One can run a minimal modal ontological argument for naturalism with just two simple premises:
1. Possibly, there is a necessarily existent essentially natural thing or stuff.[1] (i.e., the two properties are compossible).
2. What's necessary doesn't vary from possible world to possible world.
3. Therefore, there is a necessarily existent essentially natural thing or stuff.
(2) follows from Axiom S5 of S5 modal logic, and most philosophers accept S5, so it's fairly uncontroversial. So the argument comes down to the plausibility of (1). But (1) just says that being necessarily existent and being an essentially natural thing or stuff are compossible properties, which seems more plausible than the theistic possibility premise in the corresponding modal ontological argument for theism. For the truth of the latter premise requires acceptance of the compossibility of a large swath of exotic properties, such as omnipotence, omniscience, moral perfection, immateriality, and the capacity for creating individuals and/or stuffs out of nothing. It also requires the possibility of personal attributes being instantiated as basic, rather than derivative, properties, which is contrary to experience and our best scientific theories. Therefore, it appears that one has more reason to accept the minimal modal ontological argument for naturalism than the standard modal ontological argument for theism.
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[1] Or whatever ultimately composes natural things: quantum fields; wavefunction stuff (whether in ordinary 3-space or a massively higher-dimensional Hilbert space); physical forces; symmetries or invariances; the strings of string theory; the entities of causal set theory or loop quantum gravity, etc. Henceforth assume this qualification when left unstated.
