Kuru, will you hate me if I muddy the waters even more?
How about Tolkien defining a "rational" being as something from Eru? Because, we're not talking about "thinking" rationally we are talking about an individuals own state of being. And since Eru is rational, all beings of Eru are thus considered "rational beings." I can't find the exact quote at the moment, but there is a place where Tolkien does define a "rational being" as one coming from Eru.
So, now the question is in
Letter 183, does Tolkien mean "rational being" in the sense of one with the capability of thinking rationally or simply a being from Eru?