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. (shrink)

Enactivists frequently argue their account heralds a revolution in cognitive science: enactivism will unseat cognitivism as the dominant paradigm. We examine the lines of reasoning enactivists employ in stirring revolt, but show that none of these prove compelling reasons for cognitivism to be replaced by enactivism. First, we examine the hard sell of enactivism: enactivism reveals a critical explanatory gap at the heart of cognitivism. We show that enactivism does not meet the requirements to incite a paradigm shift in the (...) Kuhnian sense—there is no internal crisis in cognitivism. Nor does it provide inherently better explanations of cognition as some have claimed. Second, we consider the soft sell of enactivism: enactivism provides a more attractive, parsimonious, or clear-eyed lens on cognition. This move proves to boil down to a misunderstanding of how theories are selected in science. Instead we lend support to a broader and more desirable way to conceive of enactivism, the recent proposal that enactivism is a philosophy of nature. We explain how a philosophy of nature does more than support a single research paradigm by integrating scientific questions into a cohesive picture. (shrink)

Clarke and Beck rightly contend that the number sense allows us to directly perceive number. However, they unnecessarily assume a representationalist approach and incur a heavy theoretical cost by invoking “modes of presentation.” We suggest that the relevant evidence is better explained by adopting a radical enactivist approach that avoids characterizing the approximate number system as a system for representing number.