The aim of this article is to draw a sketch of an ontology for Realist Non-Naturalist Cognitivists. A distinction is made between moral property-universals and moral property-particulars. It is argued, first, that moral property-universals have the same ontological status as non-moral property-universals; second, that moral property-universals have many instances in the spatio-temporal world; third that these moral property-instances or -particulars have the same ontological status as non-moral property-particulars.

Many hope that our values, purged of messy human contingency, could aspire to correspond with mind-independent, rationally obligatory, and eternal ethical facts. But if the arguments of this thesis are on the right track, we should reject the search for non-natural and mind-independent moral truths.

I argue for the viability of one neglected way of developing supervenience-based objections to metaethical non-naturalism. This way goes through a principle known as ‘Hume’s Dictum’, according to which there are no necessary connections between distinct existences. I challenge several objections to the Hume’s Dictum-based argument. In the course of doing so, I formulate and motivate modest and precise versions of Hume’s Dictum, illustrate how arguments employing these principles might proceed, and argue that the Hume’s Dictum argument enjoys some advantages (...) relative to other supervenience-based objections to non-naturalism. (shrink)

Explaining the supervenience of the moral on the natural is, perhaps, the central metaphysical challenge for the non-naturalist. However, Scanlon (2014) and Fogal and Risberg (2020) have developed a strategy which purports to explain supervenience rather simply. Fogal and Risberg call it the 'Divide and Conquer' strategy. The key idea is to postulate explanatory moral principles linking the natural and the moral. The moral principles are metaphysically necessary, so trivially supervene on the natural. All other moral facts are determined by (...) the necessary moral principles and the natural facts, so they supervene on the natural too. -/- I argue that there are two versions of the Divide and Conquer strategy and both fail. The first strategy doesn’t give an adequate explanation of supervenience because it doesn't properly identify what makes a difference to the holding of supervenience. The second perhaps does give an adequate explanation of supervenience, but only by introducing something similarly puzzling that needs explanation. -/- Consequently, non-naturalists need additional metaphysical machinery to develop their view -- just appealing to moral principles or metaphysical laws won't do the job. (shrink)

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. (shrink)