# Stats Courses For Philosophers (guest post by Joshua Knobe)

The following is a guest post* by Joshua Knobe, professor of philosophy and psychology at Yale University. It first appeared at *The Brains Blog*, and follows up on post from a year ago by Knobe here at Daily Nous, “Formal Methods Training for Philosophy Graduate Students.”

**Stats Courses For Philosophers
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**by Joshua Knobe**

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.

I am not sure precisely which approach would be best, but just to get the conversation started, I thought it might be helpful to mention a few approaches that specific departments have adopted. (Most of these involve changes that were made in the past few years.)

- Yale just replaced its traditional logic requirement with a broader formal methods requirement. Students can fulfill this new requirement by taking a course in logic, but they can also fulfill it by taking a course in any other formal method that plays a role in their philosophical research (probability, game theory, statistics, etc.).
- Michigan now allows students to fulfill the logic requirement by taking a broad survey course in formal methods (logic, probability, decision theory).
- Arizona has a ‘formal requirement,’ which can be fulfilled by taking a logic course but also by taking a course in statistics (in the psychology department) or machine learning (in the computer science department).
- Stanford recently introduced at the undergraduate level a broad course on formal methods, which includes logic, probability, decision period, and statistics.
- Utah replaced its previous logic requirement with a requirement to take a course in formal methods, which can be fulfilled by a course in logic, probability theory, decision theory or statistics.
- Carnegie Mellon has a required course in formal methods, which provides a broad survey of ideas from statistics, decision theory, game theory, and formal learning theory.
- Northeastern just replaced its traditional undergraduate course in logic with a course that introduces students to both logic and probability theory.
- Edinburgh has a formal methods course for undergraduates and masters students that includes logic, probability, and more empirically-oriented models coming out of psychology about how human beings actually make decisions.
- Waterloo eliminated its logic requirement. Students are now required to conduct two “research areas.” When mastery of a formal method would serve a student’s research interests, the faculty can make that method a component of a research area.
- Matthew Mandelkern (now moving to Oxford) has a formal methods syllabus that includes logic, game theory and quantum mechanics.
- The Munich program in Logic and Philosophy of Science features courses on logic (obviously) but now includes also a two-seminar sequence on formal methods that familiarizes students with agent-based modeling and computer simulation.
- Similarly, the UCI Logic and Philosophy of Science program has a requirement in logic (again, obviously) but also has a requirement in ‘Tools of Research,’ which can be satisfied through courses that involve other formal methods.
- Toronto has a very minimal requirement in logic (which can be satisfied by taking baby logic as an undergrad) and then a ‘research tool’ requirement, which can be satisfied by taking a more serious logic course but also by taking a statistics course in the psychology department.

I would love to hear from others about which of these approaches seem especially helpful or whether there is some further thing we should be doing to help address this issue.

Thanks in advance for any suggestions you may have!

FWIW, I have a ton of relevant materials up, at the following three course websites:

http://fitelson.org/logic/

http://fitelson.org/probability/

http://fitelson.org/confirmation/

I’ve been teaching philosophy of statistics–in various forms- for over 25 years and plan to do a tutorial for philosophers (with my colleague Aris Spanos) next year. I’ve given two 3-6-week seminars on philosophy of science and philosophy of statistics at the LSE, have run a blog on the topic for over 5 years (errorstatistics.com), and am completing a book “Statistical Inference as Severe Testing”(CUP)

https://errorstatistics.com/phil6334-s14-mayo-and-spanos/phil-6334-syll abus/phil-6334-syllabus-second-installment/

Here are two recent syllabi from LMU regarding machine learning. Both are hands-on programming / model building courses:

http://gregorywheeler.org/courses/mas/syllabus-mas-social-epistemology.pdf (Multi-agent models applied to social epistemology)

http://gregorywheeler.org/courses/syllabus-machine-epistemology.pdf (Supervised Machine Learning meets Philosophy of Science)

Also, to add some additional evidence to Josh’s observation about changes in practice, I recently moved to the Frankfurt School of Finance & Management, were I will introduce and run a Machine Learning course for our graduate program in Finance, but also — together with the renowned Rainer Hegselmann — will be refocusing our undergraduate Management, Economics, and Philosophy program to emphasize Machine Learning, Behavioral Modeling, and Economics.

