This Spring quarter, Prof. Rafael Núñez is teaching a graduate seminar on the cognitive foundations of mathematics. Students from outside the Department of Cognitive Science are encouraged to enroll!
COGS 260 / Seminar on Special Topics:
Cognitive Science of Mathematics
The goal of this seminar is to provide a general overview of a rather new discipline called the Cognitive Science of Mathematics. The idea is to try to give a naturalistic account of the nature of mathematics and its conceptual structure building on relatively recent empirical findings in cognitive science. Based mainly on methodologies from cognitive semantics and psycholinguistics, experimental psychology, gesture studies, and on findings in neuroscience, we will use a technique called Mathematical Idea Analysis. We will address questions such as: How are mathematical concepts formed? How do the peculiarities of brains and bodies bring forth mathematical ideas? How do we create mathematical infinities if everything in our brains and everything we experience is finite? What do infinitesimal numbers, transfinite cardinals, and the point at infinity in projective geometry have in common? Why is the empty set a subset of every set? And how are these concepts shaped through cultural practices, notation systems, and historical processes? Developments in this field provide a new understanding of the cognitive foundations of mathematics. We will explore some implications of these results for the study of human cognition, mathematics education, and philosophy of mathematics.
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