In order to 'make explanations'; attain understandings; make judgments (as judges and hearing officers do); and generally assess the why(s); wherefore(s) and what-the-hell-really-happened of many scenarios, we use several primary kinds of algorithmic vehicles: adductive; inductive; and deductive reasoning. Adducing facts, as to the likelihood of one scenario being more probable than another, is certainly the least burdensome and among the 'simpler', 'elegant' means of arriving at a just (maybe) and equitable (ditto) outcome. Administrative law judges (I used to be one of those, although I was given the poor man's title: hearing officer) rely on background laws, policies and case law precedents, in order to-as simply and elegantly as possible-arrived at holdings on such matters. They don't ordinarily use the terms simple or elegant. Don't have to. They may be absolutely correct in their assessments of things, but may still have their decisions overturned at a higher level. Additionally, their original holding(s) may be restored at a still higher level of appeal (i.e., the court system itself). Induction and deduction are slightly different, but I won't go into that. Reduction is yet another means-but, it engenders controversy, as philosophers know full well. There are, then, different ways to skin the cat, and adductive arguments remain a gentleman's Damocles' Sword---Good luck with Ms. Lombrozo, guys!

In reading Wilfrid Sellars' SCIENCE AND METAPHYSICS (Humanities Press, 1968), I came upon remarks concerning induction and law-like statements (section 7, page 118)., Beginning with: "In philosophy, one thing always leads to another, and it is tempting, at this point, to embark on an extended discussion of induction." He continues talking about 'law-like' statements; S-assertibility; semantics and so on. To conclude the paragraph-long section, he writes: ..."to understand the point of inductive reasoning one must understand the distinctive functions of matter-of-factual statements belonging to the level below that of law-like statements." So, it would seem that Sellars recognizes the need for a healthy command of language, when it comes to seeing how things hanging together form a (the?) foundation for effective, convincing communication. I personally have always found this helpful, because no matter who one's argument is directed to, an understandable vocabulary (whether written or spoken) is, as Sellars implies, the epitome of "Categorical Reasonableness".
Put more elegantly: an audience cannot grasp an explanation which is abstract; obscure or academically obfuscatory. Just sayin'...

(For those interested in the long version of Sellars' quip regarding philosophy helping us see how things hang together, see III of Chapter VI, section 19. on page 158 of this rather difficult book. That Sellars was an analytical philosopher is obvious. For anyone not up to the challenge, ignore this footnote.)

The best explanations cause the reader or listener to actually learn something they either didnt know or ever considered; either in conjunction with something else they either knew or didn't or on its own. It's not whether or not your explanation was convincing. If your explanation was convincing or not is always seperate of its total possible value. You can teach far more than you're supposedly explaining and still have something valuable. What then does "best" mean?

“最佳解释推论”是否也可以被描述为最可取的不充分解释?以英国威尔特郡的“麦田怪圈”现象为例。虽然其中一些可以毫无疑问地解释它们是如何产生的，但有些显然不能，对于后者，所有可用的解释似乎都同样不够充分。然而，前段时间，当两个农民在离开酒馆后的一个晚上承认生产了一些香蕉时，许多人认为这个谜题已经解决了。然而，由于这类设计的数量之多及其复杂性，农民们的供词被证明和其他所有人一样错误，但仍被许多人认为已经解决了问题，大概是因为它的行为可以被普遍理解。因此，这不是最好的解释，而只是最可取的解释。在非正式逻辑的讨论中，我们不应该在相互竞争的选项中谈论“最佳解释的推论”，那么，我们不应该在同样糟糕的选项中把它重命名为“更好解释的推论”吗?

Below is an interesting example from ontology which illustrates the point I'm trying to make above about optional veracity under negative epistemic conditions:

Key-- p: an impression of a tree produced by one's imagination but believed to be real, i.e. the hallucination of a tree;
q: a visual perception;
r: a real, existing tree.

