Some Philosophical Remarks on the Concept of Structure: Framing Michał Heller’s Perspective

Abstract

Perceiving objects in a structural or relational way in the ontology of physics and mathematics, as opposed to the classical way, shows how the concept of structure remains crucial for contemporary philosophy of physics and philosophy of science. In this paper, a particular emphasis is placed on certain philosophical concepts proposed by Michał Heller, concerning the context of the structural understanding of theories and the world. The first aim is to provide a general critical survey of the main assumptions of structural realism (SR). The second aim is to interpret Heller’s philosophy of structure in accordance with the principal tenets of SR, illuminating certain criticisms of Heller’s approach. Having analyzed Heller’s approach, a question arises concerning the type of dependence on structuralism in the philosophy of physics and the philosophy of mathematics, in addition to certain metaphysical assumptions regarding the concept of structure. It is argued that Heller’s SR conflates the adoption of mathematical structures in theories (the case of the realism–anti-realism debate) with the debate on mathematical explanations and the explanatory role of mathematical constraints.