, but it is very well done (and touches on some issues such as free logic which are not dealt with in our book).
- A notch up in sophistication of approach we find the excellent Ian Chiswell and Wilfrid Hodges,Mathematical Logic (2007). This is now getting a little more ‘mathematical’ in flavour, but should be manageable at this stage. It deals nicely with natural deduction.
- Neil Tennant’s Natural Logic (1978, 1990) is also now out of print, but freely available from the author’s website. I still like this a lot as a text on natural deduction (Tennant thinks that this approach to logic is philosophically significant, and it shows); but it isn’t always an easy read which is why I list it at this point rather than earlier.
- You should now be able to cope, by way of wonderful revision summary, with Wilfrid Hodges’s ‘Elementary Predicate Logic’, in Handbook of Philosophical Logic, Vol. 1, (ed. by D. Gabbay and F. Guenthner: Reidel, 1984-89). An expanded version of this appears in the 2nd edition of the Handbook.
- Chiswell and Hodges’s book, they say, started life as teaching notes for a course based on the classic book by Dirk van Dalen, Logic and Structure (4th ed, 2004 — at this stage you can omit the last chapter). If you can cope with this book, you are doing just fine!
- Finally, for desert, look at Raymond Smullyan, First-Order Logic (first published 1968) which is an utter classic: you should certainly now be able to read Parts I and II.