A couple of days ago, Luke posted a recommendation for reforming how philosophy is taught. My department at the University of Illinois is in the midst of some potentially large-scale changes.* Hence, now seems to be a great time to think about concrete steps towards reforming or partially reforming the curriculum in an actual philosophy department. I would appreciate some help thinking through how to make changes that will (a) improve the philosophy education of our undergraduates, (b) recruit and retain better students, (c) improve faculty experiences with teaching philosophy, and (d) be salable to the rest of the philosophy faculty. To some extent, this post is me thinking out loud through what I want to say to my department's curriculum committee (probably in January).
How Things Stand Right Now
In this section, I will try to lay out the situation as I see it right now.
First, we have the following problem: philosophy courses that we offer are not sufficiently gated. In the mathematics department at my university, you can't take mathematical logic until you've taken a course called Fundamental Mathematics, which looks to be a class about proof techniques, mathematical induction, etc. And you can't take that until you've taken the second semester of calculus. Computer science, economics, physics, and most every other science curriculum works like this. If you want to take advanced courses, you have to pass through the gates of less advanced courses, which (theoretically, at least) prepare you for the material covered in the more advanced course.
By contrast, in the philosophy department, you may take a senior-level (400 at my school) course after taking a freshman-level (100 at my school) introduction to philosophy. The result is that students who take our 400-level courses are typically unprepared. At least, that has been my experience. (Shockingly, many students taking 400-level classes then complain that they were expected to know things about philosophy!) A big part of the problem here is that we do not presently have enough faculty to cover intermediate-level courses on a regular enough basis, and let's be honest, faculty members don't usually want to teach lower-level courses anyway.
Second, we have the following resource: our department currently has strong and growing connections with several world-class science or science-related departments. We have cross-appointed faculty and/or cross-listed courses with mathematics, linguistics, psychology, and physics, all of which are very strong departments. We have philosophy graduate students who do research and teach courses in these disciplines as well. And I am hoping to expand our connections to include computer science and statistics. I think there ought to be a good way to make use of these resources.
Rather than trying to reform the entire philosophy curriculum all at once, I want to focus first on our logic offerings. What we have now is the following mess.
- 102 -- Introduction to Logic: A critical thinking course almost never taught by a faculty member.
- 103 -- Quantitative Introduction to Logic: An introductory formal logic course taught by me about half the time
- 202 -- Symbolic Logic: A basic symbolic logic course (unclear in how it is different from 103 except in that it is completely restricted to deductive logic)
- 307 -- Elements of Semantics and Pragmatics: Cross-listed with linguistics
- 407 -- Logic and Linguistics: Cross-listed with linguistics
- 453 -- Formal Logic and Philosophy: An extension of 202 but with emphasis on philosophical issues
- 454 -- Advanced Symbolic Logic: Basically, a math logic course covering completeness, compactness, Lowenheim-Skolem, incompleteness, and undecidability
The only pre-requisite for 453 and 454 is 202, and 202 has no pre-requisites at all; the pre-req for 407 is 307, and 307 depends on a 100-level linguistics course or (more commonly) consent of the instructor. We also have a 400-level philosophy of mathematics course. Along with these, the mathematics department has a 400-level mathematical logic course and a 400-level course on set theory and topology, neither of which is currently cross-listed, but both of which, I think, should be cross-listed as philosophy courses, which would also raise the bar for the philosophy students interested in logic by requiring that they take the calculus sequence and the fundamentals course.
On the defects side, I think we have poor use of gating and spotty coverage of even deductive logic. For example, we have no courses on modal logics, we have no courses on intuitionist/constructivist logic, we have no courses on relevance logic, we have no courses on more exotic logics, we have no courses on set theory or category theory, and we have no courses on computation. We get sort of close to the last two in 453/454, and we might address them more directly by cross-listing with mathematics. But as it is, we do not do those things. And we have a huge gaping hole where inductive logic, probability theory, statistics, causal inference, and so on should be. On an individual level, that hole could be filled somewhat by taking courses in statistics; however, that is not quite the same as having courses available on confirmation theory or inductive logics.
So, now you know the basic situation ... what to do?
Below are some specific recommendations that I want to make to my department's curriculum committee. I would really appreciate input on how to refine my recommendations, how to make them more palatable, and so on.
First, we need to make the 100- and 200-level courses connect in a relevant way. I recommend entirely relabeling (and maybe even renumbering) 102 so that it is clear that it is a terminal, service course intended for non-majors. The course should stand to philosophy education as courses like Physics Made Easy stands to physics education. I further recommend making a relabeled (and maybe renumbered) version of 103 a pre-requisite for all 200-level logic courses. In terms of material covered, ideally 103 would introduce symbolic conventions (to be made as standard as possible across the curriculum), proof skills, and basic ideas in model theory, set theory, and probability theory. (I go back and forth between liking this idea, which fits closely with how I teach 103 now, and wanting to do something more like, deductive logic in the first half and confirmation theory in the second half with no formal exposure to set theory. The biggest barrier to the second approach is in formally developing confirmation theory without set theory.) Then 202 could do more meta-logic, go into more detail on model theory, go into more detail on set theory, or whatever.
Second, we need more courses covering inductive logic, probability theory, statistics, and so on. I recommend adding a 200-level course parallel to 202, which would cover some probability theory and some causal and statistical reasoning. Let's call this proposed course PHIL 204, since we don't offer anything under that number right now. I have in mind something slightly more advanced than CMU's Open Learning Initiative course here.
Third, I recommend expanding our 300-level course-offerings as follows. We need a second semester of inductive logic (etc.) that builds off of 204. And we need a course that does a simple survey of exotic logics, like modal logics, intuitionistic logic, relevance logic, free logic, etc. The 300-level survey of exotic logics need not be a pre-req for 400-level courses, provided the 400-level courses cover the same material that they have been covering. And that seems fine to me, although it might be in our long-term interests to drop our 454 in the event that we cross-list with mathematics on their math logic course. Depending on how their math logic course is taught, we might try to convince them that our 202 should satisfy the pre-req as effectively as their fundamentals course. (I don't know if that would be a hard sell or not.)
Fourth, I recommend cross-listing some courses with mathematics and statistics to get more regular coverage of the tools we want our students to have without necessarily having our faculty teach those courses all the time.
What Is The Goal Here?
I haven't spent any time in this write-up thinking about the goal(s) of logic education in philosophy. I am not sure whether it would be worth backing up to address this question or whether there is sufficient implicit agreement about the value and goals of logic to leave it alone. If you think I should be saying something about the place of logic in the overall curriculum or making an argument for teaching logic at all or making an argument for understanding logic broadly enough to get probability and statistics through the door, please tell me and make a suggestion about how to develop the heading.
*My department is currently much too small relative to the size of my university, but the powers that be have recently become receptive to our requests to expand (really, to replace a large number of retirements from the last five years). Hence, we are about to undergo an external review, which we hope will result in a plan for phased growth of the department to a little more than twice its current size by the end of the decade. (Yes, our numbers are seriously depleted!)