Teach yourself logic, #2: Modal logic
An expanded, improved, version of the first instalment of my planned Guide to teaching yourself logic is now here. So let’s move on to looking at books to read on modal logic.
The ordering of some of the instalments here is necessarily going to be a little bit arbitrary. But I’m putting this one next for two reasons. First, the basics of modal logic don’t involve anything mathematically more sophisticated than the elementary first-order logic covered in the first instalment. Second, and more much importantly, philosophers working in many areas surely ought to know a little modal logic, even if they can stop their logical education and manage without knowing too much about some of the fancier areas of logic we are going to be looking at later.
Again, the plan is to offer a list of books of increasing range and difficulty, choosing those which look most promising for do-it-yourself study. The place to start is clear, I think:
Rod Girle, Modal Logics and Philosophy (Acumen 2000, 2009). Girle’s logic courses in Auckland, his enthusiasm and abilities as a teacher, are justly famous. Part I of this book provides a particularly lucid introduction, which in 136 pages explains the basics, covering both trees and natural deduction for some propositional modal logics, and extending to the beginnings of quantified modal logic.
Also pretty introductory, though perhaps rather brisker than Girle at the outset, is
Graham Priest, An Introduction to Non-Classical Logic (CUP, much expanded 2nd edition 2008): read Chs 2–4, 14–18. This book — which is a terrific achievement and enviably clear and well-organized — systematically explores logics of a wide variety of kinds, always using trees in a way that can be very illuminating.
If you start with Priest’s book, then at some point you will need to supplement it by looking at a treatment of natural deduction proof systems for modal logics. A possible way in would be via the opening chapters of
James Garson, Modal Logic for Philosophers (CUP, 2006). This again is intended as a gentle introductory book: it deals with both ND and semantic tableaux (trees). But — on an admittedly rather more superficial acquaintance — this doesn’t strike me as being as approachable or as successful.
We now go a step up in sophistication:
Melvin Fitting and Richard L. Mendelsohn, First-Order Modal Logic (Kluwer 1998): also starts from scratch. But — while it should be accessible to anyone who can manage e.g. the Hodges overview article on first-order logics that I mentioned before — this goes quite a bit more snappily, with mathematical elegance. But it still also includes a good amount of philosophically interesting material. Recommended.
Getting as far as Fitting and Mendelsohn will give most philosophers a good enough grounding. Where, if anywhere, you go next in modal logic, broadly construed, would depend on your own further concerns (e.g. you might want to investigate provability logics, or temporal logics). But if you want to learn more about mainstream modal logic, here are some suggestions (skipping past older texts like the estimable Hughes and Cresswell, which now rather too much show their age). Though note, further technical developments do tend to take you rather quickly away from what is likely to be philosophically interesting territory.
Sally Popkorn, First Steps in Modal Logic (CUP, 1994). The author is, at least in this possible world, identical with the mathematician Harold Simmons. This book, entirely on propositional modal logics, is written for computer scientists. The Introduction rather boldly says ‘There are few books on this subject and even fewer books worth looking at. None of these give an acceptable mathematically correct account of the subject. This book is a first attempt to fill that gap.’ This perhaps oversells the case: but the result is still illuminating and readable — though its concerns are not especially those of philosophers.
Going further is Patrick Blackburn, Maarten de Ricke and Yde Venema, Modal Logic (CUP, 2001). One of the Cambridge Tracts in Theoretical Computer Science. But don’t let that put you off. This text on propositional modal logics is (relatively) accessibly and agreeably written, with a lot of signposting to the reader of possible routes through the book, and interesting historical notes. I think it works pretty well. However, again this isn’t directed to philosophers.
Alexander Chagrov and Michael Zakharyaschev’s Modal Logic (OUP, 1997) is a volume in the Oxford Logic Guides series and also concentrates on propositional modal logics. This one is probably for real enthusiasts: it tackles things in an unusual order, starting with a discussion of intuitionistic logic, and is pretty demanding of the reader. Still, a philosopher who already knows just a little about intuitionism might well find the opening chapters illuminating.
Nino B. Cocchiarella and Max A. Freund, Modal Logic: An Introduction to its Syntax and Semantics (OUP, 2008). The blurb announces that ‘a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight’. That sounds hopeful, and the authors are right about the unusually wide range. As noted, the previous three books only deal with propositional logics, while many of the more challenging philosophical issues about modality tangle with quantified modal logic. So the promised coverage makes the book potentially of particular interest to philosophers. However, when I looked at this book with an eye to using it for a graduate seminar, I didn’t find it appealing: I suspect that many readers will indeed find the treatments in this book uncomfortably terse and rather relentlessly hard going.
Finally, in the pretty unlikely event that you want to follow up even more, there’s the giant Handbook of Modal Logic, ed van Bentham et al., (Elsevier, 2005). You can get an idea of what’s in the volume by looking at the opening pages of entries available online here.
