Mathematics, Form and Function: Difference between revisions

Revision as of 15:56, 4 March 2012

Revision as of 00:32, 8 April 2012

Line 2:

== Mac Lane's relevance to the philosophy of mathematics ==

Mac Lane founded (with [[Samuel Eilenberg]]) [[category theory]], which enables a [[unifying theories in mathematics|unified treatment]] of mathematical structures and of the relations among them, at the cost of [[abstract nonsense|breaking away from their cognitive grounding]]. Nevertheless, his views&mdash;however informal&mdash;are a valuable contribution to the [[philosophy of mathematics|philosophy]] and [[anthropology]] of mathematics.<ref>On the anthropological grounding of mathematics, see White (1947) and Hersh (1997).</ref> His views anticipate, in some respects, the much richer and more detailed account of the [[cognitive science of mathematics|cognitive basis of mathematics]] given by [[George Lakoff]] and [[Rafael E. Núñez]] in their ''[[Where Mathematics Comes From]]''. Lakoff and Núñez argue that mathematics emerges via [[conceptual metaphor]]s grounded in the [[embodied philosophy|human body]], its motion through [[space]] and [[time]], and in human sense perceptions.

== Mathematics and human activities==