So I've discovered something pretty awesome. I have no idea if anyone's discovered it before (I assume they have, but a Web search doesn't turn anything up). Please don't tell me I'm wrong! But I don't see how I can be.
I was looking for a Quenya word for "reason" in the philosophical sense (i.e. The Dream of Reason). The only thing Parf Edhellen gave me was casta "cause," which means "reason" in one sense (as in "the reason something happened"), but not in the sense I wanted ("the power of the mind to think, understand, and form judgments by a process of logic").
But then, on another site entirely, I noticed that "casta" also means "fraction" (specifically ¼, but also, if I'm not mistaken, "fraction" in general). I came back here to verify, and sure enough, that seems to be correct.
So why is this significant? Because our English word "rationality" is derived from "ratio"; in other words, fraction! (This is not an accident; to the ancient Greeks, to reason correctly about fractions was the source or beginning of logical thinking.)
So, then, "casta" means (or rather, can mean) just exactly "reason" in the logical/philosophical sense!