Why the Euthyphro fails “....General logic, then, resolves the whole formal business of understanding and reason into its elements, and exhibits them as principles of all logical judging of our cognitions. This part of logic may, therefore, be called analytic, and is at least the negative test of truth, because all cognitions must first of all be estimated and tried according to these laws before we proceed to investigate them in respect of their content, in order to discover whether they contain positive truth in regard to their object. Because, however, the mere form of a cognition, accurately as it may accord with logical laws, is insufficient to supply us with material (objective) truth, no one, by means of logic alone, can venture to predicate anything of or decide concerning objects, unless he has obtained, independently of logic, well-grounded information about them, in order afterwards to examine, according to logical laws, into the use and connection, in a cohering whole, of that information, or, what is still better, merely to test it by them.
Notwithstanding, there lies so seductive a charm in the possession of a specious art like this—an art which gives to all our cognitions the form of the understanding, although with respect to the content thereof we may be sadly deficient—that general logic, which is merely a canon of judgement, has been employed as an organon for the actual production, or rather for the semblance of production, of objective assertions, and has thus been grossly misapplied.
Different as are the significations in which the ancients used this term for a science or an art, we may safely infer, from their actual employment of it, that with them it was nothing else than a logic of illusion—a sophistical art for giving ignorance, nay, even intentional sophistries, the colouring of truth, in which the thoroughness of procedure which logic requires was imitated, and their topic employed to cloak the empty pretensions. Now it may be taken as a safe and useful warning, that general logic, considered as an organon, must always be a logic of illusion, that is, be dialectical, for, as it teaches us nothing whatever respecting the content of our cognitions, but merely the formal conditions of their accordance with the understanding, which do not relate to and are quite indifferent in respect of objects, any attempt to employ it as an instrument (organon) in order to extend and enlarge the range of our knowledge must end in mere prating; any one being able to maintain or oppose, with some appearance of truth, any single assertion whatever....”
All that to say this.....it is possible for worthy logic to give nothing worthy, it is possible for good logic to give nothing better than.....yeah, so?
And buried in there is a resolution for understanding the Euthyphro problem: for Socrates, in opposing, the analytic, insofar as there is no apodeitic correctness for the base of the charge against him, and for Euthyphro himself, in maintaining, the dialectic, insofar as he just stomps his foot and vacates the field, for the very same lack of apodeitic correctness. As such, the Euthyphro problem doesn’t fail at all, but rather demonstrates a failure.
Exit, stage right.