I asked David Papineau (King's College, London) to share a bit about how he teaches logic at KCL, since I thought it might be of general interest:
Once philosophy students get beyond the foothills, they are likely to start coming across passing references to ideas like denumerability, Bayesian conditionalization, modal scope distinctions, logical completeness, and so on. Yet often there will be nothing in their education designed to explain these technical notions to them.
For the past few years I’ve been teaching a course at King’s College London that aims to remedy this. I’ve just published the course as a text with OUP, called Philosophical Devices. (The book’s four sections cover: sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis; analyticity, a prioricity and necessity; probability, including objective versus subjective probability, conditionalization and correlation; metalogic, starting with syntax and semantics, and finishing with a sketch of Godel’s theorem. All in under 50,000 words including exercises and solutions.)
No doubt the techies will think that a book like this can only be a bluffer’s guide. But I think that I explain everything properly, and moreover make it philosophically interesting. Of course I don’t provide the depth available from higher-level courses in mathematical logic and the like. But for those many aspirant philosophers who will never go near such courses, I at least offer a way of understanding what the experts are talking about.
My course at King’s uses half the twenty weeks the first-year students used to spend on elementary logic. I’ve long been unsure about the point of normal introductory logic courses. It is doubtful they do anything to improve argumentative skills, and they tend not to leave time for any philosophically significant metalogic. Of course, they are a necessary prerequisite for those who are going to go on in logic. But for the many who aren’t, it is not obvious what the philosophical payoff is.
Not that this need be a competition. Ideally I’d want the students to do some introductory logic alongside my introduction to technical ideas. That’s what our students at King’s now do. But if they did have to choose, I think that my course would do more for their philosophical education than an extended training in elementary logical exercises.