It hasn’t been mentioned yet in the Teach Yourself Logic Guide, so I’ve predictably been asked a fair number of times: what do I think about Ted Sider’s Logic for Philosophy (OUP 2010)? Isn’t it a rather obvious candidate for being recommended in the Guide?
Well, I did see some online draft chapters of the book a while back and wasn’t enthused. But, yes, I am more than overdue to take a look at the published version. So here goes …
The book divides almost exactly into two halves. The first half (some 132 pages), after an initial chapter ‘What is logic?’, reviews classical propositional and predicate logic and some variants. The second half (just a couple of pages longer) is all about modal logics. I’ll look at the first half of the book for this post, and leave the second half (which looks a lot more promising) to be dealt with a follow-up.
OK. I have to say that the first half of Sider’s book really seems to me to be ill-judged (showing neither the serious philosophical engagement you might hope for, or much mathematical appreciation).
Here is one preliminary point. The intended audience for this book is advanced philosophy students, so presumably students who have read or will read their Frege and their Tractatus. So what, for example, will they make of being baldly told in §1.8, without defence or explanation, that relations are in fact objects (sets of ordered pairs), and that functions are objects too (more sets of ordered pairs)? There’s nothing here about intension and extension, and about why we should identify functions with their graphs. We are equally baldly told to think of binary functions as one-place functions on ordered pairs (and the function that maps two things to their ordered pair …?). Puzzled philosophers might well want to square what they have learnt from Frege and the Wittgenstein with modern logical practice as they first encountered it in their introductory logic courses: so you’d expect a second level book designed for such students to proceed more cautiously and address the obvious worries. But that doesn’t happen here.
And in fact we get a pretty skewed description of modern logic anyway, even from the very beginning, starting with the Ps and Qs. Sider seems stuck with thinking of the Ps and Qs as Mendelson does (the one book which he says in the introduction that he is drawing on for the treatment of propositional and predicate logic). But Mendelson’s Quinean approach is actually quite unusual among logicians, and certainly doesn’t represent the shared common view of ‘modern logic’. I won’t rehearse the case again now, as I’ve explained it at length here. But students need to know there isn’t a uniform single line to be taken here.
When Sider turns to looking at formal systems for propositional logic we get sequent proofs in what is pretty much the style of Lemmon’s book. Which as anyone who spent their youth teaching a Lemmon-based course knows, students do not find user friendly. Why do things this way? And how are we to construe such a system? One natural way of understanding what is going on is that the system is a formalized meta-theory about what follows from what in a formal object-language. But no: according to Sider sequent proofs aren’t metalogic proofs because they are proofs in a formal system. Really? (Has Sider not noticed that in Mendelson too, the formal proofs are all metalogical?)
OK, so the philosophical student is introduced to an unfriendly version of a sequent calculus for propositional logic, and then to an even more unfriendly Hilbertian axiomatic system. Good things to know about, but probably not when done like this. And not — in a book addressed to puzzled philosophers — without a lot more discussion of how this all hangs together with what the student is likely to already know about, natural deduction and/or a tableau system. And not without a better discussion, too, of the way the conception of logic changed between e.g. Principia and Gentzen, from being seen as regimenting a body of special truths to being seen as regimenting inferential practice. Further, the decisions about what to cover and what not to cover are pretty inexplicable. For example, why pages actually proving the deduction theorem for axiomatic propositional logic, and later just one paragraph on the compactness theorem for FOL, which students might really need to know about and understand some applications of?
Predicate logic is then dealt with by an axiomatic system (apparently because this approach will come in handy in the second half of the book — I’m beginning to suspect that the real raison d’être of the book is indeed the discussion of modal logic). I can’t think this is the best way to equip philosophers who have a perhaps shaky grip on formal ideas with a better understanding of first-order logic. The explanation of the semantics of a first-order language isn’t bad, but not especially good either. This certainly isn’t the go-to treatment for giving philosophers what they need.
True, a nice feature of this part of Sider’s book is that it does have a discussion of some non-classical propositional logics, and has a little about descriptions and free logic. But actually the philosophically serious issues of intuitionistic logic and second-order logic are dealt with far too quickly to be useful, so the breadth of Sider’s coverage goes with superficiality.
I could go on. But the headline summary about the first part of Sider’s book is that I found it (whether wearing my mathematician’s or philosopher’s hat) irritating and unsatisfactory. Sorry to be carping!
Comments from those who have used/taught/learnt from the book?