EA: I'm wondering what sort of evidence one could have for the version of PSR that's supposed to entail (5). It seems to me that it would have to be something along the lines that it's a synthetic a priori proposition or, what, an inductive "track record" argument, or perhaps that it's a presupposition of reason? Whatever it may be, is it strong enough to undermine the intuition of the seeming possibility of a logically contingent, yet metaphysically independent ("free-standing"), being (something along the lines of Swinburne's conception of God)? My intuition is that if any version of PSR entails that such a being is metaphysically impossible, then so much the worse for that version of PSR. For it seems to me to be explanatory overkill to require an explanation of such a being -- i.e., a logically (even metaphysically) contingent, yet eternal being that has, say, indestructibility (or at least the world-indexed essential property of being indestructible-in-alpha, the actual world) as an essential property."
VR: I’m wondering if this is enough to block an argument in defense of something like theism against naturalism. The very idea of “indestructible-in-alpha” strikes me as incoherent. “Indestructible” is a claim with modal force, therefore it can’t be a world-indexed property. Do you just mean “not actually destroyed in alpha?” So how contingent is this being, really?
Of course even at best cosmological argument doesn’t prove the existence of a being omniscient, omnipotent and perfectly good, or a personal God, etc. However, if successful it does refute the naturalistic view that the physical world is all that exists.
Cosmological arguments have to deal with the termination problem. What characteristics are needed to terminate the chain of explanations? The Unmoved Mover argument holds that explanations cannot terminate in that which is in motion, but must rather terminate in an ummoved mover. The argument from contingency holds that the physical world is contingent, and therefore depends on something that is not contingent—that is, necessary. Perhaps we can develop the “argument from destructibility.” Whatever is destructible must depend for its existence on what is not destructible.
Of course, naturalistic cosmological argument critics maintain that there if we extend causal reasoning beyond the space-time manifold, there are no “termination-making characteristics” that can be applied to God but not to the physical universe. That’s the claim to be found in Parsons’ atheist manifesto. There are two ways of casting this issue. One is to suppose that a naturalistic world is beginningless. Does that beginningless world possess all the termination-making characteristics?
The matter gets more complicated when we accept the Standard Big Bang theory. With this picture the universe had a temporal beginning. Now that beginning is the beginning of time itself, so unlike the case of a Bengal tiger popping into existence, there is no time before the universe exists, when time exists and the universe does not. I have a strong intuition that nevertheless this does not dissipate the sense that there must be a cause of the physical universe. Does it make sense to say that the universe had a beginning moment but cannot possibly have a final moment?