The workshop is funded by the National Science Foundation (SES-1921688) and is aimed at bringing together academics who study the notion of mathematical explanation from philosophical and from educational/psychological perspectives. The idea is to bring together philosophers of mathematics, epistemologists, psychologists, and mathematics educators, to discuss how developments in their own fields could meaningfully contribute to the work on mathematical explanation where their fields intersect. In particular, we want to explore the ways in which mathematical explanation engenders understanding, by focusing on (1) the relationship between different types of philosophical accounts of mathematical explanation, (2) educational approaches to the characterization of effective explanations in the mathematics classroom, and (3) work at the intersection of these two perspectives.
All speakers:
Mark Colyvan
University of Sydney
Matthew Inglis
Loughborough University
Marc Lange
University of North Carolina, Chapel Hill
Tania Lombrozo
Princeton University
Alexander Renkl
University of Freiburg
Keith Weber
Rutgers University – New Brunswick
Orit Zaslavsky
New York University
When someone is in a conscious state, must they be aware of that state? The Buddhist philosopher Dignāga offers a brilliant route to answering this question by leveraging the role awareness might play as a constraint on memory. I begin by clarifying his strategy and what conclusions it might be used to establish. Here I examine different candidate directions of explanation between consciousness and inner awareness. I interpret the metaphor of consciousness as a lamp that lights itself, and use the metaphor to distinguish between his view and contemporary higher-order theories of consciousness. I then turn to explain why the memory argument fails. The first main problem is that, contrary to Dignāga’s contemporary defenders, there is no good way to use the argument to reach a conclusion about all conscious states. The second main problem is that the proposed awareness constraint on memory is highly problematic, in tension both with ancient objections as well as current psychology.
With responses from Lu Teng (NYU Shanghai)