Abstract

This paper seeks to utilize mathematical methods to formally define and analyze the metaethical theory that is ethical reductionism. In contemporary metaethics, realist-antirealist debates center on the ontology of moral properties. Our research reflects an innovative methodology using methods from Graph Theory to clarify a debated position of Meta-Ethics, previously encumbered by intrinsic vagueness and ambiguity. We employ rigorous mathematical formalism to symbolize, parse, and thus disambiguate, particular philosophical questions regarding ethical ontological materialism of the reductionist variety. In this paper, we seek to revisit the once vexed question regarding the multiple-realizability of moral properties by employing the mathematical machinery of hypergraphs and category theory. The utilization of Mathematical formalism offers explanatory flexibility specifically to the hypothesis that there are potentially an infinite number of unrelated subvening facts which may constitute supervening moral properties. We by no means have attempted to settle the argument on the side of naturalism, but have only identified an obstacle to rigorous argumentation, and pioneered a method to eliminate it. We hope our research will be of interest to both the Analytic Philosophy and the Applied Mathematics communities, and will help facilitate discussions of metaethics, particularly pertaining to ethical naturalism. We believe there is much research yet to be done.