This is a redated post, once again. The dialogue between exapologist and Steve in the comments may help to support, or not, my responses to Parsons on Secular Outpost two posts back.
In reading Steve Lovell's comments on the gap between the claim that the physical universe is contingent on the one hand, and the claim that it is dependent on the other, I think some version of the principle of sufficient reason is supposed to do th is kind of work. So I am redating this post on Wainwright's treatment of the Thomistic argument.
In trying to make sense of the Thomistic cosmological argument, I have found William Wainwright's introductory book on the philosophy of religion helpful.
Cosmological arguments seem to have two critical elements. One notes the contingency of the physical world. Every part of it is such that we can conceive of it not existing. Most people believe that if God were to exist, God would have the power to annihilate the universe completely. So there is some sense to be made of the idea that the universe is something that exists contingently, not necessarily.
But why, if the universe is contingent in this sense, couldn't the universe be contingent on nothing. That is the question Steven Carr is asking. We need explanatory principles, or what in philosophy are called principles of sufficient reason, in order to justify the claim that the universe needs something other than itself to explain it.
PSR1: For every contingent fact F some other fact F' obtains such that, given F', F must obtain.
This principle is incompatible with classical theism, for reasons which are similar to the ones Steven mentioned. It is a contingent fact that God freely chose to create a universe, according to classical theism. Or, if God had chosen to exist alone, that would be contingent.
So PSR needs to be revised. Wainwright offers some alternatives:
PSR2: There is a sufficient reason for the existence of every contingent being.
This doesn't entail tha there has to be an explanation of every property of that being, just the existence of the being. So, for example, that being freely choosing to do something can be fully nd completely contingent.
PSR3: Every contingent fact that requires a sufficient reason has one.
A contingent fact "requires" a sufficient erason if and only if 1) it is logically possible for it to have a sufficient reason and 2) it is unintelligible if it doesn't have one.
PSR4: There is at least some reason for every contingent fact.
I have seen this referred to as the principle of necessary reason, for every contingent fact there are necessary conditions for it.
Wainwright goes on:
"The weaker principles are strong enough to generate the conclusion that contingent being is caused by a self-exisent being."
The upshot of Wainwright's subsequent discussion is that at least PSR4 is supported by the success of human inquiry, and that therefore the weaker forms of PSR are more plausible than their denials. Hence, he does find some legitimacy in forms of the cosmological argument that use some of the weaker versions of PSR4, and he thinks they do lend significant support to the claim that the physical universe depends on something other than itself, which is self-existent.