Halák, Jan (2021) Mathematics Embodied: MerleauPonty on Geometry and Algebra as Fields of Motor Enaction. [Preprint]

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Abstract
This paper aims to clarify MerleauPonty’s contribution to an embodiedenactive account of mathematical cognition. I first identify the main points of interest in the current discussions of embodied higher cognition and explain how they relate to MerleauPonty and his sources, in particular Husserl’s late works. Subsequently, I explain these convergences in greater detail by more specifically discussing the domains of geometry and algebra and by clarifying the role of gestalt psychology in MerleauPonty’s account. Beyond that, I explain how, for MerleauPonty, mathematical cognition requires not only the presence and actual manipulation of some concrete perceptible symbols but, more strongly, how it is fundamentally linked to the structural transformation of the concrete configurations of symbolic systems to which these symbols appertain. Furthermore, I fill a gap in the literature by explaining MerleauPonty’s claim that these structural transformations are operated through motor intentionality. This makes it possible, in turn, to contrast MerleauPonty’s approach to ontologically idealistic and realistic views on mathematical objects. On MerleauPonty’s account, mathematical objects are relational entities, that is, gestalts that necessarily imply situated cognizers to whom they afford a specific type of engagement in the world and on whom they depend in their eventual structural transformations. I argue that, by attributing a strongly constitutive role to phenomenal configurations and their motor transformation in mathematical thinking, MerleauPonty contributes to clarifying the worldly, historical, and sociocultural aspects of mathematical truths without compromising what we perceive as their universality, certainty, and necessity.
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Keywords:  MerleauPonty; phenomenology; enactivism; higherorder cognition; motor intentionality; mathematical reasoning  
Subjects:  Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Proof General Issues > History of Philosophy of Science Specific Sciences > Cognitive Science > Perception 

Depositing User:  Dr. Jan Halák  
Date Deposited:  28 Nov 2021 20:17  
Last Modified:  28 Nov 2021 20:17  
Item ID:  19948  
Subjects:  Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > Proof General Issues > History of Philosophy of Science Specific Sciences > Cognitive Science > Perception 

Date:  2021  
URI:  https://philsciarchive.pitt.edu/id/eprint/19948 
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