Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity

  • Teun Koetsier


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.


Rational Number Target Domain Conceptual System Source Domain Conceptual Metaphor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I am grateful to Brendan Larvor and to two anonymous referees for commenting on an earlier version of this paper.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceVrije UniversiteitAmsterdamThe Netherlands

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