Gesturing mathematics a pragmatist-enactive perspective

The article explores the theoretical elements that can support a pragmatist-enactive approach to mathematical cognition through the concept of "gesture." Exploring this conceptual tool highlights its potential fruitfulness in understanding the development of mathematical reasoning from a sensorimotor perspective, offering a possible solution to filling the cognitive gap between contentless and contentful forms of cognition. The main aim of the article is to propose a pluralistic approach to gesture that seeks to combine multiple related meanings of gesture through shared features related to the motility, continuity, directionality, and communicativeness of gesture-considering these different meanings as evolving via biological, ecological, and cultural processes. This evolution is accompanied by a semantic complexification of the concept as it progresses towards greater abstraction. The article first analyses recent theories on the embodied and enacted origins of mathematical cognition to deploy this proposal. After that, it introduces the work of mathematician Giuseppe Longo, which focuses on the importance of gesture in mathematical cognition. Longo's proposal presents valuable insights but raises criticisms about his interpretation of intentionality and gesture. In particular, his broad interpretation of intention may be misleading. Furthermore, Longo employs four distinct meanings of "gesture," resulting in theoretical confusion. To clarify these issues, I suggest framing Longo's argument within a pragmatist context. From this perspective, gesture is the sensorimotor element that contributes to the making-sense processes in interactions between organisms and between organisms and their environment, which underlie the emergence of abstract language and formal reasoning. Gesture is thus both central to biosemiotic processes and essential to the sensorimotor coordination that makes the graphic sign useful to abstract concepts. The main aim of the article is to propose a pluralistic approach to gesture that seeks to integrate multiple meanings of gesture closely related through common features-motility, continuity, direction, and communication-regarding these different meanings as evolving through biological, ecological, and cultural processes, which are accompanied by a semantic complexification of the concept as we move towards greater abstraction. This investigation is part of a broader project that aims to promote a Pragmatist Enactivism, which seeks to consolidate the "pragmatic turn" in 4EA cognition (embodied, embedded, extended, enacted, affective).