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!)

New Comment
24 comments, sorted by Click to highlight new comments since:

The problem with gating classes is that it makes life difficult for students who self-studied the lower-level material. The UC Berkeley math department does not enforce prerequisites, which made my life a lot easier, since I already knew most of the material for the lower division classes despite never having taken equivalent classes, and was able to skip directly to the classes that were at a more appropriate level. So I wouldn't suggest having strictly gated classes, although it might make sense to put in weaker filters to weed out the students who really don't have the necessary background (e.g. "... or consent of instructor")

At some universities, at least, it's possible to test out of many class requirements. This is easiest to implement with math classes, but I think creating tests that gauge proficiency in logic shouldn't be that hard. Probably easier than creating a meaningful test for familiarity with the works of various philosophers.

I was going to say that the problem from the instructor's point of view is deciding whether the student really has the necessary background, but Desrtopa is probably right that some sort of testing system could be set up.

In one sense, I agree that there shouldn't be any gating. It is overly-paternalistic. Students should be allowed to risk taking advanced classes as long as they don't gripe about their failures later. But on the other hand, the actual result that I see in my classes is that many -- and here I mean maybe as many as half -- of the students in upper-division courses are not prepared to do philosophy at that level. They don't know how to engage in discussion appropriately or productively; they don't know how to write clearly or criticize arguments effectively; etc. If they only affected themselves, I could put up with it. But they don't affect only themselves, they affect the other students as well.

If you're going to back off on the gating, you need to provide sufficient guidance to the students on what they will practically need to know that they can make an informed choice. I took a course in baroque music that went very badly. If I had known how much music theory I would have to have, and how much facility I would have to have with it, I would not have taken the course.

Good point.

So, we have a few alternatives:

  1. No filters at all.
  2. Full gating (if you didn't went through the prerequisite courses, you're out).
  3. Instructor's approval.
  4. Entry tests.
  5. Big warnings about prerequisites.

I think the best way is probably a mix:

  • If you took (and passed) the prerequisite courses, you can enter.
  • Otherwise, you pass the entry test (if available).
    • Above some threshold, you can enter.
    • Below some threshold, you're toast.
    • Between them, you need instructor approval.

The idea is to make prerequisite courses optional, while keeping the actual proficiency of the prerequisite material mandatory.

I'm of the opinion that deductive logic is way over-emphasized in philosophy training, and it seems like it's even more over-emphasized than usual in your department. I actually think a lot of pathologies in the way mainstream analytic philosophy is practiced are partially attributable to the fact that philosophers learn so much logic and basically no other rigorous analytic tools. Take, for example, the fact that philosophers are usually very careful about whether their conclusions follow from their premises, but the way the premises themselves are justified is often a mess (appeals to intuition, dubious thought experiments, etc). If philosophers knew more about how to infer beliefs from evidence, their arguments would in general be much better.

Even departments that have courses in inductive logic usually treat it as an adjunct. The message philosophy students get is that their primary tool is deductive logic, and they should have a thorough grounding in that discipline, but it's also good if they pick up some elementary statistics and probability theory. I would recommend the opposite emphasis, but even equal treatment of inductive and deductive logic would be a massive improvement.

I strongly agree with your comment. What concrete steps would you take to fix the problem? Are there specific classes you would add or things you would emphasize in existing classes? Are there specific classes that you would remove or things you would de-emphasize in existing classes?

These would be the formal classes in my ideal philosophy curriculum:

  • Symbolic logic (sentential and predicate logic, some model theory)

  • Set theory and category theory

  • Mathematical logic (along the lines of your 454)

  • Scientific reasoning (elementary statistics, causal inference)

  • Probability theory and the philosophy of probability

  • Rational decision-making (decision theory, heuristics and biases)

  • Formal epistemology (Bayesian epistemology, confirmation theory, computational learning theory)

  • Some sort of "programming for philosophers" class, teaching basic programming but emphasizing the connections with the material they've learned in their logic classes.

I'm tempted to merge symbolic logic and mathematical logic. I'm not sure how they are different from each other. How would you divide them?

I'd put Probability theory before scientific reasoning, since the latter flows from the former (not historically, but this is a philosophy course, not a history one). The result should naturally include the "Bayesian epistemology" part of your formal epistemology course.

Typically, symbolic logic classes focus on reasoning with formal systems and mathematical logic classes focus more on reasoning about formal systems. So in a symbolic logic class you would mainly learn how to do proofs while in a mathematical logic class you would learn about things like Godel's theorems. Maybe "mathematical logic" is a bit of a misnomer, but it is the traditional title of these classes.

