In this post want to look at a scenario in which an 'a posteriori' theistic argument is defeated by an 'a posteriori' difficulty. For simplicity's sake we will consider only one theistic argument*, the Aristotelian proof from motion which forms the basis of the First Way. Now imagine a person, let's call him McX. McX considers the reasoning behind the proof, and the conclusions it reaches - indeed he considers it correct were it not for a sole 'empirical' defeating objection, the Law of Inertia or the existence of self-moved animals.

With that in mind he should not object to us putting his reasoning in a counter-factual manner: were it not the case that such and such then the proof from motion would go through. However I would argue that this is all we need for a successful (though maybe weaker) proof of God.

Consider: McX is using exactly the same arguments as a Thomist does to understand God and he admits these arguments and their conclusions are logically coherent - they would have worked had the world been another way. This implies the possibility of a necessary, simple being: a necessary being, a being in which Essence and Existence are one, cannot be merely contingently non-existent though: if it's possible it must be actual.

Objection: depending on what account of the Laws of Nature one holds this argument forms a species of per impossible reasoning. This is true and would weaken it somewhat but I don't think it constitutes a fatal objection. An impossible antecedent need not have an impossible consequent. If I could travel faster than the speed of light (taking this to be metaphysically impossible) I could stand at the magnetic pole of a planet in the Andromeda galaxy tomorrow - the latter is not a logical impossibility even though it comes about as a consequence of one. Here we fall back on modal intuitions and I say they're in our favour.

(The animals as self-movers objection is free from this difficulty as we all admit it’s possible for there not have been any contingent living beings)

Even if the above provides the atheist with a bolt-hole the reasoning here just highlights the price atheists must pay if they want to take the Laws of Nature to be contingent i.e. only Nomologically necessary. If taken so then laws of physics e.g. Inertia could be otherwise - if that's the case there's a possible world in which the First Way goes through, and a divine simple being exists. We all know what follows from that. To conclude: if a theistic proof fails then its failure cannot be a merely contingent one.