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(2010) Explanation and proof in mathematics, Dordrecht, Springer.
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
DOI: 10.1007/978-1-4419-0576-5_3
Full citation:
Koetsier, T. (2010)., Lakatos, Lakoff and Núñez: towards a satisfactory definition of continuity, in G. Hanna, H. N. Jahnke & H. Pulte (eds.), Explanation and proof in mathematics, Dordrecht, Springer, pp. 33-46.
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