“Even as you or I, when we stand at the window looking at what’s outside.”
“And if that statement refers to what’s on this side of the paper (and memory assures me that it does), then they are in the same context, which means they cannot both occupy the same position in it at the same time.”
“Have you ever tried to stand out in the garden and inside the sitting room all at once? It is a bit difficult.”
“So if that is the case, then this statement has to be considered just as a… thing, like rain, or a sycamore, or a garden…”
“Or a sketch of a garden. Or a statement. Or a thought. They are things too.”
“But I recall distinctly. Alfred: The statement on the other side of the paper calls this statement — this thing! — false!”
“Wouldn’t really matter if it called it true, would it — ”
“Of course it wouldn’t! In the context I just outlined, I could no more call this… thing — ” I waved the statement — “‘true’ than I could call — ” I looked out the window at the easel with my sketch — “that thing true!”
“Though that does not reflect on its potential for truth if placed in another contextual position. If, for example, the statement on the other side of the paper read: ‘Your picture is in the garden,’ then it would be perfectly fine. Actually, it can work quite serially; what we’re really establishing is simply the unidirectionality of the modular context from the real. But then, all that semiological hair-splitting… Better turn over the paper and see if your memory isn’t playing tricks on you.”
Hastily I did. And read:
The statement on the other side of this paper is false.
“Yes,” I said, “there is a statement on this side, and it does attribute truth-or-falsity to the statement on the other. Which is nonsensical. It’s standing inside the sitting room in Bernham looking out the window and calling the rain ‘true.’”
“You never really did that,” Alfred said. “We just made a model of it that we judged nonsensical — useless in a particular sort of way. Keep looking at the side of the paper you’re looking at now — that is: Set up the context in the other direction.”
I did until I had:
“It’s the same situation. If I let the other statement occupy the modeling position and this occupy the position of the modeled thing, then the fact that the other statement attributes truth or falsity to what’s on this side means it’s nonsensical too.”
Alfred nodded. “It’s like having, on either side of your paper: ‘The thing on the other side of this paper is true (or false); the thing on the other side of this paper is false (or true).’ Which is an empty situation, in the same way that if you and, say, Vanessa, both had drawing pads and pencils and were sitting where you could see each other’s paper, and I gave you the instructions: ‘Both of you draw only what the other is drawing.’ You’d both end up with empty pictures.”
“Speaking of Vanessa,” I said, “let us go see what she is doing. She is a better artist than I am, which I suspect means that on some level, she has established a more interesting modular context with reality than I have. Perhaps she will take a break from her work and have some coffee with us.”
“Splendid,” said Alfred. “Oh, you asked me what I was doing in India? Well, while I was there, I got hold of some…” But that is another story too.
28. Language suggests that “truth” (or “falsity”) may be an attribute of sentences much as “redness” may be an attribute of apples. The primary language model is the adjective “true,” the secondary one a noun, “truth,” derived from the adjective. This is not the place to begin the argument against the whole concept of attributes. (It goes back to Leibniz’s inseparable subject/verbs for true predicates; Quine has demonstrated how well we can get along in formal logic without attributes, as well as without the whole concept of propositions.) But I maintain that, subsumed under the noun “truth,” is a directed binary relation, running from the real to the uttered, by way of the mind. The problems we have concerning “truth” (such as the paradox in section 27) are problems that arise from having to model a directed binary relationship without a transitive verb.
It is as if, in those situations in which we now say “The hammer strikes the nail” and “The hammer misses the nail,” we were constrained by the language only to speak of “strike nails” and “miss nails,” and to discuss “strikeness” and “missness” as attributes a given nail might or might not possess, depending on the situation, at the same time seldom allowing a mention of the hammer and never the moment of impact.
What “truth” subsumes (as well as an adjective-derived noun can) is a process through which apprehension of some area of the real (either through the senses, or through the memory, or the reality of internal sensation — again, this is not the place to discuss their accuracy) generates a descriptive utterance. This process is rendered highly complex by the existence of choice and imagination and is totally entangled in what Quine and Ullian have called “the web of belief”: confronted with the real, the speaker may choose not to speak at all, or to speak of something else, or she may be mistaken (at any number of levels), or he may generate a description in a mode to which “truth” or “falsity” are simply not applicable (it may be in G. Spencer-Brown’s “imaginary” mode). But when the speaker does generate an utterance of the sort we wish to consider, the overall process structure is still binary, and directed from reality to the sentence.
When I look out the window and say “It is raining outside,” what I perceive outside the window is controlling my utterance in a way the internal apprehension of which is my apprehension of the statement’s “truth” or “falsity.” My utterance does not affect — save possibly in the realms of Heisenberg — whatever (rain or shine) is outside the window.
People have suggested that the problem of paradox sentences is that they are self-descriptive. Yes, but the emphasis should be on descriptive, not self.
“This sentence contains six words” is just as self-descriptive as “This sentence is false.” But the first sentence is not paradoxical; it is simply wrong. (It contains five words.) The second sentence is paradoxical because part of the description (specifically “This sentence…”) covers two things (both the sentence “This sentence is false” and the sentence that it suggests as an equivalent translation, “This sentence is true”) and does not at all refer to the relation between them. The only predicate that is visible in “This sentence is…” suggests they relate in a way they do not: “This sentence ‘This sentence is true’ is the sentence ‘This sentence is false.’” And, obviously, it isn’t. But the same situation exists in Grelling’s paradox, the paradox of the Spanish barber, as well as the set-of-all-normal-sets paradox — indeed, in all antinomies.
The real generates an utterance via a process that allows us to recognize it as “true” or “false.”