If you agree here, I'm curious why you're focusing on reforming the logic curriculum? Why not focus on shifting resources from teaching logic to teaching the standard things recommended here (probability theory, heuristics and biases, psychology etc.).

Because I see those things as part of logic. As I see it, logic as typically taught in mathematics and philosophy departments from 1950 on dropped at least half of what logic is supposed to be about. People like Church taught philosophers to think that logic is about having a formal, deductive calculus, not about the norms of reasoning. I think that's a mistake. So, in reforming the logic curriculum, I think one goal should be to restore something that has been lost: interest in norms of reasoning across the board.

Hmm, is that best accomplished by trying to reappropriate the word 'logic'? Mathematicians, philosophers etc. seem like they have a pretty firm idea about they mean by 'logic' and going against is probably hard. Trying to get a Heuristics and Biases or statistics course into the logic curriculum seems like it would get a lot of pushback. Can the word 'logic' itself be that valuable? Why not pick a new word?

I don't want to have a dispute about words. What I mean when I talk about the logic curriculum in my department, I have in mind the broader term. The entry-level course in logic does have some probability/statistics content, already. There isn't a sub-program in logic, like a minor or anything, that has a structural component for anyone to fight about. I would like to see more courses dedicated to probability and induction from a philosophical perspective. But if I get that, then I'm not going to fight about the word "logic." I'd be happy to take a more generic label, like CMU's logic, computation, and methodology.

Ah, okay, that makes sense then.

I think part of why I think I'm confused is that none of the courses you proposed are focused on psychology (heuristics and biases being the standard recommendation). Any reason for that?

That's a good point. Looks like an oversight on my part. I was probably overly focused on the formal side that aims to describe normatively correct reasoning. (Even doing that, I missed some things, e.g. decision theory.) I hope to write up a more detailed, concrete, and positive proposal in the next couple of days. I will include at least one -- and probably two -- courses that look at failures of good reasoning in that recommendation.

I look forward to it :)

Another thing that comes to mind, is that if you're advising the curriculum committee and not directly in charge, you may want to strategize about how best to convince them to take a more lesswrongy attitude. Things that spring to mind:

  • getting multiple people to say similar things
  • making the same argument repeatedly and in private with members of the committee
  • getting a speaker (luke?) to come in and make the case
  • finding articles that make the same points you do

Strongly agree.

What's the content of the PHIL 102 course? I had a "Critical Thinking" course prerequisite in college, but I don't want to assume too much with respect to uniformity between schools.

I would suggest making the introductory level logic courses a prerequisite to the classes that actually deal with the works of various philosophers. In retrospect, I considered it an oversight of the curriculum back when I was doing a double major in Philosophy that students were expected to be able to jump right into discussions of philosophical questions without first being given proper training in logic.

Ideally students should be taught to recognize and dissolve confused questions before they start grappling with philosophers who actually entertain them, to better avoid wasted time.

The content is informal logic: discourse analysis, informal fallacies (like ad hominem, ad populum, etc.). Depending on who teaches it, there might be some simple syllogistic logic or some translation problems.

I like the idea of requiring logic along with the intro course. I'll keep that one in mind.

Your "Physics Made Easy" link is to an internal Illinois site, which we can't see. (If you're talking about PHY 123, it doesn't seem like they have a useful online presence.)

I didn't realize the link I gave was not viewable: apologies for that. Also, wow. That PHYS 123 "page" is really embarrassingly bad.

When it comes to high level logic and critical thinking courses than I would propose a course that centers on fundamental questions.

Focus real world scientific debates, where there's disagreement but how we interpret evidence:

1) From John Ioannidis:

Studies have gone back and forth on the cancer-preventing powers of vitamins A, D, and E; on the heart-health benefits of eating fat and carbs; and even on the question of whether being overweight is more likely to extend or shorten your life. How should we choose among these dueling, high-profile nutritional findings? Ioannidis suggests a simple approach: ignore them all.

2) Richard Feymann article about Cargo Cult science: http://www.lhup.edu/~DSIMANEK/cargocul.htm How much of science today suffers from that problem? (Voodoo neuroscience: http://neurocritic.blogspot.de/2009/01/voodoo-correlations-in-social.html)

3) Was the Journal of Personality and Social Psychology wrong to publish Bem et al 2011?

4) Is Nassim Taleb right when he calls for the abolition of the Nobel Prize for Economics? Does the prize do good for the world?

5) The case of NASA claiming that "The definition of life has just expanded,"

There probably a bunch of other nice edge cases that are worthy of discussion. Philosophers should analyse where other fields mess up.