Zen and the Art of Expression Paradoxes
There is a paradox in metamathetics that asks the thinker to conceive of “the smallest number not describable in fewer than eleven words.” The paradox arises when the thinker notes that that description itself is ten words long, and thus any number to which it refers is, indeed, describable in fewer than eleven words.
This particular paradox is shown to be a false paradox when it’s pointed out that the number doesn’t necessarily have to exist. That is, any number which it describes would be paradoxical, but if that number doesn’t exist, there is no paradox.
Thinking along these lines, however, engenders thoughts about the whole problem of paradoxes of expressibility. Medieval theologians (such as Cusanus) endorsed the notion of God as a being so great, so Maximum, that complete comprehension of Him is impossible, that we cannot possibly understand God. Similar ideas have been expressed by others (the Taoist notion that “The Tao which can be spoken is not the eternal Tao” comes to mind), but the essential notion is that one is contemplating the uncontemplatable or expressing the inexpressible.
Many observers have pointed out paradox here. This has been taken in a variety of directions, from rationalists using it as justification for a reductio the denies God, to dialetheists using these kinds of problems as justification for a worldview wherein some contradictions hold. But these vectors rely on the notion that this is a true paradox—a notion which does not, I think, hold water.
Let us take the most easily discussable instantiation of this: a concept that is inexpressible. Lao-Tzu wrote that “The Tao which can be spoken is not the eternal Tao.” This line has been translated in ways that are less paradoxical, but this is one of the most famous, and a version with which most Taoists are familiar.
The problem, as has been pointed out, is that this seems to imply that anything said about the Tao is false. If anything said about the Tao is not true, we’ve entered a sort of Liar’s Paradox, where that statement (as well as any of the other text relating to the Tao) is also not true, and therefore of zero epistemic value to us.
The failure, here, is in a confusion of accuracy with entirety. That is, the Tao is, according to Lao-Tzu, something whose fundamental nature, whose entire quality, is beyond articulation or expression. We cannot contain it in words. But that does not mean we cannot contain parts of it in words, or that it does not have some describable qualities.
Such is the case with the Tao. It is impossible to express it directly and entirely. But it is so infinite that it does include certain expressible traits, and thus we are not perjuring ourselves when we claim that the Tao cannot be spoken.
A similar chain of reasoning holds when articulating apparently paradoxical qualities attached to other objects. If we say that God is too great to be conceived of, or more directly if we define God as that which is too great to conceived of, we arise into apparent paradox by pointing out that, in thinking of “an object to be great to be conceived,” we are conceiving of God, and thus are entering paradox. But that misjudges what is happening when we conceive of something beyond conception. When we conceive of an object beyond conception, we’re instantiating a placeholder object and giving, by fiat, the quality of inconceivability. Obviously, this object will be paradoxical, because the only quality it has is its inconceivability, and thus in conceiving of it with that quality, we are conceiving of it in entirety—this stands in violation of that quality, and thus we get paradox. But God, when defined this way, is understood to be MORE than just an unconceivable object; God is Creator or the Absolute Being or whatever else you want to add to God’s totality. But one of God’s qualities is that It is beyond full conception or understanding.
Paradoxes of these sort also resolve when we remember that expression (and even, if you construct it so, conception) is a process of representation. That is, an uttered phrase points to an actual state of affairs or an actual entity; the phrase itself is separate from the actual entity. The words are as a finger, pointing to the moon. We see paradox in these articulations when we confuse the finger for the moon.
