Lakatos, Lakoff and Núñez: Towards a satisfactory definition of continuity

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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. © 2010 Springer-Verlag US.

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Koetsier, T. (2010). Lakatos, Lakoff and Núñez: Towards a satisfactory definition of continuity. In Explanation and Proof in Mathematics: Philosophical and Educational Perspectives (pp. 33–46). Springer US. https://doi.org/10.1007/978-1-4419-0576-5_3

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