Schmid College, Chapman University
Mathematics and Society Reunited: Social Aspects of Brouwer's Intuitionism (Kati Kish Bar-On, MIT)
The Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics takes place at Chapman University as its main host, and is co-organized together with researchers from UC Riverside, CSU San Bernardino, and Pitzer College. It also occasionally integrates the Chapman University D.Sc. program in Math, Philosophy and Physics as its Graduate Colloquium.
The seminars are held in hybrid format on the Chapman University campus in the Keck Center, home of Schmid College of Science and Technology, or on Zoom. On January 12, 2024, Kati Kish Bar-On, Ph.D., presented her talk “Mathematics and Society Reunited: The Social Aspects of Brouwer’s Intuitionism.”
ABSTRACT: Brouwer’s philosophy of mathematics is usually regarded as an intra-subjective, even solipsistic approach, which also underlies his mathematical intuitionism, as he strived to create mathematics that develops out of something inner and a‑linguistic. Thus, points of connection between Brouwer’s views and the social world seem less probable and are rarely mentioned in the literature. In this lecture, I examine Brouwer’s views on the construction, use, and practice of mathematics through a socially oriented prism. I highlight the social character of mathematical practice as Brouwer addressed it in the Significs Dialogues - documented dialogues between Brouwer and other members of the Signific Circle, a social movement focused on the connection between language, mathematics, and society centered in the Netherlands. After fleshing out the connection between society, people, and mathematical knowledge in Brouwer’s thought, I pose two critical questions: (1) How do social, personal, and political events have shaped the development of intuitionism, and (2) How does Brouwer’s social perspective affected the content of his intuitionism. The lecture concludes by discussing possible implications and future research trajectories.
