Center for Cognitive Science Colloquium
Co-sponsored by Poetics Program
GEORGE LAKOFF
Department of Linguistics
University of California, Berkeley
lakoff@cogsci.berkeley.edu
What is Infinity?
The Cognitive Science of Mathematical Ideas
Wednesday, November 3, 1999
280 Park Hall
2:00-3:30 p.m.
North Campus
This is an overview of a new book by Rafael Nunez and
myself, Where Mathemtics Comes From: How the Embodied Mind
Creates Mathemtics. It is an attempt to start of discipline
of Mathematical Idea Analysis based on cognitive semantics.
We show how many of the most basic ideas in mathematics are
based on conceptual metaphors and conceptual blends,
beginning with arithmetic, set theory and logic. We then
show that there is a single Basic Metaphor of Infinity, that
all forms of infinity in mathematics (e.g., infinite sets,
points at infinity, transfinite numbers) are special cases
of. We then show how, through mathemtical idea analysis, the
relations among the main branches of classical mathematics
can be clearly seen.
The result is a new philosophy of mathematics from the
perspective of cognitive science, in which mathematical
ideas are human creations using the ordinary mechanisms of
the embodied mind.