arnie said, "The above all looks eminently sensible."
An eminence is a high-ranking person.

What's the connection, logical and etymological, between the two senses?

Eminent means "outstanding", from the Latin eminere "to stand out, project". It whas been used as an honorific for cardinals since the seventeenth century.

Yes, agreed, the concept of eminent is "standing out from all the others", be it an eminent mountain peak, an eminent member of the community, or an eminent authority.

But we also speak -- correctly -- of an "eminently reasonable" statement, which is not even part of a crowd of others. Maybe I'm being dense here, but it seems to me to have at most a tenuous connection with the other usage.

Wordnerd, do you think this 4th definition in the OED works for it? " 4. Of qualities: Remarkable in degree; conspicuously displayed. Of actions, facts, phenomena: Signal, noteworthy (now chiefly in good sense)."

I found this definition from the OED to be interesting: " b. Distinguished in character or attainments, or by success in any walk of life. (The use in bad sense is now ironical.)" What exactly do they mean by "the use in bad sense is now ironical?"

Hey, Tinman, ya think we should make a nasty statement about and excited priest here?