I’ve had a copy of Smullyan’s Theory of Formal Systems (1961) for thirty years, but to be honest I don’t think I’ve ever read it properly before. And it does date from that time when many maths books were photo-printed from typewritten originals, and looked exceedingly uninviting. Moreoever, in some ways, this volume has been superseded by Smullyan’s Gödel’s Incompleteness Theorems (1992).

But still, as I’ve found with great enjoyment, the earlier book remains quite terrific stuff. It is just so very elegant and insightful in developing Post’s ideas on formal systems and in excavating one basic line of ideas underlying incompleteness proofs (I plan to write up some notes in due course). Impressive indeed — even more so when you remember the book is essentially Smullyan’s doctoral thesis. Still very worth reading after all this time.

(And how many philosophy books, as opposed to logic books, still stand up so well after fifty years?)

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 the elements 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.

OK, with that preamble off we go (and though I don’t for a moment expect nearly fifty sets of comments as with the post on fun reads in philosophy, do please add comments — either on what you’ve found works in teaching first-order logic, or on what you’ve found particularly helpful as a student yourself). All the in-print books should be in any decent university library: order them if they aren’t in yours!

1. 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!
2. 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.
3. 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).
4. 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.
5. 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.
6. 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.
7. 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!
8. 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.

One of them, the book I’d actually gone in to buy (not knowing about the birthday celebrations), was Katrin Tent and Martin Ziegler’s new contribution to the ASL ‘Lecture Notes in Logic’ series, A Course in Model Theory. To declare an interest, I’ve wondered more than once about writing a book on model theory useful for philosophers. Well, according to the blurb, ‘This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions.’ And according to the introduction, ‘This book aims to be an introduction to model theory which can be used without any background in logic. We start from scratch, introducing first-order logic, structures, languages etc. but move on fairly quickly to the fundamental results in model theory and stability theory.’

Well, for ‘fairly quickly’ read ‘very quickly’. In fact, I would have thought that a graduate student mathmo who really did have no background in logic would find this seriously tough going with stuff going by far too fast (what on earth would even a sophisticated such reader get out of the half a page on ultraproducts on p. 13?). And this quite certainly isn’t a book for graduate philosophers who want to learn some model theory.

It’s probably best, in fact, to think of it as something to read after having really mastered e.g. Wilfrid Hodges’s classic Shorter Model Theory, by way of consolidation and then extension. Taken in that spirit, it does indeed look useful for serious mathematicians (though I’m not going to have time to work through it further at the moment).  But this is probably not a book for beginners in model theory (and surely not one for graduate philosophers, even those of a logical bent).

For once, I have been away for the better part of two weeks without a laptop, and haven’t read a word of philosophy or logic, or indeed thought about it much. So it has been novels for me (some ‘serious’, some not so — I’ve become a much entertained fan of the Falco books). I’ve also been a very latecomer to Edmund de Waal’s The Hare with Amber Eyes, which — like so very many others — I thought quite wonderful (perhaps at some level, de Waal’s story of generations of his family living through fractured times speaks to our own deep anxieties about what is to come in our troubling times). Read it.

And that in turn put me in the mood to re-read an old favorite, Nabokov’s Speak Memory (by my lights, his best book). Then, having been talking about Tony Judt’s The Memory Chalet, I found myself re-visiting that as well. Ah, the joys of traveling with an iPad with books already aboard, and a huge library available at the touch of a button …

It’s Kurt Gödel’s birthday today: back to thinking about him tomorrow.

This has been slow work. Do you remember that exchange from the Hitchhiker’s Guide to the Galaxy?

“If you’re a researcher on this book thing and you were on Earth, you must have been gathering material on it.”

“Well, I was able to extend the original entry a bit, yes.”

“Let me see what it says in this edition, then. I’ve got to see it. … What? Harmless! Is that all it’s got to say? Harmless! One word! … Well, for God’s sake I hope you managed to recitify that a bit.”

“Oh yes, well I managed to transmit a new entry off to the editor. He had to trim it a bit, but it’s still an improvement.”

“And what does it say now?” asked Arthur.

“Mostly harmless,” admitted Ford with a slightly embarrassed cough.

That’s rather how it has been at times, working on the second edition! Three days work digging around the literature. Mmm, what I said perhaps wasn’t absolutely accurate now I come to think about it again. But the exceptions are too exotic to worry about. What to do? Instead of saying P, say mostly P. And so it goes.

