Rafael Nuñez: UCSD Department of Cognitive Science

How can we “objectively” share abstract entities with others, in a stable and consistent way? How can we evaluate “Truth” when purely imaginary entities are concerned? Mathematics provides a very intriguing case for studying these questions. Indeed, mathematics, on the one hand deals with purely imaginary entities (e.g., a Euclidean point has only location, but no extension! … And there is no such “real” thing in the entire universe!), and on the other hand, it provides extremely stable patterns of true-valued inferences (i.e., theorems) that once proved, stayed proved for ever (e.g., the Pythagorean Theorem). In this talk I will analyze these issues by looking at (1) my own work on the Cognitive Science of Mathematics (with George Lakoff) taking examples from set and hyperset theory, and (2) my field work in the Andes’ highlands studying–with convergent linguistic-gestural-ethnographic methods–a very peculiar form of spatial construal of time in the Aymara culture. I’ll address the question of the role of axiom systems in generating and sustaining truth, and will show that the nature of truth and objectivity in abstract conceptual systems lie on the intricacies of the underlying bodily-grounded human cognitive mechanisms (e.g., conceptual metaphors, metonymies, analogies, blends) that make them possible.