If p then q
If q then either p or r (disjunction here is the exclusive use)
If r then q or not q
q
因此，p，由于概率更大，因为p总是q，而r只是有时。But take the converse case:

If r then q or not q
If p then q
If p then not r
q
therefore, r, --since p must be q, but r is more likely to be.

Under the assumption that p and r are visually identical, two results are produced: r can never be a mere q, that is, if it's a real tree, it's not a mere visual impression; and p can only be a q, --if it's an hallucination, then that's all of it which actually exists. How q appears in the conclusion, either as a negation of r by self-affirmation in p, or an affirmation of r by self-negation of objective status as a mere impression, appears to be a matter of taste whose matter is optional, i.e. a preference.

If the inference to the best explanation is understood as a preference for one result among equally insufficient ones, then attempting to prove it and exclude the others by its demonstration would not only be useless, but indeed a bit rude. That doesn't imply however that there might not be a rule for which preferences are good ones. As an example of the application of such a rule, take the case where an empty bookshelf is abandoned on a side walk in a residential neighborhood, and two of its residents arrive at the same time to appropriate it. Neither one needs it, but both would like to have it in their possession. Assuming that both residents' preferences are conditioned by keeping it in one piece, what's the rule to which a potential adjudication can appeal? Would it not be with regard to how it will be used? If one has books and does a lot of reading and the other doesn't, then by the rule, the abandoned book case should go to the reader.

Kant's notion of a Deduction of a concept's claim of application to an object applies a similar rule. The term derives from the court system of the time and is designed for such cases as in the example above (Critique of Pure Reason, A84/B116). Kant's famous Transcendental Deduction is provided for general concepts of experience, or the "categories". He wants one because they're already used and trusted to both common sense and the science of his time. Without a Deduction showing it's not the case that there's no good reason for them, one use might be just as good as any other, generating a skepticism for the science of his day. The Deduction doesn't prove that the concepts apply to objects, only that they're best used that way.

A short account of Kant's argument is expressed below:

关键::统觉;一种纯粹的(未掺杂任何先前经验的)创造性想象的产物，包括在他实际感知到的事物之前他间接感知到的一切事物，或在他的意识领域中他没有明确意识到的任何事物;(合成经验的)。
b: concepts of objects; (synthetic aposteriori).
c: categories of judgements; (analytic apriori).

1) b if and only if a
2) if a then not c
3) if c then b or not b
4) a,
5) therefore b,
6) therefore, if b then c. From two synthetic aposteriori premises you get an analytic apriori conclusion. The connection between the last two premises is not a valid one, but rather a condition arising from the definition of term a as conditioning any object of experience. If you have any objects at all, the categories have to already apply to them (B132-136).

A striking thing about the use of this argument is how Kant wants to therefore make the claim that all the categories analyzable from experience apply (A65/B89). If on the assumption of a unity of possible objects to which the categories apply one presupposes an unconditioned unity of these general concepts themselves, empirical knowledge is improved as a result, as shown by the progress in the physical sciences of his time. The transcendental Deduction in the first Critique is, then, an argument from Elegance: If it's true, it should improve the understanding, and if it improves the understanding, it must be true; which is a circle, but not a vicious one, since inductive results and imaginative form are reciprocally determined. The more one assumes the categories' analytic unity, the better the inductive results; and the better the inductive results, the stronger the grounds become for that assumption; which is similar to an argument from aesthetic response: If an object is beautiful on the surface, the more likely one judges correctly about what's underneath it; and the more what's underneath it is judged correctly, the more beautiful its surface becomes; (see also the Refutation of Idealism, B275-277). Kant's argument however doesn't do much better here of giving clear evidentiary or logical compulsion for his conclusion any more than the decision of whether a tree is an hallucination or not in the post of 4/10/22 above, but only that it's a generally preferable one for the understanding, or a matter of academic and, perhaps arguably to some degree aesthetic, preference.

Explanation intrigues most often in where, when and how it is offered. Rarely do they answer why questions though the best do. Explanations stop at death or at the foot of craven belief.

I got a kick out of this show. Lombrozo is fantastic, as Josh is wont to say.