Goals shape means: a pluralist response to the problem of formal representation in ontic structural realism

Abstract

The aim of the paper is to assess the relative merits of two formal representations of structure, namely, set theory and category theory. The purpose is to articulate ontic structural realism (OSR). In turn, this will facilitate a discussion on the strengths and weaknesses of both concepts, and will lead to a proposal for a pragmatics-based approach to the question of the choice of an appropriate framework. First, we present a case study from contemporary science—a comparison of the formulation of quantum mechanics in a language of Hilbert spaces and abstract \(C^\star \)-algebras. It is then shown how the method of structural representation can be determined based on the pragmatics of goal-oriented research, not a dogmatic choice. We investigate a hypothesis stating that use of the interplay between the powers of abstraction and detail of different representational methods results in adopting a pluralistic, as opposed to standard, unificatory, perspective on the role of structural representation in OSR.