It is an odd phenomenon, and a rather depressing one too. Serious logic is seemingly taught less and less, at least in UK philosophy departments. Yet logic itself is, of course, no less exciting and rewarding than it ever was, and the amount of important formally-informed work in philosophy is if anything ever greater. And anyway, logic is far too important to be left entirely to the mercies of technicians from maths or computer science departments with different agendas.
It seems then that many beginning graduate students in philosophy will need to teach themselves from books, either solo or by organising study groups. But what to read? I have just counted almost three hundred formal logic books of one kind or another on my own shelves — and of course these form only a selection of what is out there. Philosophy students need a reader’s 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. I hope it will also be useful to some mathematics students (since coverage of logic can be patchy in undergraduate mathematics courses too).
Download Teach Yourself Logic: A Study Guide, Version 9.1 (1 June 2013)
It goes without saying, of course, that all constructive comments and suggestions will be most warmly welcomed.
Thanks for this terrific list! There are a number of broad-overview-type books that did not make the list (e.g. Schoenfield’s *Mathematical Logic*, Hinman’s *Fundamentals of Mathematical Logic*). I am curious about your thoughts on those books. Were they left off beccuase they don’t fit into any of the categories in your list, or for some other reason?
Thanks for this. I’ve wondered whether to explain absences as well as presences on the list, and perhaps I should indeed say more. (It’s nicer to be positive!)
Schoenfield’s Mathematical Logic is of course a classic. But is it an approachable, reasonably reader-friendly, classic? The book came out when I was a student, and it seemed pretty hard going then, and it is quite hard-core still. That’s why I haven’t listed it (perhaps I should add a footnote saying just this.)
Hinman’s book I bought when it came out, but then didn’t find it appealing enough to look through very carefully.
Hi, Peter. I noticed that there’s no mention of Hunter’s _Metalogic_. I am curious, was that intentional or an oversight? (I ask because I use Hunter’s book in my advanced logic class).
I look forward to the next installment!
All the best,
Brad
Hi Brad. I’ve had a few emails as well now which make me think I should explain at least some omissions. I haven’t done so in versions up to now, partly for length considerations (a dauntingly long Guide could be counterproductive), and partly to avoid introducing a frequent negative tone. But I’ll experiment in Version 6.1
As to Hunter’s book, I liked it a lot when it came out (my copy is dated 1971). I’m pretty sure I used it back then in teaching as it was one of the most approachable books around, and Part Four on incompleteness/undecidability was especially helpful. But the formal systems he uses are pretty evil axiomatic ones (which is a strike against it), and things can sometimes get unnecessarily(?) messy. The pre-LaTeX typography makes also everything look more rebarbative than it need do. So forty years on, I suppose I just think there are more inviting options.
Cheers, Peter
I’d noticed that there were some explanations of omission in the most recent basic set theory list (re two in the London Mathematical Society Student Texts series). I think it raises a question of why some books are listed that way but not others and might give a more negative impression of some books (worth mentioning but not recommended for the list’s purposes?) than you intend. They might be better than books you don’t even mention, but they have a negative comment while the unmentioned books don’t.
On the other hand, it’s undeniably useful to know why some books, especially ones that are often mentioned or recommended, aren’t being recommended this time; and I’ve always like the section in Sally Popkorn’s First Steps in Modal Logic that talked about other books, even though it was largely negative. It helped me understand what the options were, the reasons for SP’s approach, and something of the history of the subject. (It also inspired me to buy a copy of Logics of Time and Computation, but it was one of the books that was praised.)
Perhaps that suggests something, when it’s all put together: that it’s worth explaining some exclusions when there’s also something positive to say about them too and when the reasons for excluding them make some larger point about something like the evolution of the subject or what philosophy students would find most accessible or most need to know.
Thanks very much for this, which seems spot on to me. As you can no doubt tell, as I (very sporadically) add sections to the Guide and (re)edit earlier sections, my conception of what I’m up to here is slowly evolving.
So I’m definitely coming round to the view “it’s worth explaining some exclusions when there’s also something positive to say about them too and when the reasons for excluding them make some larger point about something like the evolution of the subject or what philosophy students would find most accessible or most need to know”. So watch out for Version 6.1, though don’t hold your breath!
If, somehow, you felt compelled to add “just one more” entry in the border areas of first-order logic, model theory, and computability, and wished to select a treatment based on an axiomatic system, would you choose any of: Mendelson’s Introduction to Mathematical Logic, Hamilton’s Logic for Mathematicians, Ebbinghaus-Flum-Thomas’s Mathematical Logic, or Robbin’s Mathematical Logic: A First Course (with its virtue of being a Dover reprint)? I imagine Schoenfield could follow here, save for your comments concerning its omission from the guide.
Wayne
I’ve said something about Mendelson in Version 7.0, and I’ll remind myself more about the others for Version 7.1. Heck, this is a time consuming business!
I appreciate that every one has their favorite logic texts (typically the ones they used in college for their first courses in Logic, Metamathematics and Set Theory). I have mine, which are outdated, too. But, please understand that Peter Smith is one man only and, as emeritus prof, he doesn’t have use of the support services he had when on faculty. This type of correspondence is or should be near the bottom of his priority ladder.
I’m sure he knows about all of the books we remind him to mention and he has his reasons for excluding them from the guide. Please just let this guide evolve. It’s interesting and quite helpful as it is, and it’s evolution is interesting (and helpful) in its own right. Try a Taoist approach: Let it be; you’ll get more out of him if you give him the time and space to do what he wants to do.
Well, Charles, I appreciate the sentiment! But I’m finding some of the reminders very helpful (for example I’ve just had my memory jogged about Ted Sider’s Logic for Philosophy), and I can always quietly ignore excess ones. So if people have suggestions/reminders I’m very happy to get them, even if I don’t promise to respond immediately!