PHIL 4960 Philosophy of Mathematics (Spring 2024)

Description: This course will review fundamental epistemological, metaphysical, and logical challenges in the foundations of mathematics. Historical discussions of the paradoxes arising during the foundational crisis in mathematics (the Grundlagenkrise), e.g., the inconsistency of class theory, the discovery of Godel's incompleteness theorems, and the collapse of the Hilbert program will set the stage for investigation into what mathematical entities are, how we can come to have reliable knowledge of them, and what choices we ought to make in the face of paradoxes or contradictions in our representations of mathematical truth. 

INQR 1961 Feminist Critiques of Reason (Spring 2024)

Description: Feminist critiques of many disciplines have led to deep and radical revisions to their foundational assumptions. In the case of the a priori disciplines---mathematics, computation, engineering---critiques tend to be less foundational. There exist, however, threads of literature debating the role that feminist theory plays in determining the bounds of reason itself and, consequently, the contours of disciplines like mathematics. The thesis that oppressive themes are baked into the foundations of reason leads to important questions... In this course, we will review recent literature investigating the degree to which the development of logic is harmonious with or antagonistic to feminist (and other liberationist) aims. We will emphasize several styles of critique, ranging from historical to more recent work concerning the consequences for mathematics and computation in the wake of such critiques.

PHIL 4960 Non-Classical Logic (Fall 2024)

Description: This course provides an introduction to the philosophical and formal aspects of several families of non-classical logics that provide alternatives to classical (Russell-Frege) logic. Emphases will include philosophical objections to particular components of classical logic and how alternative formalizations of reasoning have emerged in order to accommodate these objections. In particular, topics to be covered will include logics of strict implication, intuitionistic logic, relevant logic, and fuzzy logic.