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International Studies in Phenomenology and Philosophy

Book | Chapter

209725

Lakatos, Lakoff and Núñez

towards a satisfactory definition of continuity

Teun Koetsier

pp. 33-46

Abstract

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.

Publication details

Published in:

Hanna Gila, Jahnke Hans Niels, Pulte Helmut (2010) Explanation and proof in mathematics: philosophical and educational perspectives. Dordrecht, Springer.

Pages: 33-46

DOI: 10.1007/978-1-4419-0576-5_3

Full citation:

Koetsier Teun (2010) „Lakatos, Lakoff and Núñez: towards a satisfactory definition of continuity“, In: G. Hanna, H. Jahnke & H. Pulte (eds.), Explanation and proof in mathematics, Dordrecht, Springer, 33–46.