The Center for the Advancement of Logic, its Philosophy, History and Applications presents
"Visualization and O-minimality"
with J. Ethan Galebach, Graduate Student, Department of Logic & Philosophy of Science, UC Irvine
March 12, 2014
Social Science Tower, Room 777
Recent work by Marcus Giaquinto on visual thinking in mathematics has provided us with new appreciation for the role of visualization in the formation of basic beliefs in elementary arithmetic and geometry. However, Giaquinto is more skeptical about the epistemic role that visualization can play in elementary analysis and calculus. His reason is that our visual faculties seem to be unreliable guides to the “limiting behavior” of certain continuous functions. But a recent branch of mathematical logic, namely o-minimality, takes as one of its primary objects ‘definable continuous functions’. Gaelbach will argue that our visual faculties are reliable guides to the behavior of these objects. More specifically, he will argue that the o-minimal Intermediate Value Theorem is subject to knowledge-by-vision despite Giaquinto’s (sound) argument for the claim that the real analytic IVT is not subject to knowledge-by-vision. Thus, contrary to Giaquinto’s view-- which is the received view-- perhaps the foundations of analysis and calculus can be based in part on visual reasoning. But o-minimality is unlike other traditional foundational programs in mathematics: it is not obviously axiomatic, and it does not obviously have an intended model. He will suggest that the link to visualization can serve to dissipate these concerns about o-minimality qua foundation and to help us to understand what the subject-matter of o-minimality really is.
For further information, please contact Patty Jones, email@example.com or 949-824-1520.