As a follow-up to my previous post, I took it upon myself to survey graduate program logic requirements. Of the top 50 US PhD programs (according to the Gourmet Report), every one has a logic requirement of some form or another. 15 require only an introductory course in formal logic (propositional and predicate logic, formalization, and proofs). I was surprised that Harvard and MIT are among them. The others require at least some metatheory: 17 programs want their students to do completeness, Löwenheim-Skolem and compactness proofs. At some schools (Rutgers, Pitt, Texas, Wisconsin, Washington), the advanced logic requirement is satisfied by a one-semester course covering completeness, undecidability and incompleteness. (I suppose it’s possible to do that, but I have a hard time getting all that covered in an entire year.) Only at Arizona you can get away without taking logic.
Very few programs seem to make their students learn logic that’s specifically interesting for philosophy. At CUNY, Rohit Parikh teaches the Logic Core course that covers propositional and predicate logic, Kripke semantics, Lewis’s and Stalnaker’s theory of conditionals, and incompleteness. That is the only program, as far as I can tell, that requires a specifically philosophical logic course. Several others have a requirement that stipulates that students take “an approved logic course,” and I assume a course in modal logic or formal semantics would count there (Irvine, Davis, UMass, Syracuse, UConn, UVa, and Miami).
At the undergraduate level, logic requirements are also still common in the US. Only Arizona, Cornell, Duke, Johns Hopkins, UConn, and USC don’t seem to have a required logic course in their BA programs. Almost all the top 30 require formal logic; however, almost none of the programs between 30 and 50 require more than informal logic.
Of the five ranked Canadian programs, Toronto and Western require formal logic; McGill requires a course in metalogic; UBC doesn’t have a logic requirement; and I couldn’t tell from their website if Alberta does or not. Outside North America, I had a hard time figuring out program requirements. It seems that UK and Australasian departments don’t have formal breadth/depth/etc. requirements. I found reference to a logic requirement only on LSE’s website.
So: The consensus still seems to be that it’s important to a philosophy graduate education to learn logical metatheory (at least model theory). That’s good, I think. It gives students an appreciation for what logic is about. I don’t know what to think of the one-semester course on everything (completeness, incompleteness, undecidability, etc.). That seems to me to be way too much to cover in one term; at least, too much to cover well and in depth in one term. But maybe someone can tell me how to do it? Is that a more useful course to have than just a basic metalogic course? And is it better to have a course like that, or like Parikh’s?
UPDATE: I started putting up the results of that survey here.