On the Training of Philosophers in Formal Methods

Back when I was in graduate school, all students were required to take a course in logic. People had a vague understanding that there were also various other formal methods that used in philosophy – probability theory, decision theory, game theory, statistics – but courses in those topics did not fulfill the requirement, and students only rarely took them. At the time, this approach was widely regarded as a very reasonable one. Logic seemed to be more important to the discipline than all of these other formal methods put together.

But over the past decade or so, things have clearly changed. These days, philosophers are using all sorts of different formal methods. There are still lots of philosophers using logic, but it is no longer the case that logic eclipses all other formal methods.There are now tons of philosophers using probability theory (e.g., in formal epistemology), even more drawing on work that uses statistics (in everything from philosophy of mind to moral psychology to feminist philosophy), and a whole lot of other formal methods on the rise as well (causal Bayes nets, machine learning, Monte Carlo simulation).

The result has been a growing recognition that we need to make some important change in the requirements governing philosophical education. In one way or another, we need to make sure that students get a chance to master the formal methods that they will actually need to use in their subsequent research.--Joshua Knobe "Stats Courses For Philosophers" [HT Daily Nous;  @Philosophy of Brains Blog]

Knobe's post was widely and favorably shared among my friends in social media (not a surprise because many of my professional friends are philosophers of science). As some of the commentators at Daily Nous and elsewhere have noted, quite a few departments (where formal philosophy or naturalistic projects have taken deep roots) have already advanced down some version of the path suggested by Knobe. Of course, in practice, graduate students that use formal methods in their own research  and/or that engage with highly technical literature in the sciences (or math)  may well need competencies that go far beyond the required courses in an average graduate curriculum (and may require considerable extra training outside philosophy in some sense).  [I leave aside here, the very different organization of European PhD programs (these are  increasingly pure research with no room for coursework).]

And, in principle, it is easy to get on board with Knobe's essay because he does not really explore the opportunity costs involved with a change in the curriculum. Economists love the idea of opportunity cost; philosophers less so. (Who told you that these possibilities are mutually exclusive; there is no logical/metaphysical reason for that...) But because a curriculum rations a scarce good (time/attention, etc.) it is a useful concept to deploy here. In Knobe's essay, he toys with the idea of displacing the logic requirement with a different requirement. In fact, he mentions quite a few departments that have changed the logic requirement into a formal methods requirement at both the undergraduate and graduate level. So, obviously, lots of peers are willing to go down this path.

Knobe does not mention, although it is clearly embedded in some of the examples he mentions, that in addition to fiddling around with the logic requirement, one can make room for more formal methods by abolishing (a) the language requirement or (b) the history requirement or (c) some kind of traditional distribution requirement (or some combination of these); that's clearly already happening in some of the formal philosophy departments. (I just checked the CMU program's curriculum, and  it has gone down some version of this path. It also offers PhD degrees that are only very partially in philosophy.) I suspect that until China overtakes the USA politically and economically, the language requirement will be under pressure in philosophy departments (unless there are local reasons -- accreditation or divisional requirements, etc. -- to stick with it) Obviously, in very strong history or Continental-friendly departments language may be more secure.

I want to offer two further observations:

First, one consequence of removing logic from shared curriculum is to facilitate increasing specialization within and divergence among analytical philosophers. A notable side-effect of expecting increasing technical facility in whole parts of the discipline is  that you cannot get an average graduate student to understand the issues in a field with one, maybe two graduate seminars. That is, previously professional philosophy was both capable of recruiting lots of smart people and simultaneously keeping barriers to enter any given philosophical conversation fairly low otherwise. (This also generated permissiveness toward the annoying tendency of boy wonders pontificating on any topic they put their intellectual spotlight on.) But Knobe's proposal and the evidence he provides for the curricular changes in the graduate curriculum provide some evidence for my claim from a few years ago, when I mused about the likelihood that there will be a divergence between formal philosophy and analytical philosophy.

Second, based on my own experience in the philosophy of economics, I agree with the spirit behind an observation by Richard Zach: I haven’t looked at any other formal methods course but I suspect that a) you’ll need more mathematical background and b) you’ll learn less how to think mathematically [than by taking a logic course] and [c)] more how to just apply various tools without proving anything." (emphasis added). I am unsure how to cash out mathematical thinking -- that just makes me stutter -- or the significance of proving anything, but I do think I understand what Zach is getting at; logic (and modal logic) really help me to ask very important and foundational questions in economics, including the foundations of statistics. (This is distinct from the fact that for a while set theory turned out to be very important in the practice of mathematical economics.) These are questions I was really not sensitized to ask by my prior exposure to graduate level statistics. A lot of graduate training in a formal area, is really learning how to apply a tool.

