Philosophical, Logical, and Experimental routes to substructurality

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Published February 4, 2026 | Version Published online
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Cognitive Modelism

Authors/Creators

  • 1. ROR icon Ruhr University Bochum
  • 2. ROR icon University of Turin

Description

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.

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https://academic.oup.com/philmat/advance-article/doi/10.1093/philmat/nkaf027/8460754

Funding

European Commission
PLEXUS - Philosophical, Logical, and Experimental routes to substructurality 101086295

Dates

Available
2026-02-04

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