The legendary Prester (Presbyter/Elder) John shows up in the writings of Shakespeare, Robert Lewis Stevenson, and Umberto Eco, and in the pages of Marvel and DC Comics. In the Middle Ages, he appeared on maps which were meant to be serious, maps which variously located him in Central Asia, India, and Ethiopia. Many believed that the spiritual progeny of the Apostle Thomas had somehow carved out a marvelous, somewhat-Christian kingdom (the citizens being Nestorians, who had trouble with the divine/human unity of Jesus’ nature) in the midst of Muslim lands, and that this John now presided over it.
Which brings us to a curious proposition upon which British philosopher, Bertrand Russell worked out, namely, ‘The present king of France is bald.’ No, Prester John was not the king of France, but both figures were non-entities, the king of France in Russell’s day and Prester John in any day. And, for our purposes, we may apply the same analysis.
Philosophers of the logical persuasion have been interested in the “truth value” of each proposition. (BTW, a proposition is not the same as a sentence since the same proposition may be expressed in very different sentences—‘It’s raining’; ‘Es regnet’: ‘Il pleure.’) That way, they can be rolled into chains of thought and argument. Take, for instance, what’s called modus ponens (from modus ponendo ponens, meaning, “By affirming, I affirm”). It simply says that the combination of ‘If A, then B’ and ‘A’ will give you ‘B.’ Fill in whatever you want, and it works. Start with “If my dog has fleas” for “If A”; for “then B,” add “then I’ll give him away.” So it’s spring loaded. Affirm that your dog has fleas, and it follows that you’re giving him away. The same goes for other setups, e.g., “If you heat water to 100 degrees centigrade, then it boils.” And there are other such logical rules, expressible in different schemes, with names like “disjunctive syllogism” and De Morgan’s Law. But to make them work, you need to have propositions which are either true or false (according to the Law of Excluded Middle) and not both true and false (according to the Law of Non-Contradiction). It’s like binary, digital computer program.
So what shall we make of ‘Prester John is bald’? (And I don’t mean ‘Prester John’ as a strictly literary figure; we’re not asking whether Hester Prynne and Superman were wearing red letters on their chests.) It hard to say whether it’s either true or false, for there’s no such person as Prester John. It’s a non-starter when it comes to truth. But Russell pressed ahead. He said that we should treat ‘The present king of France is bald’ as the conjunction of three propositions:
(a) There exists something that is the present king of France.
(b) There is only one thing that is the present king of France.
(c) Anything that is the present king of France is bald.
This, then, would render the proposition false. Done and done. Crisis of indeterminacy averted.
Alas, there are other troublesome propositions to bedevil the logicians and those who dream of a comprehensive systemization of knowledge, with everything in its proper place. The most prominent one goes back to the ancient philosopher from Crete, Epimenides, who said, “All Cretans are liars.” The problem was that he himself was a Cretan, and if what he says is true, then it’s false; it’s a lie. But if it’s false, it’s true, since it makes the point of Cretan mendacity. (By the way, some say that the Apostle Paul was confused about this in Titus 1:12, when he was criticizing Cretans. They say he mistook Epimenides’ philosophical puzzle for a moral pronouncement. But I think it’s the other way around. Epimenides was simply playing off the well-deserved reputation of his people, a reputation with which Paul was well acquainted.)
The puzzle has been refined to the statement, ‘This sentence is false.’ (If false true, if true false; so both—a contradiction.) And it’s been mapped onto a number of enterprises, including mathematics (by Kurt Gödel) and set theory. In this later connection, Bertrand Russell (according to Martin Gardiner) asked us to consider the barber who shaved every man in town who didn’t shave himself. So does the barber shave himself? Well, if he does, he doesn’t, but if he doesn’t, he does. Doh! Or, to put it otherwise, is this barber to found within the set of those whom he shaves?
To address the paradox, set theorists have simply disallowed the membership of a set within itself. It’s a little bit like the scene where Groucho Marx is playing a doctor: The patient raises his arm and complains it hurts when he does that. “Dr. Hackenbush” responds, “Well, don’t do that.” (The same goes for ‘This sentence is false.’ Declare it bogus and move on.)
The big problem is that, if you allow a contradiction into the system, you can prove anything. To demonstrate, let’s stipulate that ‘B’ means something crazy, like ‘Chickens are whales.’ So here goes, a look at the logical fallout of contradicting oneself:
Step 1: A and not-A. (a contradiction)
Step 2: A (If both A and not-A are true, then A alone is true all by itself.)
Step 3: A or B. (If A is true, then it doesn’t matter what you put for B; all it takes is for one side of the ‘or’ to make the whole sentence true.)
Step 4: not-A (If both A and not-A are true, then not-A alone is true all by itself.)
Step 5: B (If, as it says in Step 3, that it’s either A or B or both, then by eliminating the A side, with the “trump card” of Step 4, you’re left with B, which, again, is crazy. But it’s been “proven.”)
So a contradiction is like a virus. Let it into your computer, and it’ll eat everything.
Of course, this leaves open the question of whether language and knowledge are so orderly as all that, or if this is even an ideal. Metaphors, for one thing, are right unruly, yet sentences containing them can be quite meaningful. So too paradoxes. How about the opening to Dickens’ A Tale of Two Cities, “It was the best of times, it was the worst of times . . .”?