Moral ontology is the branch of meta-ethics concerned with the ontology or metaphysics of moral facts and properties. Within the field of moral ontology, it is a commonplace that the nature of moral facts and properties fall into one of three categories: natural, nonnatural, or supernatural. Natural facts and properties are those facts and properties studied by the natural and social sciences, including sociology, psychology, and biology. Supernatural facts and properties are those facts and properties studied by religion and theology. Nonnatural facts and properties are a bit harder to define. In the broad sense, the nonnatural refers to anything that is not natural and hence includes the supernatural. In the narrow sense, nonnatural facts and properties are irreducible, sui generis facts and properties that cannot be further analyzed or explained. Unless otherwise stated, I shall use the term ‘nonnatural’ in the narrow sense.
Ethical naturalism is the view that moral facts and properties are nothing but natural facts and properties, whereas ethical supernaturalism is the view that moral facts and properties are nothing but supernatural facts and properties. Since both ethical naturalism and ethical supernaturalism claim that moral facts and properties ultimately reduce to some other type of facts and properties, the two theories may be grouped together as ‘reductive’ theories. In contrast, ethical nonnaturalism is non-reductive, since it claims that moral facts and properties are irreducible.
Unfortunately, many writers assume that moral objectivism entails ethical nonnaturalism. Geoffrey Sayre-McCord observes, “Objectivism in ethics has suffered from the mistaken assumption that objectivists must hold that moral properties are nonnatural …”. The metaphysical nature of moral properties can only be determined by a thesis about moral semantics, not by the “metaphysically neutral” theory of moral objectivism. Mere (moral) objectivism neither logically entails nor makes probable the view that moral properties are nonnatural properties. As John Post writes, moral objectivism does not require “some shadowy Platonic realm ‘out there,’ perhaps beyond space and time.” Rather, moral objectivism is simply the view that there is an objective “truth of the matter as regards the correctness or incorrectness of our value judgments.”
Here I want to sketch one way to formulate an argument from moral ontology to theism which I haven’t seen explicitly discussed as such in the literature on religion and morality. One method of arguing from objective moral truths to traditional theism is by a process of elimination: start with the premise that objective moral truths exist and then show that objective moral truths cannot be natural or nonnatural properties. Although I am not aware of anyone who has explicitly defended just such an argument in precisely that way, Michael Beaty, Carlton Fisher, and Mark Nelson allude to such an argument in a recent essay. More formally, such an argument may be formulated as follows:
(1) There are objective moral truths.
(2) If there are any objective moral truths, they must be truths about natural, nonnatural, or supernatural facts or properties.
(3) Objective moral truths are not truths about either natural or nonnatural facts or properties.
(4) Therefore, objective moral truths must be truths about supernatural facts or properties. [from (1)-(3)]
(5) If theism were true, we would expect supernatural facts or properties to exist.
(6) If metaphysical naturalism were true, supernatural facts or properties would not exist.
(7) Therefore, theism is probably true. [abductive inference from (4)-(6)]
 Geoffrey Sayre-McCord, “Introduction: The Many Moral Realisms” Essays on Moral Realism (ed. Geoffrey Sayre-McCord, Ithaca: Cornell University Press, 1988), 20.
 David O. Brink, Moral Realism and the Foundations of Ethics (New York: Cambridge University Press, 1989), 22.
 John F. Post, The Faces of Existence: An Essay in Nonreductive Metaphysics (Ithaca: Cornell University Press, 1987), 252, 256.
 Michael Beaty, Carlton Fisher, and Mark Nelson, “Editors’ Introduction” Christian Theism and Moral Philosophy (Macon, Georgia: Mercer University Press, 1998), 2-13.