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 bimodal 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.
Original language  English 

Article number  55 
Number of pages  26 
Journal  Synthese 
Volume  202 
Issue number  55 
DOIs  
Publication status  Published  9 Aug 2023 
Bibliographical note
© The Author(s) 2023Projects

Fictionalist Mathematical Structuralism
Project: Research project (funded) › Research