Mathematics Embodied: Merleau-Ponty on Geometry and Algebra as Fields of Motor Enaction

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15210%2F22%3A73608585" target="_blank" >RIV/61989592:15210/22:73608585 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/content/pdf/10.1007/s11229-022-03526-z.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s11229-022-03526-z.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11229-022-03526-z" target="_blank" >10.1007/s11229-022-03526-z</a>

Result language

angličtina

Original language name

Mathematics Embodied: Merleau-Ponty on Geometry and Algebra as Fields of Motor Enaction

Original language description

This paper aims to clarify Merleau-Ponty’s contribution to an embodied-enactive 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 Merleau-Ponty 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 Merleau-Ponty’s account. Beyond that, I explain how, for Merleau-Ponty, 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 Merleau-Ponty’s claim that these structural transformations are operated through motor intentionality. This makes it possible, in turn, to contrast Merleau-Ponty’s approach to ontologically idealistic and realistic views on mathematical objects. On Merleau-Ponty’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, Merleau-Ponty contributes to clarifying the worldly, historical, and socio-cultural aspects of mathematical truths without compromising what we perceive as their universality, certainty, and necessity.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

60301 - Philosophy, History and Philosophy of science and technology

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SYNTHESE

ISSN

0039-7857

e-ISSN

1573-0964

Volume of the periodical

200

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

28

Pages from-to

1-28

UT code for WoS article

000760246100004

EID of the result in the Scopus database

2-s2.0-85125468075