Abstract
As a result of the increasing popularity of the decoherence-based interpretations of quantum mechanics, various conceptual difficulties have become better understood, particularly with respect to [1] the emergence of the ‘classical’ features of nature from the more fundamental quantum mechanical features; and [2] the problem of relating the local to the global in an extensive continuum—e.g., the infamous problem of relating quantum theory and general relativity. The central difficulty in both of these cases is that the conventional formulation of spatiotemporal extension is grounded in set-theoretic structure, where extension is fundamentally metrical—i.e., such that objects are fundamental to relations.
The solution proposed by philosopher Michael Epperson and physicist and mathematician Elias Zafiris is to delve beneath this set theoretic framework to the more substrative category theoretic framework where extension is fundamentally topological rather than metrical. In this way, fundamental quanta are defined as ‘units of logico-physical relation’ rather than ‘units of physical relata.’ By this framework, objects are always understood as relata, such that objects and relations are mutually implicative. This work is presented in a forthcoming volume, co-authored by Epperson and Zafiris, Foundations of Relational Realism: Quantum Mechanics, Category Theory, and the Philosophy of Process, Lexington Books (2013).