Workshop “From Basic Cognition to Mathematical Practices”

University of Seville, Institute of Mathematics (IMUS), 19-21 Sept. 2016

In recent years, much discussion has been devoted to the relation between cognition and mathematical practice, thanks to the work of cognitive scientists, philosophers and historians of mathematics devoted to the topic. Initially, the investigation focused in particular on the question which ‘core’ cognitive systems might ground several mathematical notions and results — especially the number concept, but also elementary geometry. More recently it has moved towards discussion of mathematics as a product of ’embodied cognition’, evaluating the role of conceptual metaphors, bodily experience, and external representations in mathematical practice and mathematical understanding.

Some of these proposals claim that mathematics is a unique type of human conceptual system, which is sustained by specific neural activity and bodily functions, and brought forth via the recruitment of everyday cognitive mechanisms that make human imagination, abstraction, and notation-making processes possible. The question of the nature of mathematics has been addressed as an empirical question subject to methodological investigations of an interdisciplinary nature, involving hypothesis testing.

At the same time, however, such claims have been received with skepticism, be it that they are considered premature or because their actual links with mathematical knowledge (properly speaking) are found wanting.

This workshop will address the question, what brings us from basic cognition to the practice of mathematics, gathering together scholars from different disciplines with the aim to develop common points of view. The focus will be, primarily, on what separates mathematics properly speaking from basic cognition, and which cognitive ingredients may act as bridges between both.

The invited speakers are: Valeria Giardino (CNRS/Archives Poincaré, Nancy), Rafael Núñez (UC San Diego), and Dirk Schlimm (McGill Univ.).

Contributed papers will be welcome on topics relevant to the workshop such as the following:

– basic cognitive systems and processes of mathematical conceptualization

– the role of external representations (diagrams and/or notation) in the practice of mathematics

– possibilities and limits to the interaction between cognitive science and the philosophy of mathematics

– the role of conceptual metaphors in the practice of mathematics; mathematics and the body (e.g. the role of gestures)

– the nature of mathematics as an empirical question subject to methodological investigations of an interdisciplinary kind.

Proposals should be of a max. length of 500 words. Please send them to María de Paz. The call for papers is open until May 27.

Organizing comité: José Ferreirós, María de Paz, María de Ponte.