I’ll teach a masterclass on digital humanities methods in Amsterdam in December. http://www.ozsw.nl/activity/masterclass-digital-humanities-social-epistemology-virtue-theory/

I’m hoping to make this a yearly thing.

Thanks so much! These resources are all super helpful, and I think they will really come in handy for philosophers who are thinking about new approaches to this aspect of graduate education.

Some of the courses described in these comments seem to be designed to give students the tools they need to actually do original research using formal methods. This Is a wonderful opportunity for students who want to pursue that kind of thing, but I should emphasize that many formal methods courses have a much less ambitious goal.

Suppose you are a feminist philosopher interested in implicit bias, or suppose you are philosopher of mind working on consciousness. Even if you are never going to do any empirical work yourself, you are presumably going to be reading a lot of papers that report statistical results. To do that effectively, it might be helpful to have some broad familiarity with ideas from statistics. The need to have this sort of level of familiarity is clearly far more widespread than the need to actually be able to conduct original research using the methods in question.

Now, if one requires all graduate students to take a broad survey course in formal methods, it probably isn’t realistic to think that students are going to emerge from such a course being able to really do serious original research using such methods. However, it does seem realistic to think that they will emerge with a familiarity that allows them to understand work relevant to their own field, and that is a deeply valuable educational opportunity in itself.

My impression of the Formal Methods course at Carnegie Mellon is that a large part of its purpose is precisely to ensure that even where we work in different mathematical frameworks we all have enough common background to ensure we can communicate with each other about what we’re up to. It would not give enough information to make somebody a competent researcher in the fields surveyed, and there are other courses (which are not mandatory) available for students interested in pursuing the relevant formal material to a higher level. In my anecdotal experience the Formal Methods course seems to be pretty successful in ensuring we have enough common ground to communicate, even where we work in quite different traditions.

(I should note that at CMU we are also required to pass a logic requirement.)

I teach experimental philosophy at Oxford Brookes for third-year (in the UK that is final-year) honours students. The course is ambitious in that I teach about 40% stats, including the principles underlying it and doing work on the computer with SPSS, 40% experimental philosophy and 20% research design where they can brainstorm in groups on how to design an experiment for various hypothetical scenarios. We do two replications: the Knobe effect, and Shaun Nichols’ coder study on the genealogy of morals. Students perform the tests themselves, and recruit coders/participants. It’s a lot of fun and feedback is positive (another plus is that they really need to be there for each class due to the hands-on approach) Details here: http://helendecruz.net/docs/syllabi/syllabus_xphi.pdf

FWIW about 13 years ago I compiled a list of logic requirements and course offerings at the then top 36 US programs. It would be interesting to re-do that to see if/how requirements have changed.

https://www.ucalgary.ca/rzach/blog/2004/10/formal-logic-and-philosophy-iii.html

Since Josh framed this as a question about requirements: I think there’s still a lot to be said for a basic logic requirement (truth tables, countermodels, a proof system like natural deduction). I’m not sure what I think about a *meta*logic requirement for philosophy grad students. On the one hand, I don’t think your average philosophy grad student needs to be able to prove completeness (or have once seen a completeness proof) to be a good philosopher. (Back in ’04, the majority of programs on the list did think so.) On the other hand, the main skill students come away with from such a course isn’t so much that they can use/apply logic, it’s that they are trained in how to give a rigorous mathematical argument (basically without any prior mathematical background). At least I like to tell myself that when I teach such a course, and I emphasize it. 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 and more how to just apply various tools without proving anything. So the main learning goal of a metalogic course is (maybe, as I see it?) wouldn’t be achieved by a survey formal methods course.

