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.

At Wisconsin, there is one course, 511, that automatically satisfies the advanced logic requirement, but others can be substituted. For instance, modal logic would work. I think that one or two courses in the math department might even work too (e.g., set theory).When I took 511, Mike Byrd used a draft of the textbook he’s been writing, “Godel’s Theorems: History, Logic, Philosophy” (as it was called at the time). We spent almost the entire semester proving Godel’s first incompleteness theorem. We also did a little at the end on Tarski’s and Church’s theorems. So the course didn’t really cover ‘everything’.Ellery Eells also teaches 511, and I think he covers more topics, but I’m less familiar with how much time he spends on each topic.–Jeff Johnson

Peter Smith, Philosophy, University of Cambridge (ps218@cam.ac.uk)UK grad programs tend not to have any “required courses” — the course component of MA/MPhil programs is usually entirely pick-and-mix, and PhDs usually have no taught component at all. True, it is the case that a few UK undergraduate courses do cover the ground. E.g. here in Cambridge we have a third year Math Logic course that covers quite a bit, see http://www.phil.cam.ac.uk/u_grads/Tripos/Math_Logic/Course_Outline/II_P_7_03MathLogic.html But we are nowadays fairly exceptional in offering this kind of course.And even for us, this is very much an optional course: we don’t make those grads who arrive from elsewhere catch up. There is, and has been for some time, a substantial number of people eventually getting UK philosophy jobs whose knowledge of logic is pretty minimal (which can make it quite difficult to argue with colleagues for the preservation of serious logic courses at the core of the syllabus). So structurally, the situation is not good for logic. Though as I said in my comment on an earlier post, we are in one of those phases where as it happens a fair number of good grad students are interested in logical matters.

marc moffett, university of wyoming.The actual demand for advanced logic in PhD programs is, of course, rather greater than your survey suggests. At Boulder (where I was a grad student) it was sufficient for meeting the formal requirements that a student simply have a formal logic course. But it was clear that anyone working on the M&E side of the fence must, for all intents and purposes, take an advanced logic course and most of us took a number of them. In fact, the demand for advanced logic courses clearly outstripped the department’s ability to supply them (despite the best efforts of Leeds, Bealer and Oddie). The fact is that most students are well aware of the demands placed on them by the job market and tend to be guided more by those considerations than the formal requirements of the department. And I suspect that almost anyone working in M&E sees advanced logic as essential to research success and a great AOC on their CV.

This brings up a related issue – actually more of a question – in my mind. As you noted, it is no longer the case that pure logicians work in philosophy departments – logicians are usually, in addition to pure logic work, are also encouraged (forced?) to apply their logical approach to other areas, such as computer science, music, ethics, etc. But, I think it’s still pretty clear and undisputed that logicians “belong” or naturally fit into philosophy departments. People, usually non-philosophers, then ask “what is the connection between philosophy and computer science/music/etc.” – and the intermediate link seems to be logic. To a logician, it is obvious why logic, a seemingly “scientific and concerete” field, has philosophical aspects. To someone who is deeply involved in the fields that logicians/philosophers study, it is obvious that philosophical questions are there to be explored – e.g. a musician can appreciate a philosophy of music, much like a mathematician or scientist can appreciate of a philosophy of their field. But to an academic unrelated to both (and actually, I’ve heard this question asked by philosophers who disconnected from logic – and work in say, political philosophy or philosophy of law, or ancient philosophy) how can one clearly explain why philosophy works so well with the seemingly “scientific and concerete” fields like music/cs or even formal logic? I have never heard an explanation that does not seem to require a deep understanding of the field that’s being philosophized about. For example, to explain a basic point about the philosophical aspects of of computability theory (or more broadly, CS), one could work by explaining Turing machines, Church’s theorem, etc. — this is already technical.

Following up on the UK scene… In St Andrews the second year undergraduates have a course on Formal and Philosophical logic. Alongside a philosophy of logic component, they learn basic modal systems, conditional logics and intuitionistic logic. Mostly this is done through tableau, with bits and pieces of semantics (e.g. for the conditional logics especially). They don’t do classical metatheory until the third year. I thought this very impressive. I arrived knowing (comparatively) lots of classical metatheory, but not even knowing the names of the basic modal systems.

“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.)”As a grad student at one of the schools you mention here, and having taken the one semester course covering all this, I’ll tell you it was *very* difficult – on the professor, I think, as much as the students! Go for depth not breadth, it seems to me, on a one semester only course

Not sure Pitt’s Advanced Logic core course covers quite as much as you think. From this term’s course descriptions : “This course introduces students to some of the fundamental results of classical propositional and first-order logics: Deduction Theorems, Soundness and Completeness Theorems, and Compactness Theorems. If we have time, we shall take a brief look at Gödel’s Incompleteness Theorems. Recommended text: Introduction to Mathematical Logic (fourth edition) by Elliott Mendelson. Prerequisites. P1500 or equivalent; that is, familiarity with the notation and proof techniques of classical first-order logic. “That looks like a fairly typical second semester graduate-level course in metatheory. Note students without a first course in logic may have to take one to make up the prerequisite.

At Penn (now in the 30-50 group, I guess) there is no informal logic course- the one the majors must take is the same one as grad students must take. It’s taught ever year (at least) in a large lecture hall. It’s a great class, but quite hard- it was at the time the hardest logic class I’d taken, and I’d take several before. When Tom Ricketts taught it we used a draft of Warren Goldfarb’s new logic text- a very good text, I think. Scott Weinstein uses that as a sort of guide, but mostly doesn’t use a text, I believe. To my mind it might actually be useful to have a less rigorous logic class here, but that’s not the view of the professors!

The logic requirement at Irvine is quite somewhat rigourous than Richard indicated above, at least in the LPS track of the PhD program. We have a year-long, 3-quarter sequence covering (i) set theory (up to ordinal/cardinal arithmetic, induction etc. but no independence proofs), (ii) standard metatheory (completeness, compactness, up and down L-S, some second-order logic, etc), and (iii) computability and Goedel’s incompleteness theorems. I believe such a requirement is rare or even unique among Philosophy PhD programs. Posted by Aldo Antonelli

The LSE is also a notable exception. I am currently studying BSc Philosophy, Logic and Scientific Method there. As the title of the degree implies, logic is a major component of my studies. By the time I finish my undergraduate degree I will have completed courses in First-Order Predicate Logic, Set Theory, Mathematical Logic, and Philosophical Logic. Posted by Andrew Goldfinch