The phrase "intelligible explanation" is correct and usable in written English
You can use it when referring to an explanation that is clear and easy to understand.
Example: "The teacher provided an intelligible explanation of the complex theory, making it accessible to all students."
Alternatives: "clear explanation" or "understandable explanation"
At least that was the most charitable – not to say intelligible – explanation for the unreserved enthusiasm with which the shadow home secretary greeted her statement.
No, the only intelligible explanation is that a Conservative administration now wishes to get on with things that the Lib Dems would have blocked, above all setting in train all those benefit cuts which Mr Cameron declined to spell out for the voters.
The rational necessity of postulating such a necessary being or a causality of freedom satisfies the rational demand for intelligible explanation.
Determining final causes involved a speculation that outstripped human understanding, while formal causes were dismissed as occult qualities, simple assertions that things worked without an intelligible explanation of how they did so.
The way to make sense of Hume's remarks in The History of England is that they reveal that he implicitly accepts the Mechanists' insistence – explicitly associated with Boyle —that theirs was the only program that offered the possibility of intelligible explanation (even if in the hands of many of its practitioners it only offered hope of post-facto rational reconstruction).
At the moment, we do not have an intelligible explanation for this finding, especially, having in mind that the amount of blood protein bound radioactivity found by incubating [F]FProp-C*RRETAWAC*-OH with human serum was low and metabolic stability was high.
On the negative side, Leibniz thought that by postulating what he understood to be an irreducible force holding between bodies and acting at a distance, Newton had abandoned the intelligible explanations of the mechanical philosophy, and returned to uninformative scholastic accounts that rested content with the postulation of primitive powers.
Instead, each lister comes across as a wild-eyed junk dealer at a flea market, pressing esoteric wares on passersby with half-intelligible explanations of their value.
In addition, the learner must come to see the new explanation as intelligible (easily understood), plausible (credible), and fruitful (useful for explaining other phenomena), drawing their criteria from studies of what causes scientific communities to adopt a new theory.
Thus, although the thesis positions satisfy reason's demand for the unconditioned, they do so by fleeing (however unwittingly) into an intelligible realm, by providing explanations that abstract from that which is or could be given in any spatio-temporal experience.
Since Campbell allows that reason explanations make actions intelligible without falling under exceptionless generalizations (mental anomalism), he can't object that physical properties cannot make reasons intelligible simply because of an anomalous relation between them.
