Geodesic
On Conceptual Metaphors In Mathematics
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 9 (2017) no. 1, pp. 85-98.

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This paper contains a few critical remarks concerning some fundamental assumptions and claims propagated by Lakoff and Núñez in their monograph Lakoff, Núñez (2000). Our attitude is skeptical (cf. also Pogonowski,2011). We agree with the idea that conceptual metaphors may play some role in the formation of elementary mathematical notions. However, we disagree with the authors’ claim that such metaphors provide the main mechanism in the emergence of new notions in advanced mathematics.
Keywords: conceptual metaphor, embodied cognition, analogy 
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Pogonowski, Jerzy. On Conceptual Metaphors In Mathematics. Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 9 (2017) no. 1, pp. 85-98. http://geodesic.mathdoc.fr/item/AUPCDM_2017_9_1_a3/