Philosopher Graham Priest is notorious for his claim that there are true contradictions. I have to confess that when I first heard this years ago, I thought the people telling me were pulling my leg. But, they were not. Priest is deadly serious, and has developed paraconsistent logics – logical systems which allow some true contradictions. And he’s vigorously defended his claims against all comers, as in this recent book.
No, he doesn’t say that all contradictions are true – only some of them. And the ones which are true are also false. He claims that this thesis of dialetheism solves the liar paradox and others.
Very rarely, some theologian will come along, and assert that the Trinity doctrine is a true contradiction – not a merely apparent contradiction, but a real one.
Most Christians, though, eschew such a claim. Mysterian James Anderson discusses and rejects this approach to Christian mysteries in his book Paradox in Christian Theology.
Much to my surprise, I recently found a move like Priest’s in Gregory of Nazianzus (d. c. 390), in his Third Theological Oration.
Gregory is considering an argument by Arians, a premise of which is that the Son who the Father begot either was or was not in existence – I take it, prior or “prior” to his being begotten. (It is clear at the end of this section that Gregory takes them to mean literally before.)
Gregory asserts that this claim “contains an absurdity, and not a difficulty to answer.” He then gives a non-too-clear time example, which I’ll skip. Then he argues,
…in regard to this expression, “I am now telling a lie,” admit one of these alternatives, either that it is true, or that it is a falsehood, without qualification (for we cannot admit that it is both). But this cannot be. For necessarily he either is lying, and so is telling the truth, or else he is telling the truth, and so is lying. What wonder is it then that, as in this case [of the liar paradox] contraries are true, so in that case [concerning the Arians’ premise above] they [i.e. both alternatives] should both be untrue, and so your clever puzzle prove mere foolishness?
I take it that the “contraries” he mentions would be: “the man is lying” and “the man is telling the truth”. Contraries are often defined nowadays – I’m not sure how they were defined in his day – as claims that can’t both be true. But here, Gregory asserts that both are true – the one who says “I am now telling a lie” is both lying and telling the truth! His point is in the last sentence of the quotation.
Now as currently defined, contraries can’t both be true, but they can both be false. Thus, if a man is currently silent, it’ll be false that he’s lying, and false that he’s telling the truth. But Gregory asserts that one or the other of the alternatives here must be true of the one who says “I am lying.” This makes me think that the relevant alternatives he has in mind are really contradictories, not mere contraries – so that the alternatives are “the man is lying” and “it is not the case that the man is lying”. These can be defined modally, as a pair of claims such that necessarily, one is false and the other is true (so necessarily, they are not both true, and necessarily, they are not both false) or syntactically, as being a pair of claim with the form “P or not-P”. If this is indeed what Gregory is thinking, then is he the first known dialetheist in Western thought? I don’t know.
It seems to me that he doesn’t really know what he’s doing here; does he really want to assert that it is possible for contrary claims to both be true? This is saying that there are some claims which can’t possibly both be true, which, by the way, are both true. This is to implicitly assert and deny the same thing (that those claims are both true). Again, it seems to me that to defend against the Arian argument, he doesn’t need the controversial claim that contradictories can be true, either.
The point he really wants to make is at the end of this section – that the Arians’ question “Did the Son exist before he was begotten?” is a “stupid” (his word) one, “For such a question arises only as to matter divisible by time.”
Update: I’m not confident of this interpretation – see the comments below.