There's a rather famous essay by Richard Cartwright called "On the Logical Problem of the Trinity" (available online here). In it, Cartwright argues that the doctrine of the Trinity as enunciated in the Athanasian Creed cannot be made sense of using ordinary intuitions about identity and difference, genus and species. The Maverick Philosopher gave the essay a rather charitable interpretation in a post from a year and a half ago, but I'm inclined to think that Cartwright, like David Hume, knows what follows of logical necessity and what does not, and so leaves tell-tale cigarette butts all over the house hoping that his roommates will assume that he is a smoker.
I've been spending much of my summer vacation (what little of it there is) working on a paper on Anselm's De processione Spiritus Sancti, which starts from precisely the same beginning as Cartwright but which draws an entirely different conclusion. Anselm is writing, ostensibly, for the benefit of the Greeks who deny the propriety of inserting the Filioque clause into the Nicene Creed, and, in the end, he draws the inference that one must accept that the Holy Spirit proceeds both from the Father and the Son, that this, indeed, follows by logical necessity from the concepts and relations involved in the Most Holy Trinity.
This is a rather startling difference: one person argues that the whole setup is logical nonsense, the other that it leads inexorably to a sure and certain conclusion that is perfectly logically coherent. The difference lies in the way the two conceive of the notions of identity and difference, and one cannot help but recall, as one reads through these essays, the monumental amount of work Plato put into the deciphering of just these two properties in such works as the Parmenides, the Sophist, and other dialogues. Independently of whether human reason can grasp something like the Trinity, it is interesting to find that Plato, 2350 years ago, was already on to what is centrally important to philosophy and human experience. It turns out to be things about which we already have lively intuitions but which, upon closer examination, prove to be more stubborn in their explication than we had ever imagined.