And this second point gets me to voice a suspicion. It would be really cool if philosophers became much more sophisticated about the use of statistics or simulation software (etc.) and the evidential uses of statistics (simulation software, probability theory, etc.). But I think that not because I think philosophers should become equal partners in various non-trivial empirical/experimental research or teaching enterprises (in my political science department I teach works that have non-trivial statistical components). To be sure, I am all for folk striking out in that direction and to turn themselves into hybrid philosophers and empirical scientists (of the sort that Joshua Knobe exemplifies so nicely); but I really worry we would be losing something important, no supremely valuable, if we didn't try to keep training folk that can ask questions that are, in some sense, orthogonal to existing normal science, and I think the old logic requirement was, unintentionally, fertile ground for that within the larger philosophy curriculum.

Comments

[RrrichardZach]

What I had in mind with the "mathematical thinking" comment was that either formal or informal methods of proof, as taught in an undergraduate intro logic class, don't really go far enough to competently follow some philosophical arguments. As an example, suppose someone defines a concept and then claim that all instances of it have some property. You need to know how to prove that, and you need to know what a counterexample would be like, to engage with this. Drawing out consequences and coming up with counterexamples are two important things philosophers do. Naive set theory is a good way to train this: how to apply a definition, how to prove things using definitions and various methods of proof, how to find a counterexample, or combinations thereof, e.g., proving by contradiction by assuming there is a counterexample etc. That skill is important even if you don't do logic or philosophy of math. (That you come away knowing some set theory of course also is.)

[Joshua Knobe]

Hi Eric,

Thanks for your engagement with this issue. I really appreciate this thoughtful response, and I'd love to have a chance to hear a little bit more about how you think we ought to go about dealing with these issues.

To begin with, consider an especially extreme option. A department could say that at least one course in logic is required for all graduate students but that courses in statistics do not count toward requirements in any way. My sense is that this extreme option does not make any real sense as a way to prepare students for philosophy as it is currently practiced. To put it in the terms Richard introduced, philosophers these days rely heavily not only on mathematical thinking but also on empirical thinking, and a proper graduate education needs to prepare them for the kind of thinking they are actually going to use.

However, as the discipline moves away from this extreme option, there are still plenty of other options to choose from. Do you feel like any of the remaining options would address the concerns you lay out in your post?

[Eric Schliesser]

Well, I raise different kind of concerns, but yes keeping the logic requirement in addresses some important ones. There is another concern that I did not mention, but Eric Brown did in response to my post on facebook: "Quite apart from its utility as a tool, formal logic is not just a traditional field of philosophical inquiry but also, arguably, the one in which philosophers have made the most progress"

On how to prepare philosophy graduate students in empirical thinking, that's a very interesting and important question. One could demand that one take courses in probability/statistical/empirical methods as an undergraduate before they are allowed to enter a PhD program. That is, not unlike some the prerequisites in medicine, you just stipulate they need to be taken somewhere during undergraduate life or remedial work before grad school. (Even in our rather non-technical MA program in political science, we demand something like that--of course, students can take some of our own poli sci methods courses, but they can also do these in other fields.)
One could also create hybrid degrees (not unlike HPS), where one demands a MA in an empirical field alongside the PhD.

The nice thing about the two options just mentioned is that you can keep the philosophy curriculum in tact without sacrificing some of the things that make it worthy.

But my own sense is that things are moving in the direction that you want within philosophy, but that as a consequence there will be increasing divergence of expectations and standards within it.

[Robert Gressis]

Departments could require that graduate students who don't meet certain formal requirements have to take an intensive summer course in formal methods before starting the program.

[Eric Steinhart]

Hi Eric, I've long supported having more math in philosophy curricula. As you may know, I wrote a book on math that philosophers can use:

More Precisely: The Math You Need to do Philosophy
http://www.ericsteinhart.com/TOOLS/tools-home.html

It might be useful!
- Eric

[Graham White]

Well, I have a background in mathematics, but I don't really do philosophy of mathematics (or, indeed, philosophical logic); mostly I do metaphysics and the philosophy of action. Looking at the use of logic in philosophy from the outside, it seems to be really rather strange as a selection of logical topics: no proof theory, no higher order logic, no type theory, no category theory (all of these are areas of logic that are used a lot in computer science, for example, and that aren't obviously irrelevant to philosophy). Now one can, of course, say the usual things: finite time in a PhD course, too many prerequisites for quite a lot of this stuff, and so on. What this amounts to is the limitations of finiteness, and what follows from it: the essential contingency of any selection of technical topics to teach to philosophers. But what's strange about the philosophical logic done in the Good Old Days (the 50s to the 70s, or so) is that it looked, from the inside, as if it was based on a natural and obvious selection of technical material: that philosophers could be happy that they knew the correct technical material, and that no more was needed. This was a very strange set of affairs, and what might be an advantage in the present setup is that the selection of topics at least looks contingent from the inside. (The question about the fragmentation of the profession is, of course, another matter, and the present situation might not be advantageous from that point of view).