Authors
Valeria Giardino
Centre National de la Recherche Scientifique
Abstract
In the first part of the paper, previous work about embodied mathematics and the practice of topology will be presented. According to the proposed view, in order to become experts, topologists have to learn how to use manipulative imagination: representations are cognitive tools whose functioning depends from pre-existing cognitive abilities and from specific training. In the second part of the paper, the notion of imagination as “make-believe” is discussed to give an account of cognitive tools in mathematics as props; to better specify the claim, the notion of “affordance” is explored in its possible extension from concrete objects to representations.
Keywords embodied cognition, embodied mathematics, cognitive tools, manipulative imagination, “make-believe”, affordances
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DOI 10.1387/theoria.17871
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References found in this work BETA

Metaphors We Live By.George Lakoff & Mark Johnson - 1980 - University of Chicago Press.
Perceptual Symbol Systems.Lawrence W. Barsalou - 1999 - Behavioral and Brain Sciences 22 (4):577-660.
The Ecological Approach to Visual Perception.Marc H. Bornstein - 1980 - Journal of Aesthetics and Art Criticism 39 (2):203-206.
Metaphors We Live By.Max Black - 1980 - Journal of Aesthetics and Art Criticism 40 (2):208-210.

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“Free rides” in Mathematics.Jessica Carter - forthcoming - Synthese:1-24.

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