Philosophy is kind of interesting because philosophers break their own rules. As far as I know they always do; I haven’t studied them all. (Ha ha.)
I got to watch R. C. Sproul make himself look unintelligent. The man is intelligent, but he went ahead and broke his own rule, on video. He explained the difference between a contradiction (two statements that cannot both be true) and a paradox (a seeming contradiction resulting from inadequate understanding or definition of terms). Then he proceeded to tell a story about Paul Tillich lecturing a class on his concept that God is neither personal nor impersonal, but rather the ground of being.
“A student asked, ‘Professor Tillich, is God personal?'” Sproul said. “And Tillich got very angry and said, ‘I told you that God is neither personal nor impersonal,’ but of course, that is not possible! Impersonal is defined as that which is not personal, so everything must be either personal or impersonal.”
Alas to be teaching philosophy with such an inflexible mind! Paul Tillich is wrong in his teaching, but he is not making an invalid argument. It is a paradox, not a contradiction. If we accept that all humans are either male or female, then what is humanity? Male or female? Neither, of course, because a distinction belonging to one category is applied to another. Or even if we accept that everything must be either personal or impersonal–what then is everything? Collectively, all together now, considered at once: what is everything? Personal or impersonal?
This of course is very close to what Paul Tillich was getting at. But since Paul Tillich’s theology is not correct, we are reduced to saying that a studied philosopher is running around babbling brute contradictions. Play fair, sir; play fair.