The History and Philosophy of Mathematics (HPM) group at McGill offers a unique opportunity to study mathematical knowledge and reasoning from an historically informed philosophical point of view.
Instead of focusing on a narrow set of questions that have dominated the traditional discussions in philosophy of mathematics of the past decades (like, 'Do numbers exist?' and 'What is mathematical truth?'), we pursue a distinctive approach to mathematical knowledge and reasoning that is based in an essential way on the history of mathematics and on philosophical reflections on mathematical practice. As such, we consider ‘philosophy of mathematics’ to cut across the entire history of philosophy as well as philosophical approaches that are often considered as excluding each other (e. g., analytical philosophy and phenomenology).
Moreover, we also are open to the study of mathematical reasoning from the perspective of current cognitive science, mathematics education, etc. Some examples of topics that fall under our research interests are: astronomical computations in ancient science, Medieval reflections on logic, Kant’s use of mathematics to illustrate synthetic a priori knowledge, the conceptual underpinnings of the development of set theory and of non-Euclidean geometries in the 19th century, philosophical reflections on the impact of Gödel’s incompleteness theorems, the development and efficacy of mathematical notation, and contemporary work on mathematical cognition.
Last but not least, we consider mathematics to be a prime case study for practicing one’s philosophical skills in general and as an ideal whetstone for sharpening one’s intellectual abilities in accord with Plato’s saying that “in all departments of knowledge, as experience proves, any one who has studied geometry is infinitely quicker of apprehension than one who has not” (The Republic, Bk. VII).
For further information, please contact any of our faculty members!