Philosophy 290-3

Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs (neo-logicism, modified Hilbert’s program, varieties of constructivism etc.), analytic approaches to epistemology and ontology of mathematics (nominalism, platonism etc.), and developments at the intersection of history and philosophy of mathematics (Lakatos and others). But anyone even partially familiar with contemporary philosophy of mathematics will not have failed to notice a loud call for approaches to the philosophy of mathematics that will pay closer attention to mathematical practice than has hitherto been the case. The seminar will focus on this latter direction of work. It will be divided into two parts. The first part will cover some approaches to the philosophy of mathematical practice from the 1960s to the 1990s (Lakatos, Kitcher, and Maddy, among others). The second part will consist of readings from a new generation of philosophers of mathematics whose appeal to mathematical practice differs in significant ways from those studied in the first part of the seminar. Most of the readings for the second part will come from a forthcoming volume, “The Philosophy of Mathematical Practice”, which I am editing for Oxford University Press. Among the topics to be covered are diagrammatic reasoning, visualization, explanation, purity of methods, fruitfulness of concept, etc. Time permitting, some attention will be devoted to the philosophical problems emerging from developments in category theory, computer science, and mathematical physics.