Instructor for 80-212 ‘‘Arguments and Logical Analysis’’

Instructor of Record for the course 80-212 ‘‘Arguments and Logical Analysis’’. Syllabus here.

“What counts as a “successful” argument? Is it one based on evidence? If so, what counts as “good” evidence? Suppose we could answer this question - is that enough? What does it mean to “base” an argument on evidence? Surely there are incorrect ways to deploy even very good evidence. Can we categorize them? Questions such as the above form the basis of the branch of philosophy known as “epistemology”. Epistemology is the study of “reasoning”. It answers questions both concerning how we ought to properly reason, but also how we tend to reason in practice. Broadly speaking, this course is focused on exploring epistemology. We will be focused on different ways of understanding what counts as a “successful” argument. We hope to be able to not only identify and distinguish such arguments from unsuccessful ones, but to understand the myriad and complex ways in which such arguments work. This course will also take an even narrower approach. Epistemology is (literally) an ancient discipline, but massive strides have been made in the last 100-150 years, particularly connecting concepts in epistemology up to those in formal mathematics. This is a branch of mathematical modeling, or applied mathematics, known as “formal epistemology”. These different mathematical models have made exploring the nuances of argumentation more feasible than ever before. However, our purposes are more applied. The limitations of a semester mean that we only have so much time to delve into the nuances of formal epistemology. So, the course aims to introduce a handful of the most basic and universal formal epistemic tools, namely those of Boolean logic and probability theory. With these in hand, the second half of the course is dedicated to the application of these tools. It would be quite frustrating and disappointing of these formal tools did not, in fact, help us to understand more day to day arguments, but instead remained abstract tools. So the second half of this course is dedicated to applying what we learn in the first half towards arguments made in first natural science, and then political science. The hope is that these formal tools will let us not only understand how rich and complex some of these arguments are, but they will help us to more subtly and carefully evaluate these arguments, understand where some succeed, and where others fail.”

Description here.

Pedagogical Goals:

I was assigned to teach this course in the second half of the summer of 2024, and my colleague Owen Milner was assigned to teach it in the first half. I had already taught Introduction to Philosophy and Logic and Proofs, and TA’d for Nature of Reason (which I would in fact teach the next summer). Arguments and Logical Analysis had not been offered for a few semesters, and we quickly realized that the content of the course was currently being covered by other courses in the roster. So, Owen and I were given a fairly free hand in redesigning the course from the ground up. In line with all of the pragmatic thinking I have alluded to so far, our goal was to make learning formal philosophy as relevant and practical for the students as possible. To that end, we decided to break the course into two halves.

The first half would cover formal methods, largely propositional logic and probability theory. Assignments in this first half were 3 problem sets, each due at the end of the week, to ensure the students mastered these skills (a summer course is 6 weeks long). The second half of the course was itself broken into two halves. The idea was that in the second half of the course, we would apply what we learned in the first half towards scientific and political texts in order to sharpen our critiques of those texts. In the beginning of this second half, we covered scientific reasoning with a focus on Darwin and Francis Galton. In particular with Galton, we were able to use the probabilistic tools we had already developed to give a formal account of Darwinian Natural Selection that seemed compelling, but were able to show that Galton’s actual stated argument, justifying a program of eugenics, did not hold. The same assumptions which applied to the natural selection argument did not apply to Galton’s intended setting (which was an application of the logic portion of the course). In the first of two long form essays, my students were able to walk through this line of reasoning step by step and evaluate it in their own words very successfully. In fact, this portion of the course generated some of the best writing I’ve ever gotten from students. I believe this was because students were, in fact, able to use the formal tools to very clearly understand and describe the structure of the arguments, which I believe helped my students be far more specific in their analysis of the arguments. It is worth noting that many of the students I taught in this course were highschoolers, which made me even more surprised by how successfully they were able to work through the difficulties of these arguments so cogently. My main takeaway is that it is possible to teach formal tools in a philosphical context with the emphasis on applying those tools in evaluating arguments. But, one has to be very specific and deliberate in planning how the formal tools will line up with the arguments that will be analyzed. It is not enough, if this is the skill one wishes to foster, to gesture at the idea abstractly and hope it will stick. I believe the course was a big success, and I believe the course evaluations support this conclusion. Owen and I have iterated on this concept as well, applying further revisions to tighten the connection between the two halves and to make the applications even more salient.