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!

Hi Joshua – I teach experimental philosophy for third-year (that is, in the UK, final year) honours students. The course is an ambitious attempt to give them both the basics of stats (concepts of probability, normal distribution, significance, effect sizes) and teach them how and when to use such tests as the t-test, chi-square tests, and find correlations. I let them replicate the Knobe effect by giving each of them 10 participants to survey, and let them do the stats on the results (it replicated beautifully). On my website you can find the syllabus (I cannot post the link here because the website then rejects my comment as spam)

Link to Helen’s syllabus: https://helendecruz.net/docs/syllabi/syllabus_xphi.pdf

Josh, forgive the shameless self-promotion, but this is precisely why I wrote Good Thinking (Cambridge, 2012).

Most of us are insulated within our particular disciplines. Philosophers and lawyers know all about argumentation, but don’t know the first thing about scientific investigation. Scientists know all about hypothesis-testing, but know little about logic and even less about moral theory. Too few of us other than economists know anything about decision theories that drive the equity market and underlie economic policies that impact our lives. And aside from psychologist and neuroscientists, few of us know how the way the brain is wired shapes the way we think, act, and feel. And then we take jobs as policy-makers, writers, scientists, lawyers, and professors—bumping about in life with holes where some crucial bits of knowledge ought to be.

I decided to address these knowledge gaps, and wrote Good Thinking. The books gives concise summaries of

1. Rational Choice: Choose what is most likely to give you what you want.

2. Game Theory: What to do when you’re not the only one making choices.

3. Moral Judgment: How do we tell the difference between right and wrong.

4. Scientific Reasoning, which consists of hypothesis-testing: The search for truth by evaluating evidence, and causal reasoning: Explaining, predicting, and preventing events.

5. Logic: The search for truth through argumentation.

6. Problem Solving: The search for solutions to unwanted situations.

7. Analogical Reasoning: The heart and soul of insight, discovery, and genius.

It seems it shouldn’t be decided a priori for any particular grad student. One might need differential equations, another might require probability/stats. Another mathematical logic. Another more traditional logic. Someone doing Phil of Neuro likely has very different needs than ethics.

As you know, my own book More Precisely: The Math You Need to do Philosophy, was written specifically to address these needs! No logic, just math that is useful for philosophers.

Here’s the link to More Precisely.

https://www.amazon.com/More-Precisely-Philosophy-Broadview-Guides/dp/1551119099/

And a link to more information about it on Eric’s website:

https://www.ericsteinhart.com/TOOLS/tools-home.html

Just to add that as a neuroscientist this makes me really happy to see that philosophy seems to be moving away from the focus on logic as the only formal discipline. I do think that logic is very helpful for thinking about neuroscience experiments and generating word models of different phenomena. However, for really digging in and understanding/critically evaluating first-order neuroscience it’s all about stats, diff-eq, and linear algebra.

Stepping away from neuroscience, I also think programming could be incredibly helpful for people doing technical philosophy. Matlab and Python are extremely easy to learn at this point.

Running simulations, even very simple ones, is a great way to check one’s intuitions. It is often easy to formalize one’s intuitions, run the simulation, and see how they match up. I literally cannot count how many times they do not match up, and I learn so much by figuring out what is wrong with my intuitions about why a simulation a certain way.

Science is moving toward open…everything. We are starting to put our code and even our data online. It is required by most sources of funding. Philosophers who can read such code, run it, and tweak it could be at a big advantage.

Thanks everyone! These comments and suggestions are all extraordinarily helpful, exactly the kind of thing I was looking for.

If you have taught a course on this topic or written a book that would be good for such a course, please do feel free to include a link for people who want more information. I’m sure people who are thinking of moving in this direction would be very interested to learn more about what you have done.

Yes, and if you have any trouble getting links past the spam filter just email me: jlschwenkler at gmail

I taught a course at UIUC for several years that was cross-listed in Philosophy and Psychology based on materials that eventually became Good Thinking. Info about it can be found at my website http://www.denisecummins.com. Here is the Amazon link to the book: https://www.amazon.com/dp/0521145503?_encoding=UTF8&isInIframe=0&n=283155&portal-device-attributes=desktop&ref_=dp_proddesc_0&s=books&showDetailProductDesc=1#product-description_feature_div

Hi everyone,

So sorry for this annoying request, but a copy of this post is now up at Daily Nous:

https://dailynous.com/2017/05/29/stats-courses-philosophers-guest-post-joshua-knobe/

So if you would like more people to read your comments, you might want to take exactly the comment you already posted here and post it there as well.

Hello Joshua. I’ve a thought from the other direction, as it were. I stumbled across your article, and just wanted to say that as a statistician, I found it very interesting. In the programmes I’ve attended, formal logic wasn’t required. Yet it should be. I understood so much more about maths and stats after doing a course in formal logic on my own. Rather than replace logic, surely it should be kept, and additional courses added. For those maths and stats programmes that do not require formal logic, they should start. Philosophy courses in probability would be welcome as well.

Hi L Thomas,

What an interesting idea! Within philosophy, there is definitely no one suggesting that we should replace the logic requirement with a statistics requirement. The suggestion is rather that it would be good to *broaden* the requirements in some way – either by offering a single course that provides instruction in multiple formal methods or by offering students a choice between different possible courses. It’s fascinating to hear that people in statistics might be interested in broadening their own requirements in a similar fashion.