Here is an F-inductive argument for theism based on ontologically objective moral values. Note that this argument assumes that such things exist. If you don’t think they exist, then you may want to skip reading this post.
As usual, let B be our background information; E be the evidence to be explained (in this case, the existence of ontologically objective moral values); T be theism; and N be naturalism. Here is the explanatory argument.
1. E is known to be true, i.e., Pr(E) is close to 1. [assumption]
2. N is not intrinsically much more probable than T, i.e., Pr(|N|) is not much greater than Pr(|T|).
3. Pr(E | T) =1 > Pr(E | N).
4. Other evidence held equal, N is probably false, i.e., Pr(N | B & E) < 1/2.
Theism logically entails that moral values such as goodness, badness, and the like are ontologically objective in the sense that their truthmakers are not in any way dependent upon the subjective states of human beings or even intersubjective agreement among all human beings. In other words, if theism is true, it is impossible for metaethical views like nihilism, subjectivism, error theory, and so forth to be true. In contrast, metaphysical naturalism does not entail that moral values are ontologically objective.
Is this a good F-inductive moral argument for theism and against naturalism?
There are many possible objections; I will mention just one. It goes like this.
While it’s true that metaphysical naturalism doesn’t entail that ontologically objective moral values exist, it may be the case that ontologically objective moral values exist necessarily. If that is the case, then this would seem to be a fatal objection to this argument, since it would then be the case that Pr(E | T ) = Pr(E | N) = 1.
In order to fully assess this argument, then, one will need to answer this question: on the assumption that ontologically objective moral values exist, do they exist necessarily?