Alexandre Billon has a discussion of the question whether there can be an infinite regress of explanations, at Marcus Arvan's Substack, "New Work in Philosophy". The discussion is quite interesting, but I think the framing has some significant problems, which I think are common problems in these kinds of discussions:
(1) Billon incorrectly conflates 'infinite regress of causes' with 'infinite regress of explanations'. This is common mistake, and not surprising, because causes explain and explanations appeal to causes (in a broad sense of the term). But causes and explanations are not the same. Causes are real beings that must actually exist to occupy a place in a series. Explanations are mental constructs that may sometimes include the merely possible or even counterfactual. Thus, despite the connections between the two kinds of series, we should not assume that all properties and characteristics of one carry over to the other. An infinite regress of causes does seem to imply an infinite regress of explanations; it's not clear that the reverse is always true.
(2) Billon's attempt to be more specific about what is meant by explanation arguably misidentifies what is actually explanatory. Billon takes the example of two events E2 (= "This ball is dropped h meters from the ground") and E1 (= "This ball hits the ground with velocity v"); these events are described by an equation, v^2 = 2gh. The parameters of E1 then depend functionally on E2, which Billon takes to be the actual explanation relation. However, it's not actually obvious that this is right. While we might in some sense say that E2 causes E1, what is actually explanatory in this explanation is not E2 but the relation described by the equation, v^2 = 2gh; this general relation explains the relation between particular events with the right parameters, and when combined with E2, lets us infer E1. For that matter, it lets us do the reverse and infer E1 when combined with E2, because the actual explanation here concerns something that is not time-asymmetric. In short, the relation between E2 and E1 is the explanandum here; the explanans is actually the general relation that in physics we describe with an equation.
(3) If we do take functional dependence to be 'explanation', then Billon is quite clearly right that you can have infinite regresses of explanation in this sense. But this is less surprising than it might seem, because the chain of explanations in Billon's sense is quite clearly of the sort that is associated historically with per accidens series of causes, and it has been fairly generally thought that a per accidens series of causes can infinitely regress.