Hi Richard,

Thanks for your thoughtful response, definitely very much appreciated.

Thinking from a more practical standpoint, I wonder what might be the best approach to dealing with the concerns you raise here. I don’t think the best solution would be to have a system in which students are exclusively taught logic and not given any exposure to any of the other formal methods used in contemporary philosophy. However,if the discipline moves away from that one option, we still have a broad variety of other possible options to consider. Do you have any thoughts about which of those other options might be best?

I don’t think there can be a one-size-fits-all solution. Some departments emphasize some approaches, and some others (even if “emphasize” just means having a number of supervisors in one area). I doubt that in one semester you can cover all of the formal methods you mention in enough depth that it prepares students to use those methods effectively. If we’re talking about multiple courses that have to be offered every year, especially at the graduate level, you’ll soon run into problems staffing them — if you even have people qualified to teach them. (Many departments at least still have someone who can teach logic; stats, not so much.) I think every department will sort out its priorities. If you have people doing x-phi, offer them a stats course. If you have formal epistemologists, probability theory. Metaphysicians, more set theory and modal logic. Etc. But it’s definitely a great idea to collect syllabi and materials for such courses aimed at philosophers. We don’t even have a lot of (advanced) logic for philosophers textbooks — something the open logic project is trying to ameliorate.

Thanks Richard! The one thing I would want to add in response to your comment is just that departments that have tried to create more flexible formal methods requirements have generally not done so by offering a greater selection of courses themselves. Instead, they have simply given students the option of taking courses from outside the philosophy department.

For example, here at Yale, the philosophy department itself does not offer any instruction in statistics. Students who need an understanding of statistics for their research have to take statistics courses from other departments (usually either the psych department or the stats department). We recently made an important change to encourage this sort of thing, but the change did not involve offering any additional courses ourselves. Instead, we simply allowed these courses from other departments to count toward our departmental requirements.

p.s. Thanks for all your work on the open logic project! It’s a wonderful resource, and something we should definitely be pursuing in other areas as well.

I just wanted to chime in, as a grad student who took a traditional metalogic course (we worked through Boolos and Jeffrey) but who had never done any math before, that the exposure to proofs and, well, math (as well as to cool ideas about computability etc) was really helpful for the reasons Richard Zach describes. And this may be more a sign of my poor pre-grad-school math education than anything else, but taking that course was what really made concrete talk of functions (and, relatedly, ‘determination’, ‘supervenience’ etc) in philosophy of language and elsewhere. Furthermore, and again this may admittedly just be me, the metalogic proof-writing course also helped with developing intellectual / problem-solving tenacity, grit, and focus.

This isn’t meant to be a defense of the traditional logic requirement, though. I also think that Joshua Knobe is absolutely right about stats also being just as, if not more, important for most people. My own sense is that all of these tools / courses can be helpful in various ways, and perhaps what departments should do is just let students decide what skills they need or want to acquire — with the proviso that the relatively non-obvious value of certain courses be made explicit (e.g. a metalogic course, surprising as it may first seem, can be really helpful for philosophy of mind).

I would so welcome people’s ideas on how to make these things explicit in the Open Logic Project!

Hi Grad Student,

These are all very good points. The one thing I would add is just that all of these points apply to statistics courses as well.

After all, taking stats courses is not just a matter of acquiring a bunch of technical skills; it is also a matter of gradually mastering a certain kind of thinking – what we might call ‘statistical thinking.’ Once you have become adept at this kind of thinking, you immediately find yourself applying it to philosophical problems, even when you are not directly making use of the mathematical tools acquired in a statistics course.

Of course, none of this is to disagree with anything you and Richard have said. It is just to say that everything you say about logic also applies, mutatis mutandis, to other kinds of formal methods.

Here’s a question I’ve had for a while.

Every now and again I see workshops for post-Ph. D. philosophers who are interested in refreshers on experimental methods or statistics. However, I have lost track of all of the various institutions that offer such boot camps.

