Over the years my wife Mari and I have spent many wonderful months on the beautiful and busy island of Crete. We have come especially to love our many friends there. So, when someone casts dispersions on these people we naturally get a little upset. Well, it turns out that right there in the Bible (Paul’s letter to so must refer to Titus 1:12) a Cretan poet says about his own people: “Cretans are always liars.” Not only is this a surprising thing for a person to say about his own people, but it seems to involve a logical paradox that has puzzled logicians for centuries.
The problem is that here is a Cretan person saying that all Cretans are always liars. Now either what he is saying is true, in which case he himself must be a liar and this very statement is a lie and therefore untrue. Or what he is saying is true and not a lie, which also contradicts his more general statement. So, either the original statement is wrong and itself a lie, or it is correct and entails that this original statement was itself a lie. Either way, the original statement seems to be both true and false. This seems very paradoxical indeed.
The great logician Bertrand Russell even troubled himself about this paradox and solved it to his own satisfaction, but not to everyone’s it seems. Quite a few learned journal articles have been written over the years by various logicians trying to criticize or defend Russell’s argument. Russell “solved” the problem by pointing out that there are different logical levels involved in the statements of the paradox and once these are distinguished the so-called ‘paradox” disappears. As I said above, not all logicians seemed to have agreed of Lord Russell.
Fortunately, we need not worry ourselves about these controverses here. But we are still left with the puzzle over how a statement can be both correct and false at the same time. Russell avoided the problem by cleverly introducing the “levels of language” gambit, but basically we are still left, at our own everyday level, with what seems to be a logical contradiction. How can a statement be both true and false at one and the same time?
The problem, then, has to do with the logical difficulties that arise when we try to speak about the very statement we are currently uttering. It’s called the “paradox of self-reference” and leads to many muddles. The Cretans in question could get themselves off the hook by inserting a logical qualifier that exempts the speaker from being included as one of the many subjects in the class “All Cretans”. Thus “All Cretans, except for the speaker, are always liars”.
This solution works for all such statements involving self-reference. Now, this may sound like a rather esoteric problem and clearly solvable, but it pats to pay attention to such idiosyncratic puzzles because they cast light on the nature of language and logic themselves. We run into this difficulty whenever we say things like “I now believe falsely that I am speaking English.” Most of the time we sail right through such potential problems and that is well and good. But its always fun, and wise, to acknowledge the logical difficulties built into language itself.