Lakatos, Lakoff and Núñez
towards a satisfactory definition of continuity
pp. 33-46
in: Gila Hanna, Hans N. Jahnke, Helmut Pulte (eds), Explanation and proof in mathematics, Berlin, Springer, 2010Abstract
Lakoff and Núñez have argued that all of mathematics is a conceptual system created through metaphors on the basis of the ideas and modes of reasoning grounded in the sensory motor system. This paper explores this view by means of a Lakatosian reconstruction of the history and prehistory of the intermediate-value theorem, in which the notion of continuity plays an essential role. I conclude that in order to give an acceptable description of the actual development of mathematics, Lakoff's and Núñez's view must be amended: Mathematics can be viewed as a system of conceptual metaphors; however, it is permanently refined through proofs and refutations.
