What follows are some further ruminations occasioned by the article by Tomas Bogardus first referenced and commented upon here. I will begin by explaining the distinction between personal and impersonal explanations.  The explanation I am about to give is itself a personal explanation, as should become clear after I define 'personal explanation.'

A lightning bolt hits a tree and it bursts into flame. A young child  coming on the scene sees a tree on fire and asks me why it is on fire. The child desires to understand why the tree is on fire. I seek to satisfy the child's desire by providing an explanation. I explain to the child that the tree is on fire because it was struck by a bolt of lightning.

Personal explanation

My explanation to the child  is an example of a personal as opposed to an impersonal explanation. One person explains something to another person,  or to a group of persons, or in the zero-case of personal explanation, to oneself.  Personal explanations of the first type — the only type I will consider here — have a triadic structure and involve a minimum of three terms: P1, P2, and E where E is a proposition. One person conveys a proposition to a second person. In the example, I convey the proposition A lightning strike caused the tree to explode into flame to the child. This communicative process or act of explaining is not itself a truth-bearer: it is neither true nor false.

Neither true nor false, it is either successful or unsuccessful.  The act of explaining is successful if  the recipient of the explanation 'gets it' and comes to understand something he did not understand before. It is unsuccessful if the recipient fails to 'get it.' Now I nuance the point with a further distinction.

Strongly successful versus weakly successful

Two conditions must be satisfied for a personal explanation to be what I will call strongly successful. First, the proposition conveyed must be true. Second, the proposition must be understandable and understood by the recipient of the explanation. If either condition goes unsatisfied, the personal explanation is not strongly successful. For a personal explanation to be what I will call weakly successful, it suffices that the recipient of the explanation be satisfied by the explanation, where satisfaction requires only that the recipient understand the proposition conveyed in the explanation, and find it believable, whether or not the proposition is true.

Although the act of explaining is not a truth-bearer and thus not a proposition, the act of explaining embeds a proposition. Call the latter the content of the act of explaining. Every act of personal explaining has a content which may or may not be true. But the explaining, although it includes a propositional content, is not itself a proposition.  As a performance of a concrete person it is itself concrete and thus not abstract as is a proposition. Note also that the performance as an individual event is categorially barred from being either true or false. 

Impersonal explanation

Impersonal explanations are two-termed, both terms being propositions that record events. For example Lightning struck the tree explains The tree burst into flame. Schematically, p explains q, where 'p' and 'q' are free variables the values of which can only be propositions. No person is a proposition, although of course there are plenty of (infinitely many) propositions about every person, some true, the others false. 

Now if two propositions are related by the impersonal explanation relation, then the result is itself a proposition. We could say that an impersonal explanation is a dyadic relational proposition.

I think it is obvious that the explains relation must not be confused with the causation relation, assuming that causation is in fact a relation. (To dilate further on whether causation is, strictly speaking, a relation would open up a can of worms that is best put on the back burner for the nonce, if you will forgive my highly unappetizing mixed metaphor).  What is the difference? Well, the impersonal explains relation relates propositions which are abstracta whereas the causal relation relates events which are concreta.  Roughly, explanation is at the level of thought; empirical causation is at the level of concrete reality.

Complete impersonal explanations

Now consider the second premise in Bogardus's main argument:

2) Any explanation can be successful only if it crucially involves no element that calls
out for explanation but lacks one.

In the simple example I gave, call the two events Strike and Ignition.  Strike is the salient cause of  Ignition. I won't pause to proffer a rigorous definition of 'salient cause,'  but you know what I mean. Salient cause as opposed to all the many causal factors that have to be in place for Ignition to occur.  If there is no oxygen in the atmosphere around the tree, for example, then there is no Ignition. Nobody will say that the cause of Ignition is the presence of oxygen even though its presence is a necessary condition of Ignition, a condition without which Ignition is nomologically impossible.  (The nomologically possible is that which is possible given the laws of nature.  These laws are themselves presumably broadly logically, i.e. metaphysically, contingent.)

I read "no element" in (2) as covering both salient causes and what I am calling causal factors. I also read (2) as telling us that one cannot provide a successful causal explanation of  any particular empirical fact unless (i) it is possible in principle to explain every temporally antecedent salient event and causal factor in the entire series of events  and factors culminating in the fact to be explained (Ignition in the example) subject to the proviso  that (ii) the explanation cannot 'bottom out' in brute  or unexplainable facts.

I am having trouble understanding (2): it strikes me as ambiguous as between

2a) Any personal explanation can be successful only if it crucially involves no element that calls out for explanation but lacks one

and

2b) Any impersonal explanation can be complete only if it crucially involves no element that calls out for explanation but lacks one.

It seems to me that (2a) is false, whereas (2b) is true.  (2a) is false because I can stop explaining right after citing the lightning strike.  I do not need to explain that lightning is an atmospheric  electrical discharge,  caused by  electrostatic activity occurring between two electrically charged regions, etc.  Same with the other example I gave. Kid asks, "Why did the crops fail, Grandpa?" Old man replies, "Because of the drought." The kid's desire to understand has been satisfied, and so the personal explanation is successful without being complete.  There is no need to regress further although one could, and in some context should.

To fully appreciate this, we must understand what Bogardus takes to be the link between explanation and understanding.  The following is from one of his endnotes:

Recall the link between explanation and understanding. A successful explanation can produce in us understanding of the phenomenon, an understanding of why or how it’s happening. But if there’s part of a proposed explanation that cannot be understood, because it’s brute – how can it produce in us understanding of why or how the phenomenon is happening? Yet if it cannot produce in us that understanding, then it isn’t a successful explanation. In each of these cases, there is a part of the proposed explanation that cannot be understood – in the first, the mare, in the second, the meal – and, so, in neither case do we have a successful explanation. To put it another way, to understand why (or how) is to understand an acceptable answer to the relevant ‘Why?’ (or ‘How?’) question. But if part of that answer is unintelligible, unable to be understood, totally mysterious, then one cannot understand the answer. And, in that case, one cannot understand why (or how) the phenomenon is happening. But, if so, then these answers cannot be successful explanations. In that case, they are not counterexamples to premise 2, despite appearances.

On the basis of this passage and other things Bogardus says in his article, I fear that he may be confusing personal with impersonal explanation.  He seems to be talking about personal explanation above. If so, how, given that our paltry minds are notoriously finite, could we grasp or understand any complete explanation? I am also wondering whether 'brutality,' brute-factuality is a red herring here.

Suppose I grant him arguendo that there are no brute facts.  I could then easily grant him that a complete impersonal explanation of an event such as Ignition must take the form of  proposition of the form X explains Y, where Y is the proposition Ignition occurs and X is a huge conjunction of propositions (and thus a conjunctive proposition) the conjuncts of which record all of the salient causes and causal factors involved at every step in the causal regress from Ignition back in time.

But as I said, our minds are finite. Being exceedingly finite, they cannot 'process,' i.e., understand an impersonal explanation given that an impersonal explanation is a proposition with a huge number of conjuncts, even if the number of conjuncts is itself finite.  An explanation we cannot understand may be, in itself, complete, but for us, must be unintelligible.  An unintelligible explanation, however, cannot count as either strongly or weakly successful as I defined these terms above.  To be either, it must be able to satisfy our desire for understanding.

Dilemma: Explanation is either personal or impersonal.  If the former, the explanation may be successful  in generating understanding,  but cannot be completely true.  If the latter, the explanation may be completely  true, but cannot be  successful in generating understanding in finite minds like ours.

I may take up the ex nihilo mare and meal examples in a separate post.