On Sider’s Logic for Philosophers — 1

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 but wasn’t enthused. Still, 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 briefly 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).

Let’s start with a couple of preliminary points.   (1) The intended audience for this book is advanced philosophy students, so presumably students who have read or will read their Frege. So just 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 why we should identify functions that have the same graph, let alone anything about  why we should actually 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 from the Tractatus —  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 would not just uncritically rehearse the standard identifications without comment (when, ironically, good logic texts often present them more cautiously).

(2) 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.

The kind of carelessness shown here isn’t very encouraging (and there’s more of the same). But what about when Sider turns to looking at formal details? He starts with a system for propositional logic of 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 as 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 his favourite text, Mendelson, the formal proofs are all metalogical?)

So the philosophy 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 not when done like this, and certainly not as the focus of a course for the non-mathematical. And it is odd — in a book addressed to puzzled philosophers — not to give significantly more discussion of how this all hangs together with what the student is likely to already know about, i.e. natural deduction and/or a tableau system. (And we might have expected, too, more discussion 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 technical details to cover in some depth and what to skim over are pretty inexplicable. For example, why are there pages tediously proving the mathematically unexciting deduction theorem for axiomatic propositional logic, yet later just one paragraph on the deep compactness theorem for FOL, which students might really need to know about and understand some applications of?

Predicate logic is dealt with by an axiomatic system only (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). Again, 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 how a deductive calculus for first-order logic might work. The explanation of the semantics of a first-order language isn’t bad, but not especially good either. So — by my lights — this certainly isn’t the go-to treatment for giving philosophers what they might need.

True, a potentially attractive additional feature of this part of Sider’s book is that it does contain discussions about e.g. some non-classical propositional logics, and about descriptions and free logic.  But e.g. the more philosophically serious (and mathematically interesting) issue of  second-order logic is dealt with far too quickly to be useful. And at this stage too, the treatment of intuitionistic logic is far too fast. So the breadth of Sider’s coverage here 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) irritatingly unsatisfactory. David Bostock’s Intermediate Logic similar coverage is much better.

Comments from those who have used/taught/learnt from Sider’s book?