Titel
Structuralism and informal provability
Autor*in
John Wigglesworth
University of York
Abstract
Mathematical structuralism can be understood as a theory of mathematical ontology, of the objects that mathematics is about. It can also be understood as a theory of the semantics for mathematical discourse, of how and to what mathematical terms refer. In this paper we propose an epistemological interpretation of mathematical structuralism. According to this interpretation, the main epistemological claim is that mathematical knowledge is purely structural in character; mathematical statements contain purely structural information. To make this more precise, we invoke a notion that is central to mathematical epistemology, the notion of (informal) proof. Appealing to the notion of proof, an epistemological version of the structuralist thesis can be formulated as: Every mathematical statement that is provable expresses purely structural information. We introduce a bi-modal framework that formalizes the notions of structural information and informal provability in order to draw connections between them and confirm that the epistemological structuralist thesis holds.
Stichwort
General Social SciencesPhilosophyMathematical StructuralismModal SemanticsInformal ProvabilityMathematical Epistemology
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:1763840
Erschienen in
Titel
Synthese
Band
202
Ausgabe
2
ISSN
1573-0964
Erscheinungsdatum
2023
Verlag
Springer Science and Business Media LLC
Erscheinungsdatum
2023
Zugänglichkeit
Rechteangabe
© The Author(s) 2023

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