WiP - Lorenzo Rossi / Cognitive Modelism
WiP - Lorenzo Rossi / Cognitive Modelism
Wednesday our Work in Progress series welcomes Lorenzo Rossi, from the University of Turin, who will presentjoint work with Matteo De Benedetto of Ruhr-Universität Bochum, abstracted below.
Structures are ubiquitous in mathematics. But how should they be understood? Modelists argue that they should be understood as model-theoretic structures (Button and Walsh, 2018). This thesis can be understood in at least two fundamental ways: as a thesis on how we talk about set-theoretic structures, or as a thesis on how we conceptualize them. Objects-modelism, as articulated by Button and Walsh, developed the first thesis, while the second one leads to concepts-modelism, which however did not receive much attention. In this paper, we articulate and defend a version of concepts-modelism, which we call cognitive modelism, by building upon recent cognitive science of mathematical concepts and conceptual development. More specifically, we employ Carey’s (2009) theory of core cognition, in its application to mathematical concepts. We then show how cognitive modelism addresses the challenges that Button and Walsh pose for the development of a conceptual account of mathematical structures, and observe some of its implications for classical foundational debates in the philosophy of mathematics.