Following Aquinas’s example, visualize a hand pushing a stick, and that stick in turn is pushing a big rock, which In turn is pushing a medium sized rock, which is pushing a small rock. The medium sized rock is borrowing or deriving its “power” to push from the bigger rock, which is borrowing its power to push from the stick, which is borrowing from the hand. It’s all occurring at once. Scotus calls this an "essentially ordered series," Aquinas calls it a "per se series," and Feser calls it a hierarchical regress.
A hierarchical regress is different from a linear/temporal regress. A temporal series is an example of what Scotus calls "an accidentally ordered series" and Aquinas calls a "per accidens series," which is a series wherein later members don't depend on earlier members. In contrast, a hierarchical regress occurs right here and right now, and is one in which the members depend on a logically-prior member (explained more below). Visualize a similar hierarchical regress occurring within the totality/fabric of reality itself— one level of reality depending on a logically/explanatorily prior level, which depends on yet a prior level, etc. all at once.
Again, this isn’t necessarily about contemporary states depending on past states; that’s not what “prior” means in a hierarchical regress. Imagine that the hand in the aforementioned example has been pushing the stick since eternity past, with the series of past events/movements having no beginning in time. In that case, we could still say that the movement of the hand is logically or explanatorily prior to the movement of the stick. Or, following Kant, imagine that a heavy ball has been resting on a cushion for eternity-- or opposite extreme, imagine the ball resting on the cushion timelessly -- in either case we could still maintain that the weight and roundness of the ball are logically/explanatorily prior to the indentation in the cushion. Aristotle, Augustine, Aquinas, Edward Feser (eg 2008, 2017 among others), David Bentley Hart (2014), Rasmussen (2018, 2019 among others), etc. (Koons, Pruss, Kerr, etc) would argue that even an eternal universe with no beginning would still be contingent and dependent in similar ways and would still involve explanatory hierarchical regresses at any and every moment.
Classical theism says that the hierarchical regress--or the series of explanations that derive or borrow their explanatory capacity from a logically-prior explanation-- must have a bottom level, which is the First Member or First Cause or First Explanation (regardless of whether time has a beginning). It would be the equivalent of the hand in that example of the hand pushing the stick etc. but in this case at the deepest level of reality.
(The example of the hand pushing the stick can cause confusion if one imagines the hand approaching the stick and then picking it up, which would involve temporal changes in time. Instead, conceive of something akin to gears all moving at once. Or, in Feser's example, imagine a book resting on a coffee table which is in the floor etc wherein the explanation and the effect being explained occur together simultaneously.)
Classical theism calls that first member of the hierarchical series of reality "God." Traditionally, classical theists argue that the First Member of the hierarchical regress of reality must be indivisible (just One), without parts (so can’t be material), fully actual without any potentiality requiring actualization a la Feser or Aristotle (which also rules out more than one since differentiation requires different members to have potentialities that the others lack), and must possess—or just be—intellect, will, etc. There are sophisticated arguments for these attributes (with rejoinders...) by the aforementioned authors with serious rigor, but most atheists (and believers alike) are simply ignorant of the literature. I won't detail their arguments in this post but strongly encourage reading their academic work. Again, an infinite past would be irrelevant. Imagine an infinite series of mirrors each reflecting the image of a face. Each mirror is deriving its image from a explanatorily-prior mirror, but an infinite number of mirrors still could not account for the image of the face, which must exist outside of the series.
POLYTHEISM AND GOD OF THE GAPS
In contrast to classical theism, the gods of polytheism would be more like the stick, or the large/medium sized rocks, or the mirrors; they (the gods of polytheism) occur later in the explanatory series. Arguments for/against classical theism are mostly different from arguments for/against the gods of polytheism. So e.g. the arguments for classical theism based on the principle of sufficient reason/PSR (I prefer "ubiquity of intelligibility"), the contingency of physical reality, the reality of the actualization of potential in Aquinas and Feser, mathematical realism and the problem of universals, etc. would not be arguments for polytheism. And, similarly, arguments *against* polytheism based on science (eg we no longer invoke Zeus to explain lightning) are *not* arguments against classical theism. Relatedly, debunking "god of the gaps" arguments (I.e. debunking arguments that use “God” to plug up holes in our current scientific understanding) is not the same as debunking classical theism, because the latter is a philosophical/metaphysical concept about what (if anything) grounds the very possibility of the existence of the domain studied by science. Worthy non-believing/Atheistic philosophers include Graham Oppy, Jl Mackie, Alex Malpass, William Rowe, and others. Worthy believing philosophers were mentioned earlier. Below is a list of publications from both sides of the debate that ought to be read by anyone interested in natural theology.
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