Article ID: CBB074170500

Mathematics embodied: Merleau-Ponty on geometry and algebra as fields of motor enaction (2022)


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. Furthemore, 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.

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Authors & Contributors
Panza, Marco
Merleau-Ponty, Maurice
Bellosta, Hélène
Rashed, Roshdi
Michel, Alain P.
Nakamura, Shigeru
Foundations of Science
Arabic Sciences and Philosophy
科学史研究 Kagakusi Kenkyu (History of Science)
Science in Context
Physis: Rivista Internazionale di Storia della Scienza
European Legacy
Presses Universitaires de France
Brill Academic
Mathematical Association of America
Duke University
Raffaello Cortina Editore
Philosophy of mathematics
Mathematics and its relationship to science
Philosophy of science
Lagrange, Joseph Louis
Husserl, Edmund
Merleau-Ponty, Maurice
ibn Qurra, Thabit
Ibn al-Haytham, Abū ʿAlī al-Ḥasan
Time Periods
20th century
19th century
18th century
17th century
10th century

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