Can anyone offer some help on this?

it seems to me there is one obvious disadvantage with replacing a logic requirement with a formal methods one, particularly at the undergraduate level. Logic is quite often a subject that philosophers are uniquely qualified to teach, and teaching it is the bread and butter of many departments. In the US, for example, many philosophy departments have worked hard to get a logic/critical thinking course as a general education requirement that all undergraduates (or at least undergraduates in the humanities) are required to take, and having a course or group of course that puts so many seats in their chairs is very important. If philosophy departments stopped requiring such a course in favor of a formal methods course of their own majors, it might start looking a bit odd for them to require it of everyone else. And it isn’t clear at all that philosophers are better equipped to teach formal methods generally than anyone in a social sciences department. So I would think twice before voluntarily giving up a class that so many departments depend on in part to help justify their existence.

At Northeastern, we have changed the logic sequence in the following way. In the first semester is 1/2 truth-functional logic, and 1/2 probability calculus (treated semantically/algebraically, as a simple numerical/algebraic extension of truth-functional logic) — with application to qualitative vs quantitative evaluations of argument strength. In the second semester, we introduce quantifiers and proof methods for first order logic. There is no worry that other departments will be able to teach this (as well as we can). And, in this way, students who are serious about philosophy take both semesters of the sequence and learn all about first-order deductive logic (as well as probability calculus and basic inductive logic).

Hang on. Either there’s a genuinely good academic argument to get all humanities undergraduates to do logic, or there isn’t. If there is, fine. But if there isn’t, the fact that it would be awkward for the philosophy departments finances to get rid of it doesn’t seem a good *educational* reason to keep doing it.

These most recent comments take the discussion in an important new direction. I was originally asking about courses designed to provide an understanding of the formal methods used in philosophy specifically, but as these comments emphasize, philosophers often teach general education courses designed to give students an understanding of mathematical tools that will be helpful in their reasoning more generally.

For this latter purpose, a broad approach definitely seems like it has a lot of potential. If students are looking for a general introduction to ways of reasoning more clearly and precisely, it doesn’t seem like the ideal strategy would be to devote the entire semester just to logic. A more natural solution would be to expose students at least briefly to a range of different tools. (For example, one could provide a brief introduction to logic, probability and statistics).

I’m in agreement with Josh about the value of learning formal methods beyond logic for contemporary philosophers (including the point made above that becoming adept with these methods can provide new ways of thinking, which can often be applied to philosophical problems).

Shameless plug: Jonathan Livengood and I dedicate significant space in the second half of our recent text

The Theory and Practice of Experimental Philosophyto providing an introduction to statistical methods aimed at philosophers. While our goal in this part of the book is to offer a practical guide for those interested in doing experimental philosophy, we hope that the discussion will also be useful for those who want to improve their understanding of work that employs these methods.If one would simply like to learn some basic stats, and also learn a bit how to code, then I would recommend “Learning Statistics with R”:

https://health.adelaide.edu.au/psychology/ccs/teaching/lsr/

It has the virtues of being rather good, and also free–as is R, which was basically “made” for doing stats, and is rather intuitive when you are doing inferential statistics.

Good evening everybody and thanks for the great ideas and material shared in this discussion. I do apologize for my english before I start, hoping I’ll be understood and that my opinion won’t be so off-topic.

I agree with Joshua when he proposes to give students the possibility to broaden their range of formal system “tools” such as logic, theory of games, etc. Nonetheless I think that what we are calling “tools” are not just the tools we use in ordinary life, they cannot be changed and replaced easily when we have finished to use them. Formal systems, primarily logic, shape and model our way of thinking like native language forges our way of speaking. If so, even if a student could benefit from these new “tools” he would never be able to use it in a proper way because he’s already looking the world through the lens of logic.

If my purpose is to give an alternative range of formal system that can be used and not only studied, then this move must be done previously.

I think experimental philosophy could be a good choice not only for extra-curricular school project but for the actual school programs in order to support and help other subjects of study.