This is another post in a series attempting to make sense of Aquinas's Third Way.
This is from William Wainwright's Philosophy of Religion. (Wadsworth, 2nd. ed, 1999).
Aquinas concedes that infinite temporal regresses are possible. Each change or causal activity could be preceded by an earlier one. Each change or causal activity could be preceded by an earlier one. He thinks, howe ver, that series of simultaneously occurring changes or causes must have first members--the activity that is the source of change but isn't itself susceptible to change or a causal activity that is not, and could not be, derived from another. The ultimate ground of change ("the first mover") or causal activity ("the first cause") is God.
These cosmological arguments are historically important. Their plausibility, however, depends on assumptions that are no longer widely held. Ancient and medieval science, for example, thoght in terms of hierarchies of simultaneously occurring causes of different ontological kinds. Effects at lower levels of being we explained by causal activities at higher levels of being. Ancient and medieval metaphysics also assumed that the less perfect can be explained only by the more perfect.
Modern versions of the cosmological argumemt dispense with these assumptions. Most of them focus on contingent existence.
I'm wondering if this isn't perhaps too hasty of a dismissal. The underlying consideration seems to be the idea regardless of what past causes there might be for any contingent thing, there still has to be a contemporaneously existing thing or things which cause the existence of something now. That leads to a commitment to an infinite number of contingent things (perhaps an absurdity given the finite size of the universe) or a necessary being on which all things depend.