(The following is a revised version of my “Arguing from Moral Ontology by Eliminating Nontheistic Alternatives.”)
2. The Argument from First-Order Ethical Beliefs for Objective Moral Properties
(2) There are no empirical or a priori reasons to believe that first-level moral beliefs are all false.
(3) It is more reasonable to believe there are objective moral properties than not to believe this.
(4) There is no reason to believe that the conjunction of (1) and (2) is a defective reason to believe objective moral properties.
(5) Therefore, the belief in objective moral properties is indefeasibly justified.
(6) Therefore, there are objective moral properties.
(See here for more about this argument.)
Let E be the failure of ethical naturalists to locate the exact identity of natural moral properties.
(7) E is known to be true.
(8) E is more probable on the assumption that ethical naturalism is false than on the assumption that ethical naturalism is true.
(9) The prior probability of ethical naturalism is not significantly higher than its denial.
(10) Therefore, other evidence held equal, ethical naturalism is probably false.
The following argument was inspired by William Lane Craig. Craig writes:
First, it’s difficult even to comprehend this view. What does it mean to say, for example, that the moral value Justice just exists? It’s hard to know what to make of this. It is clear what is meant when it is said that a person is just; but it is bewildering when it is said that in the absence of any people, Justice itself exists. Moral values seem to exist as properties of persons, not as mere abstractions—or at any rate, it is hard to know what it is for a moral value to exist as a mere abstraction. Curiously, since the abstract object Justice is not itself just (just as Quickness is not quick or Laziness lazy), it would seem to follow that in the absence of any people justice does not exist—which seems to contradict the hypothesis! Atheistic moral Platonists seem to lack any adequate foundation in reality for moral values but just leave them floating in an unintelligible way.
This suggests the following argument. (Not that Craig would agree with it in its present form.)
(11) If ethical non-naturalism is true, then moral properties can exist as mere abstractions, i.e., even in the absence of any people.
(12) The hypothesis that moral properties can exist as mere abstractions is unintelligible.
(13) If a hypothesis is unintelligible, it is probably false.
(14) Therefore, ethical non-naturalism is probably false.
5. The Moral Ontological Argument against Metaphysical Naturalism
(6) There are objective moral properties.
(15) If there are any objective moral properties, they must be natural, nonnatural, or supernatural properties.
(16) Objective moral properties are not natural properties. [from (10)]
(17) Objective moral properties are not nonnatural properties. [from (14)]
(18) Therefore, objective moral properties must be supernatural properties. [from (6), (15), (16), and (17)]
(19) If there are supernatural properties, there exists at least one supernatural being. [by definition]
(20) Metaphysical naturalism entails the nonexistence of supernatural beings.[by definition]
(21) Therefore, metaphysical naturalism is false. [from (18)-(20)]