Ryan Stringer, a contributor to the internet infidels community, proposes that there are modal arguments for Atheism which have the following form:
A. It is possible that p.
B. Necessarily, if it is possible that God exists, then it is necessary that God exists.
C. Necessarily, if God exists, then it is not the case that p.
D. Therefore, it is not possible that God exists. (from A, B, & C)
Stringer then proposes that modal arguments for Atheism can be generated by simply stipulating values for p. He presents a few suggestions of his own: 1) Gratuitous Evil, 2) All Minds are physically realized, 3′) the world’s metaphysically free, non-God creatures produce more moral evil than moral goodness such that their freedom is not worth the cost, and so on. For his whole article, I invite people to check out this link here. I think this is a valid and interesting way to formulate arguments for Atheism, and the method may be of pedagogical merit for theists as well. Whatever value can stand in for p is something which the theist will have to argue is not only non-actual, but not possible. Take gratuitous evil as an example, about which I’ve written previously; one will find that if gratuitous evil is possible then a maximally great being exists in no possible world, and if a maximally great being exists in any possible world then gratuitous evil exists in no possible world.
Suppose the theist thinks that God’s existence is an analytic truth (as do I); she will then end in thinking that for any value satisfying p, it is an analytic truth that ~p, even if the entailment isn’t obvious to everyone (i.e., it isn’t obvious to those who don’t think theism is an analytic truth and recognize God and p to be logically exclusive). This form of argument can make more obvious to the theist and atheist alike what kinds of things are countenanced as possible on a theistic view of modality.
Now, I anticipate that somebody may object to me by citing a methodological inconsistency on my part. I have said before that as a general methodological rule one should always presume possibility in place of presuming impossibility. In other words, the claim that something is impossible requires a burden of proof not demanded of the more modest claim that something is possible. One should always differ, in the absence of a defeater, to the view which enriches, rather than impoverishes, one’s view of modality. I have even used such a methodological rule to undermine atheological parodies of the ontological argument since the atheological parodies depend on impoverishing rather than enriching the range of the possible. ‘However,’ one may object ‘you forget that if more than one value satisfies p then, by your own methodological rule, you should prefer to accept as possible all values satisfying p instead of preferring to accept the possibility of a maximally great being, shouldn’t you?‘ This is an interesting objection, especially since part of the reason I think theism is an analytic truth is that I think it can be inferred from an obviously sound cosmological argument in combination with (or supplemented by) a logically valid and self-evidently sound ontological argument, and one of the arguments I’ve given for the ontological argument is that the major modal objection against it (which comes from atheological parodies) impoverishes modality such that, as a methodological principle, one should prefer the theological to the atheological conclusion.
However, since nothing which satisfies p is going to be an analytic truth, and since theism seems to be an analytic truth, one cannot argue that just because many values satisfy p one should prefer to accept p as possible even if it entails that theism is impossible. Theism, being an analytic truth, can only be presented to some modal-opponent to which we should differ in its place if that modal-opponent is proposed as an analytic truth. I suspect that there are no values satisfying p which are stipulated as analytic truths, and so no matter how many values satisfy p, the set of such values will never act as a defeater for theism since they are not analytic. The same could be said for values of q satisfying the condition that q⊃~PNC where PNC stands for the principle of non-contradiction.