Motivated by examples from general relativity and Newtonian gravitation, this essay attempts to distinguish between the dynamical structure associated with a theory in physics, and its kinematical structure. This enables a distinction to be made between a structural realist interpretation of a theory based on its dynamical structure, and a structural realist interpretation of spacetime, as described by a theory, based on its kinematical structure. I offer category-theoretic formulations of dynamical and kinematical structure and indicate the extent to which such (...) formulations deflect recent criticism of the radical ontic structural realist's conception of structure as "relations devoid of relata". (shrink)

Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called “substitutional”. In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, (...) is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the Nominalist’s reach. (shrink)

Radical Ontic Structural Realism (ROSR) claims that structure exists independently of objects that may instantiate it. Critics of ROSR contend that this claim is conceptually incoherent, insofar as, (i) it entails there can be relations without relata, and (ii) there is a conceptual dependence between relations and relata. In this essay I suggest that (ii) is motivated by a set-theoretic formulation of structure, and that adopting a category-theoretic formulation may provide ROSR with more support. In particular, I consider how a (...) category-theoretic formulation of structure can be developed that denies (ii), and can be made to do work in the context of formulating theories in physics. Keywords: structural realism, category theory, general relativity.. (shrink)

Radical ontic structural realism (ROSR) asserts an ontological commitment to ‘free-standing’ physical structures understood solely in terms of fundamental relations, without any recourse to relata that stand in these relations. Bain ([2013], pp.1621–35) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category theory (...) does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalizations of general relativity do not warrant the claim that these theories describe ‘object-free’ structures. We conclude that category theory offers little if any comfort to ROSR. 1 Introduction: Ridding Structures of Objects2 The Set-theoretic Peril for Radical Ontic Structural Realism3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism4 Throwing out the Relations with the Relata5 Categorial and Set-theoretical Structures6 Radical Suggestions from Topological Quantum Field Theory?7 Sheaves of Einstein Algebras as Radical Structures?8 Conclusions. (shrink)