Anyway, rather belatedly, here is the current draft so far. Enjoy! And as always, comments and corrections are most welcome. The previously posted version was downloaded over 450 times, and although it would be too much of a good thing if everyone commented, far fewer do than you might guess. So please don’t hesitate to add your two pennyworth, even if you have simply spotted a silly typo. (A table of contents and the biblio can be found here.)

I’ve been looking along my shelves for inspiration: but since I’ve recently given away a lot of my books, keeping what’s now a mostly rather austere logical collection, that’s not a great deal of help. Here, however, are a few things that come to mind:

1. Simon Blackburn, Truth: A Guide (OUP, 2005) [Blackburn always writes enviably well, and can be very funny (try his Lust): this is serious, wide-ranging, philosophy done very readably.]
2. Daniel Dennett, Elbow Room (OUP, 1984) [Dennett is always worth reading: what to choose? This is short, full of ideas, and perhaps these days less well-known than it should be.]
3. Paul Feyerabend, Against Method (NLB, 1975). [Still a provocation.]
4. Imre Lakatos, Proofs and Refutations (CUP, 1976). [Maybe it's not clear where this leads, but the journey is fun! Maybe more philosophy could be written as this kind of dialogue.]
5. David Lewis, On the Plurality of Worlds (Blackwell, 1986) [David Lewis writes so well that almost anything of his will be worth reading: but experience shows that students can get particularly caught up in the madness of this book! Perhaps I'm cheating by having this on the list, though, as -- like Naming and Necessity -- it is already such a staple of reading lists. But don't miss out if you haven't read it.]
6. Hilary Putnam, Mind, Language and Reality (CUP, 1975). [Another oldie. Does it count as fun? Well, I certainly remember the excitement of reading the papers in the first two volumes of Putnam's Philosophical Papers when they came out: this is the second of those volumes. There is much here that is still very worth reading for its own sake, and which will illuminate later debates too. Dip into it!]
7. R. M. Sainsbury, Paradoxes (CUP, 3rd edn 2009) [OK, this is more like a conventional student text than others on the list -- but these are fun topics, well handled.]
8. Alan Sokal and Jean Bricmont, Intellectual Impostures (Profile Books, 1998) [Sokal famously wrote a parody of post-modernist abuse of scientic terminology, a farrago of nonsense which was accepted and published in a pomo journal. His book with Bricmont explores the misuse of science, and contains some sane philosophy along with way.]

And now what? Surely some Fodor: but which? Add Quine’s Quiddities perhaps? I gulped down Eric Olson’s The Human Animal when it came out and admire it a lot. In a quite different vein, Edward Craig’s The Mind of God and the Works of Man is wonderful.

But what would you put on your list? (Or if you are still a student, what off-piste reading have you found particularly enjoyable/illuminating?)

Added April 16 A link on Brian Leiter’s estimable blog has attracted readers outside the usual logicky people who follow Logic Matters, so there’s been a welcome little flurry of further suggestions — which shows, inter alia, how very varying people’s ideas of philosophical fun can be!

No women philosophers in my list above? Guilty as charged. The lack has been rectified in some of the later comments below! In a wider-ranging list I’d have certainly included Martha Nussbaum’s Fragility of Goodness and perhaps some others of hers. In the Great Retirement Book Dispersal, hers are indeed are among the few non logic/language/m&e books to survive.

1. On Matthias Baaz et al., eds, Kurt Gödel and the Foundations of Mathematics: Horizons of Truth (CUP, 2011), in Philosophia Mathematica
2. (With Luca Incurvati) on Penelope Maddy, Defending the Axioms (OUP, 2011) forthcoming in Mind.

The first is a terse summary of comments already posted here on the blog. The second will probably be of more interest.

So over the last couple of days, I have checked and repaired (I hope!) all the external and internal links, removed a few defunct links, and added a number of new ones. I have added a new page of links to other relevant LaTeX sites. The LaTeX for Logicians Guide to Sam Buss’s bussproofs.sty has also been updated.  And there have been some aesthetic improvements.

Now it’s over to you. Let me know (by posting comments) about any links which are still broken and do please suggest new ones. Please also spread the word, especially among your graduate students. And if you have a webpage which links to the LaTeX pages make sure your link still works. Note, by the way, the pages have their own permanent URL: www.latexforlogicians.net

In another bit of constructive procrastination, for I really should be getting on with IGT2, I’ve put a front page on the whole Logic Matters site (nicer icons to follow). This will make navigation easier for the many visitors who don’t come for the blog.