LPS 241: Gauge Theories (Graduate Seminar, Fall 2012)
Our most fundamental theories of matter and its interactions are members of a class of physical theories known as (quantum) gauge theories. This course will address the mathematical and philosophical foundations of these theories by focusing on the foundations of classical field theory, in which context many of the most important conceptual questions concerning gauge theories arise without the additional complications associated with quantum theories. The first four weeks of the course will cover mostly mathematical topics in differential geometry and mathematical physics (smooth manifolds, tensor fields, fiber bundles, Lie groups and principal bundles, Lagrangian field theory) needed to understand the foundations of classical field theories. The second half of the course will cover philosophical questions related to these theories, including questions concerning the nature and origin of gauge symmetry, interpretations of gauge quantities (including issues related to locality and separability), and symmetry breaking.
Social Science H1G: Naturalized Epistemology and the Social Sciences (Fall 2012, w/ Jeff Barrett)
This course concerns epistemology—the study of human knowledge and justified belief—addressed from an interdisciplinary perspective including methods characteristic of philosophy, history, and the social sciences. We begin by describing the traditional philosophical view of what knowledge amounts to. Then we will discuss two famous challenges to the idea that we can know anything about the world at all, due to philosophers Rene Descartes and David Hume. Following a suggestion by Hume, we will next consider what empirical research in the social sciences can contribute to our understanding of human knowledge. We will discover that a number of classic findings of the social sciences reveal that the faculties we rely on in the acquisition of knowledge are systematically unreliable, misleading, and subject to deception in myriad ways we never anticipated. We will then explore Thomas Kuhn’s famous suggestion that the theories and methods we use to establish these scientific results are themselves open to an important skeptical challenge. We will suggest that the upshot of this investigation is that we cannot acquire any knowledge at all without making some assumptions about the nature of the world and the processes of inquiry—and yet, as we will have seen, many of the assumptions we rarely question have been undermined by empirical research. We will conclude by proposing an alternative picture of human knowledge as an ongoing process of belief revision and problem solving, according to which it is possible to provide justification for many of our beliefs about the world even as we constantly update our assumptions about the nature of our faculties and methods in light of new research in the social sciences.
LPS 31: Introduction to Inductive Logic (Spring 2011)
This course is an introduction to inductive logic and rational choice. Inductive logic is the study of reasoning under uncertainty, which, after all, is how most of our reasoning is done. Rational choice theory, meanwhile, is the study of how logical inference can be used to inform decision-making. The principal question we will be asking is, how should evidence affect our beliefs and actions? Our basic tool for studying this question will be the probability calculus, and especially Bayes’ theorem. We will study how to assign probabilities to possible propositions and how to update those probabilities as we learn new things about the world. Finally, since this is a philosophy course, we will spend some time discussing some issues that arise at the foundations of probability theory.