Cognitive Modelism
Year: 2025
Type: article
Abstract: Structures are ubiquitous in mathematics. But how should they be understood? Modelists claim they are model-theoretic structures. This thesis can be read in two ways: as a claim about what structures refer to, or about how we conceptualize them. Objects-modelism, developed by Button and Walsh, pursues the first; the second leads to concepts-modelism, which remains underexplored. In this paper we develop and defend a version of concepts-modelism, cognitive modelism, drawing on Carey’s theory of conceptual development, and we show how it addresses the challenges Button and Walsh pose for a conceptual account of mathematical structures.
Source: Philosophia Mathematica
Authors: Matteo De Benedetto, Lorenzo Rossi
Institutions: IMT School for Advanced Studies Lucca, University of Turin
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,533
OpenAlex ID: W7128051399