Is the Trinity a Contradiction?

Not too long ago I read an article written by a professor of philosophy who was not only rejecting Christian theism, but ridiculing it saying that at the heart of historic Christianity we find the doctrine of the Trinity. And he was saying in his essay that he couldn't understand how any rational person could embrace Christianity precisely because of its doctrine of Trinity. 

And then he went on to say that the idea of the Trinity is absurd, it's ridiculous because it violates the law of contradiction. That was the charge, that the doctrine of the Trinity violates logic and the law of non-contradiction. Now, I was really surprised to see that in that particular essay.

Not that people would make fun of Christianity or accuse of it of being irrational, I mean, you hear that all the time. Nor was it a surprise to me that somebody would say that the Trinity is contradictory. What surprised me was that the charge that the doctrine of the Trinity is a contradiction was leveled by a professor of philosophy. 

I realize that people can be educated in America and indeed achieve their PhDs in various subjects in America without ever having a single course in logic. In fact, most institutions of higher learning no longer require logic, but I can't imagine getting a graduate degree in the field of philosophy without having at least an introductory course in logic and be at least basically familiar with the law of non-contradiction.

And if this professor of philosophy had had an elementary course in logic, he should have understood, at least, that the Christian doctrine of the Trinity is not a contradiction. It does not violate the law of non-contradiction, because the doctrine of the Trinity says this, that God is one in essence and three in person. That's the classical formula for the Trinity.

God is one in essence or one in substance and three in person. And so if we break that down, we would say that God is one in A and three in B. We're saying that with respect to one qualification, He has unity, but with respect to a different predicate, He has diversity or plurality. 

Now, if we said, for example, that God were one in essence and three in essence, then indeed we would be violating the law of non-contradiction. Or if we said that God was one in person and three in person, likewise, we would be violating the law of non-contradiction. But to say that He is one in one thing and three in another thing is not to violate that particular law of reason.