LPS 240: Seminar on Evidence

Introduction. The purpose of this seminar is to study how we do (and/or should) transition from various bodies of evidence to assessments about how and how well they support or undermine various aspects of a given scientific theory. We will be primarily concerned with the typical case where the evidence at hand is indeterminate, because there is error in our measurements, our models are simplifications of complex phenomena, etc. In particular, we will examine some ways in which evidence in its most basic form is manipulated and transformed into some more useful mathematical object(s) that then bear(s) on a precise question in a precise way.

Mathematical requirements. There are no formal requirements for this course, although students should be willing to pick up some basic techniques on the fly. The first part of the course will be largely quantitative in nature, and certain assumptions may have to be taken on faith by some. I will try, though, to make the centrally important points accessible to those whose background in linear algebra and real analysis is largely limited to what they've acquired in this course. (Although not all of our authors will use them, all integrals may be assumed to be Riemann integrals, except when explicitly noted otherwise.)

Expectations. Those enrolled in the course will be expected to be actively engaged in the discussion components of the course. They will also be expected to give at least one in-class presentation, and to submit a term paper of the usual length and maturity.

Presentations. A major point of giving presentations is as preparation for giving professional talks and presentations. For this reason, I offer the following recommendations. Those presenting technical material should try to relate it to some relevant conceptual issues. In particular, the presentation should be accessible to persons without a technical background, so that they can see what the relevant issues are and why they matter. Those presenting more conceptual material should try to relate it to the nitty-gritty details of actual practices/methods, so as to illustrate how some philosophical idea(s) are (or are not) realized in real life.

The course is divided into two main parts, described below. A preliminary and provisionary syllabus can be found here.

Part A: Some theoretical aspects of statistical methods. In this first part of the course, we will examine some foundational aspects of ordinary statistical methods. Many of these methods (e.g., correlation, regression, anova, statistical inference) can be usefully viewed as phenomena occurring in high-dimensional Euclidean space. We will see why this is so, and also establish some parallel results that place the evidence in other (unique) geometries when it contains different kinds of uncertainty or randomness. Although this presentation does not resemble how such methods are introduced in undergraduate textbooks, it is, I believe, a vastly more powerful and flexible framework from which to understand and utilize statistical methods. In this overview, I will tack heavily towards a theoretical understanding of the methods, and away from many of the practical issues of implementing them. However, throughout the course, we will frequently examine the multifaceted space between cases where these methods do Good Works, and cases where they are in bondage to sin, and cannot free themselves. Readings will be drawn from selections from:
You will want to obtain a copy of Wickens 1995 and Bulmer 1979. I will upload pdfs of the relevant portions of the other texts.

Part B: Topics. In this second part of the course, we will examine a variety of issues of philosophical relevance from a mathematically informed empirical perspective. What material we cover in this part will be partly determined by the interests of the participants. The readings break into three general topics: (i) using/analyzing statistical methods in philosophical contexts, (ii) further statistical theory of relevance to philosophy, (iii) expert decision making (i.e., do we really need all these methods, or are we better off just training ourselves to make informal, holistic professional judgments?).