Benjamin Eva

ABSTRACT Topos quantum theory is standardly portrayed as a kind of ‘neo-realist’ reformulation of quantum mechanics.1 1 In this article, I study the extent to which TQT can really be characterized as a realist formulation of the theory, and examine the question of whether the kind of realism that is provided by TQT satisfies the philosophical motivations that are usually associated with the search for a realist reformulation of quantum theory. Specifically, I show that the notion of the quantum state is problematic for those who view TQT as a realist reformulation of quantum theory. 1Introduction 2Topos Quantum Theory 2.1Phase space 2.2Hilbert space 2.3Beyond Hilbert space 2.4Defining realism 2.5The spectral presheaf 2.6The logic of topos quantum theory 3Interpreting States in Topos Quantum Theory 4Interpreting Truth Values and Clopen Subobjects in Topos Quantum Theory 4.1Interpreting the truth values 4.2Interpreting Subcl 5Neo-realism 5.1The covariant approach 6Conclusion

As a metaphysical theory, radical ontic structural realism is characterised mainly in terms of the ontological primacy it places on relations and structures, as opposed to the individual relata and objects that inhabit these relations/structures. The most popular criticism of ROSR is that its central thesis is incoherent. Bain attempts to address this criticism by arguing that the mathematical language of category theory allows for a coherent articulation of ROSR’s key thesis. Subsequently, Wüthrich and Lam and Lal and Teh have criticised Bain’s arguments and claimed that category theory fares no better than set theory in coherently articulating the main ideas of ROSR. In this paper, we defend Bain’s main arguments against these critiques, and attempt to elaborate on the sense in which category theory can be seen as providing a coherent articulation of ROSR. We also consider the relationship between ROSR and Categorical Quantum Mechanics.