I remember having a conversation years ago with an Episcopal priest who is now part of ACNA. It was just after the action of General Convention in 2003 to consent to the election of Gene Robinson as bishop of New Hampshire. He and I chanced to meet each other as we made our way out of chapel one morning.
I asked him what he was thinking about what was going on. “Now we have clarity” he replied.
That’s a pretty common theme with many people in the church right now. We need to have clarity. We can stand no more confusion. Something either is A or it is not A. There’s no middle ground, no matter what people like me keep trying to insist. (That middle ground exists and is important is actually the main theme of this blog. And has been since I began writing it years ago as blog about the contradictions between scientific and religious thought.)
So I’m very excited to read a column in the New York Times today about a new field developing in the area of formal logic: dialetheisms.
The article starts off by positing the ancient liar’s paradox – a local version of which might read: “Everything you read on this blog is a lie”. If that’s true, then everything you read on the blog is a lie, except that statement which is true. Or conversely if the statement is a lie then everything on the blog is true except the statement. The “Liar’s paradox” (known to the ancients) is the classic example of a sort of contradiction that has no clarity.
“According to this theory, some contradictions are actually true, and the conclusion of the Liar Paradox is a paradigm example of one such contradiction. The theory calls a true contradiction a dialetheia (Greek: ‘di’ = two (way); ‘aletheia’ = truth), and the view itself is called dialetheism. One thing that drives the view is that cogent diagnoses of what is wrong with the Liar argument are seemingly impossible to find. Suppose you say, for example, that paradoxical sentences of this kind are simply meaningless (or neither true nor false, or some such). Then what if Professor Greene had written on the board:
Everything written on the board in Room 33 is either false or meaningless.
If this were true or false, we would be in the same bind as before. And if it’s meaningless, then it’s either false or meaningless, so it’s true. We are back with a contradiction. This sort of situation (often called a strengthened paradox) affects virtually all suggested attempts to explain what has gone wrong with the reasoning in the Liar Paradox.
In a way this is the more robust expression of a class of logic that is sometimes called “fuzzy logic” or tri-state logic. There are engineering problems (like the cooking of rice or robotic vacuum cleaner programing) that need to make use of this sort of thinking. It allows one to make an inference that is neither true nor false – more a “maybe” than anything else.
In other words, sometimes there’s no “clarity” to be had. No matter how hard we want to find it. It’s just not possible. The best we can do is to say something is a paradox and leave it at that. Living into the Mystery is what the Theologians call it.
Now science is starting to realize that there might be something to all this. Perhaps it will help us to resolve some of the great problems of science by leaving them as paradoxes.
If dialetheias are pretty rare, and if they appear to be fairly esoteric things like the Liar sentence, you might wonder why we should bother about them at all. Why not just ignore them? One ignores them at great risk. Scientific advances are often triggered by taking oddities seriously. For example, at the end of the 19th century, most physicists thought that their subject was pretty much sewn up, except for a few oddities that no one could account for, such as the phenomenon of black-body radiation. Consideration of this eventually generated quantum theory. Had it been ignored, we would not have had the revolution in physics produced by the theory. Similarly, if Cantor had not taken Galileo’s paradox seriously, one of the most important revolutions in mathematics would never have happened either.
Revolutions in logic (of various kinds) have certainly occurred in the past. Arguably, the greatest of these was around the turn of the 20th century, when traditional Aristotelian logic was overthrown, and the mathematical techniques of contemporary logic were ushered in. Perhaps we are on the brink of another.”
You can, and you should, read the full essay here.