Abstract
https://www.csuchico.edu/phil/colloquium-series/index.shtml
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 a set-theoretic structure, where extension is fundamentally metrical. In this way, objects are understood in the classical sense as fundamental to relations—i.e., relations presuppose objects but objects do not presuppose relations. Prior to quantum mechanics, this deficiency went largely unnoticed; but since it is a signature feature of quantum mechanics that it definitively proscribes specifying the existence of objects in abstraction from their relations, the attempt to depict quantum mechanical extensiveness as fundamentally metrical—again, such that objects are more fundamental than relations—is doomed from the beginning.
The solution proposed by philosopher Michael Epperson and physicist and mathematician Elias Zafiris is to delve beneath this set theoretic framework and explore the more substrative category theoretic framework, where extension is understood as fundamentally mereotopological 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 not only do relations presuppose objects, but objects presuppose relations. In this way, objects and relations are properly understood as mutually implicative, precisely as exemplified in quantum mechanics. This work is presented in a forthcoming volume, co-authored by Epperson and Zafiris, Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature, Lexington Books (2013).