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.
He brings up the liar example for exactly the same reason he brings up the ‘time in time’ and the ‘presence at one’s own generation’ paradoxes: it presents a dilemma which, if the Arians “think, in accordance with [their] dialectic assumptions, that one or other of these alternatives must necessarily be true in every case,” will result in absurdity. The examples are to show that the Arian dialectical assumptions are untenable;the Arian must hold that one is definitely true and the other definitely false (“without qualification”) but this leads to absurdity.
Here’s the passage:
IX. Well, but the Father begat a Son who either was or was not in existence. [This is the Arian dilemma, “Did the Son exist before he was begotten?”] What utter nonsense! This is a question which applies to you or me, who on the one hand were in existence, as for instance Levi in the loins of Abraham [Heb. vii. 10.] and on the other hand came into existence; and so in some sense we are partly of what existed, and partly of what was nonexistent; whereas the contrary is the case with the original matter, which was certainly created out of what was non-existent, notwithstanding that some pretend that it is unbegotten. But in this case “to be begotten,” even from the beginning, is concurrent with “to be.” On what then will you base this captious question? For what is older than that which is from the beginning, if we may place there the previous existence or non-existence of the Son? In either case we destroy its claim to be the Beginning. Or perhaps you will say, if we were to ask you whether the Father was of existent or non-existent substance, that he is twofold, partly pre-existing, partly existing; or that His case is the same with that of the Son; that is, that He was created out of non-existing matter, because of your ridiculous questions and your houses of sand, which cannot stand against the merest ripple.
I do not admit either solution, and I declare that your question contains an absurdity, and not a difficulty to answer. If however you think, in accordance with your dialectic assumptions, that one or other of these alternatives must necessarily be true in every case, let me ask you one little question: Is time in time, or is it not in time? If it is contained in time, then in what time, and what is it but that time, and how does it contain it? But if it is not contained in time, what is that surpassing wisdom which can conceive of a time which is timeless? Now, 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 contraries are true, so in that case they should both be untrue, and so your clever puzzle prove mere foolishness? Solve me one more riddle. Were you present at your own generation, and are you now present to yourself, or is neither the case? If you were and are present, who were you, and with whom are you present? And how did your single self become thus both subject and object? But if neither of the above is the case, how did you get separated from yourself, and what is the cause of this disjoining? But, you will say, it is stupid to make a fuss about the question whether or no a single individual is present to himself; for the expression is not used of oneself but of others. Well, you may be certain that it is even more stupid to discuss the question whether That which was begotten from the beginning existed before its generation or not. For such a question arises only as to matter divisible by time.
Brandon – great comments. And thanks for the correction – it is the third, not the second oration. aka his 29th oration is some editions.
I agree with many people that it doesn’t seem correct that anything whatever should follow from a contradiction, and you make a good point about there being different paraconsistent systems.
Certainly, X is lying (saying what he believes to be false) and X is (intentionally) telling the truth surely are contraries, not contradictories – both could be false, such as when a man is silent, or when he unknowingly says a falsehood about weapons of mass destruction. 🙂
If you’re right about interpreting Gregory, then my mistake in the post is this part:
“But Gregory asserts that one or the other of the alternatives here must be true of the one who says “I am lying.””
I took him to be asserting this, whereas you argue that he’s say that must be so only on the Arians’ mistaken assumption. He certainly does announce at the start that their dilemma is a false one.
You may be right – but in your reading, why does he bring up the liar example? Doesn’t he commit himself to the claim that one who says “I am now telling a lie” is both lying and telling the truth? I’m struggling to see what the point of the example is, on your reading. It looks like his point is that if not contradictories, at least contraries can both be true.
Below I paste the whole passage, so others can join in.
Strictly speaking, paraconsistent systems are systems in which contradiction does not lead to explosion. In the ‘classical’ logic we learn in school contradictions explode: if you assume a contradiction, you can prove anything. There are inconveniences with this in a lot of areas of reasoning; thus the development of paraconsistent logic. One way to do this is to allow contradictions to be true; such paraconsistent systems are called dialethic systems. It’s also possible to have paraconsistent systems in which all contradictions are necessarily false (but imply nothing, or only some things, rather than everything). In fact, most logical systems proposed throughout history have been paraconsistent; as Priest likes to point out, Aristotle’s logic is technically paraconsistent, not classical, so paraconsistent logic pre-dates classical logic. But Aristotle, of course, has no tolerance for the idea that contradictions might be true.
I think you mean the Third Theological Oration, not the Second. I’m not convinced that Gregory is putting it forward as his own position here, and I have a different interpretation. The Arians have put forward a dilemma, and insisted that one of the two disjuncts must be true. Gregory responds with a series of paradoxes, each of which has to be seen as making the same sort of response to the Arian argument; they are all problems that arise from insisting that one of two mutually exclusive options must be true. And when he wraps up he wraps up by concluding that the Arian dilemma is a false dilemma which has no application to the divine case, as you note. So I think it’s pretty clear that he’s actually arguing on his opponent’s assumptions here, and he really does mean ‘contraries’, not ‘contradictories’. He’s not claiming that the conjuncts of a contradictory conjunction are true; he is mocking the Arians for uncritically thinking that dilemmas mean that one of the disjuncts must be true — in the liar case, it gives the obviously absurd result that two contraries are true, so why is it so difficult to think that the disjuncts of the Arian dilemma might both be false?
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