A new argument for atheism?

Peter Fritz, Tien-Chun Lo, and Joseph C. Schmid wrote a great paper that has been accepted for publication in Nous. They argue that the reverse modal ontological argument for the claim that God doesn't exist avoids in S4 the well-known symmetry problem faced by the modal ontological argument for the existence of God in S5. Now, I've recently posted here a suggestion for a (likely) new symmetry breaker in favor of the modal ontological argument in S5 for God's existence. Yet, the symmetry breaker I propose might not be strong enough.

In what follows I focus on the reverse ontological argument for atheism in S4 as proposed by the authors. Initially, while reading their paper, I thought that their argument might be the first argument for atheism that we cannot immediately refute. I have since read the paper in full, though. My first response was that if the accessibility relation between possible worlds is reasonably taken to be symmetric - as is often done in metaphysical enquiries into possibility and necessity -, then one of their premises (i.e., P1) entails a proposition (i.e., P1*) that they must reject in order to ensure that their argument for atheism doesn't collapse into a logical inconsistency. This, I thought, would seem sufficient to refute the authors' argument. However, while studying their paper, I've come to realize that symmetry might be a property that metaphysicians should actually not ascribe to the accessibility relation between possible worlds, as I further explain in this post. An appeal to symmetry thus seems dialectically to be a "weak move" to refute the authors' argument.

So, does their new argument for atheism stand unrefuted? Not quite. If we plausibly accept a neo-Aristotelian account of modality (according to which something is possible in a possible world just in case that world has the resources to bring it about - or to bring about something that can bring it about, and so on), then the authors' new argument for atheism fails. For on the aforementioned account of modality, it's not difficult to see that the authors should - in addition to accepting premises P1, P2 and P2* - reasonably also accept premise P1*, which then leads to a contradiction. Let me explain why the authors should accept P1* on said account. If God doesn't exist, nothing has the resources to (in)directly bring it about that God exists, so that it is neccesarily true that God doesn't exist.

The neo-Aristotelian account can also be used to motivate P1, as Joseph C. Schmid has pointed out to me in personal communication. Here's why: If God exists, nothing has the resources to (in)directly bring it about that God doesn't exist, so that it follows that God exists necessarily. Now, I take it that it is more plausibly true that nothing can (in)directly create God than that nothing can (in)directly destroy God. Indeed, couldn't perhaps God destroy God? Or couldn't there perhaps be a diabolic entity that may be able to destroy God? But without God, nothing seems to be able to create God. In fact, not even God can create God, since nothing can cause itself. So, given this considerations, I take it that P1* is prima facie more plausibly true than P1. Consequently, the modal ontological argument for God’s existence in S4 (from P1*, P2 and P2* - while not accepting P1 to avoid inconsistency) is prima facie stronger than the modal ontological argument for atheism in S4 (from P1, P2 and P2* - while not accepting P1* to avoid inconsistency). That is to say, the authors' paper actually leads to a new argument for theism in S4. A perhaps surprising conclusion, to say the least.