I'd like to respond to at least some of the comments on the Argument from Contingency. I probably won't get to them all on this post, so be patient.
Remember, although I am a believer in the existence of God I have not, at this point, endorsed this version of the cosmological argument.
Steve Esser thinks that the argument refutes physicalism, because it shows that there must be something that make an individual objects parts be a unified individual. But could that which unifies a thing's parts be something other than God? But the argument, of course is designed to show that God is the necessary being on which the contingent objects in the universe depend. That is certainly Godlike though, of course, we are still a long way from John 3: 16.
David correctly points out that the argument I presented was not Aquinas's Third Way. That's true, but Aquinas's Third Way, as stated, seems to have some serious problems with it. Aquinas suggests that if there is an infinite series of contingent existents, then it is possible for each of them to cease to exist, and if it is possible, then in the course of an infinite period of time every possibility would have to be actualized, and if so that would mean that the possibility that everything goes out of existence would have to have been actual. That being true, if the universe is in existence now, it would have had to come into existence out of nothing, but nothing comes from nothing, so therefore there has to be a necessary being. But an infinite time would not guarantee the actualization of all possibilities. The infinite series of multiples of 3, for instance, does not include 22. So I think the version of the argument I presented actually avoids some difficulties that the original argument had.
Though I understand that the best source for Thomist thought on these arguments is the Summa Contra Gentiles rather than the Summa Theologica.
Steve responded by saying that he saw something problematic about the idea of a changeless entity causing the universe, and David responded that while this might be difficult to understand there is no proof that the idea is incoherent.
Clayton argued that an infinite series of contingent objects is not a patent absurdity, appealing to Hume's (and Paul Edwards') argument that if you can account for each individual in the series, it makes no sense to say that you can't account for the whole series.
He also makes an important point when he says that Aquinas objects to some infinite regresses but does not maintain that an actual infinite is impossible. If he took that view, he would then have an argument in favor of the claim that the universe had to have a beginning (the now familiar Kalam argument made famous by William Craig) but Aquinas explicitly says that this is an article of faith.
I think Aquinas holds that every object has to have a contemporanously existing cause, and that an infinite serious of those objects would generate an absurdity, while he would not say that about in infinite series of past causes.