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EnactionToward a New Paradigm for Cognitive Science$
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John Stewart, Olivier Gapenne, and Ezequiel A. Di Paolo

Print publication date: 2010

Print ISBN-13: 9780262014601

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262014601.001.0001

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Enacting Infinity: Bringing Transfinite Cardinals into Being

Enacting Infinity: Bringing Transfinite Cardinals into Being

Chapter:
(p.307) 11 Enacting Infinity: Bringing Transfinite Cardinals into Being
Source:
Enaction
Author(s):

Rafael E. Núñez

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262014601.003.0012

This chapter argues that cases wherein an empirically observable physical reality is lacking—when there is no pregiven world to be mentally re-presented—are provided by mathematics. In particular, it argues that mathematical infinity, as a form of cognition which by definition is not directly available to experience due to the finite nature of living systems, is an excellent candidate for fully exploring the power of enaction as a paradigm for cognitive science. The chapter focuses on a particular form of actual infinity—or infinity as a complete entity—namely, the transfinite cardinal numbers as they were conceived by one of the most controversial characters in the history of mathematics, the nineteenth-century mathematician Georg Cantor.

Keywords:   empirically observable, physical reality, mathematics, mathematical infinity, enaction, cognitive science, actual infinity, transfinite cardinal numbers, Georg Cantor

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