If we introduce verbs into the language to stand for the specific generative processes, we fill a much stumbled-over gap. By recovering what is on both sides of the interface, and the direction the relation between them runs, we clarify much that was confused because unstated. Let us coin “generyte” and “misgeneryte,” and let us make clear that these processes are specifically mental and of the particular neurocybernetic nature that produce the utterances which, through a host of overdeter- mined and partially determined reasons, we have been recognizing as “true” and “false.” If we introduce these verbs into our paradox, it stands revealed simply as two incorrect statements.
On one side of the paper instead of “The sentence on the other side of this paper is true,” we write:
“What is on this side of the paper generytes the sentence on the other side.”
And on the other side instead of “The sentence on the other side of this paper is false,” we write:
“What is on this side of the paper misgenerytes the sentence on the other side.”
Looking at either sentence, then turning the paper over to see if it does what it claims, we can simply respond, for both cases: “No, it does not.” One (among many) properties that lets us recognize a generyted (or misgeneryted) sentence is that it is in the form of a description of whatever generyted (or misgeneryted) it; neither sentence is in that form.[38]
A last comment on all this:
The whole problem of relating mathematics to logic is basically the problem of how, logically, to get from conjunctions like “1 + 1 = 2 and 1 +? 1 ≠ 3,” which is the sort of thing we can describe in mathematics, to the self-evident (yet all but unprovable) logical implication: “1 + 1 = 2 therefore 1 + 1 ≠3,” which is the process that propels us through all mathematical proofs.
Now consider the following sentences, one a conjunction, one an implication:
“This sentence contains ten words and it misgenerytes itself.”
“If this sentence contains ten words, then it misgenerytes itself.”
About the first sentence we can certainly say: “That sentence contains nine words, therefore it misgenerytes itself.” If that self-evident there-fore can be considered an implication, and assumed equivalent to (“to have the same truth values as” in our outmoded parlance) the implication of the second sentence, then, working from the side of language, we have, self-evidently, bridged the logical gap into mathematics!
Before making such an assumption, however, count the words in the second sentence…
29. Vanessa Harpington (during a period when she [not I] thought her work was going badly), shortly after Alfred’s departure for Rumania:
“What use is love?
“It assures neither kindness, compassion, nor intelligence between the people who feel it for one another.
“The best you can say is that when good people love, they behave well… sometimes.
“When bad people love, they behave appallingly.
“I wonder what the brilliant Alfred will have to say about a paradox like that!’
“First of all, Vanessa,” I reminded her as we walked the cobbled streets, with the Arno, dull silver, down every block, through the Italian summer, “you simply cannot take such abstract problems so seriously. Remember, you and Alfred are both fictions: neither of you exists. The closest I’ve ever been to passing a summer in an English country house was a weekend at John and Margery Brunner’s in Somerset, and though I spent a few weeks in Venice once, I’ve never stayed in an Italian villa in my life! I’ve never even been in Florence — ”
“Oh, really,” Vanessa said. “You just don’t understand at all!” and, for the rest of the walk back, stayed a step or two ahead of me, arms folded and looking mostly somewhere else, though we did eventually talk — about other things.
30. Finished reading Gombrich’s Art and Illusion yesterday. The oversized paperback seems to be losing most of its pages. A thought: When I hold up my hand in front of my face, what I see is my hand, in focus, and, behind it, a slightly unfocussed, double image of the rest of the room, those images further away blurrier and slightly further apart. (Actually, parts of the double image keep suppressing other parts, and then the suppression pattern changes.) How odd that in the search for more and more striking illusions of reality, no artist has ever tried to paint this.
One reason, I suspect, is that art has never really been interested in painting What You See; from the most abstract to the most representational, art is interested in purveying the concept of What Is There. Representationalists have, from time to time, used a limited number of tricks of the eye to emphasize (by making their paintings look more like what you see) that the subject is there. Abstractionists use the reality of paint, brush stroke, and material for the same end.
31. A common argument between philosophers often runs like this:
A. I have a problem within this particular context.
B. I have a context within which I can solve your particular problem.
A. But I want a solution within my context!
B. But I can translate your context, in all particulars that interest me, into my context.
A. But you can’t translate my problem into your context so that it is still a problem and then produce a solution for it that will fit mine! Is there any way you can prove that, within my context, my problem is insoluble?
B. I’m not interested in proving your problem insoluble! I’m interested in solving it! And I have!
A. If you are interested in proving my old problem insoluble, then I am not interested in your new context! It doesn’t relate to my problem!
32. The greatest distress to me of Structural Anthropology is its sexism. The primary descriptive model, “Society operates by the exchange of women,” as a purely descriptive model, has the value of any other: There are certainly contexts in which it is useful. The same can be said of such other famous descriptive models as: “Jews are responsible for the financial evils of Europe,” or “Blacks are lazy and shiftless but have a good sense of rhythm.” It is the nature of descriptions that, as long as they model some fraction of the reality, however minute (even to the fact that persons A and B have agreed to use model p as a description of situation s [which is the case with individual words]) they can be called useful. But pure descriptive usefulness is not in the least contingent on how much the internal structure of the description reflects the way in which the fragment of reality it models relates to the rest of the case. Such descriptions that try to mirror these relations, to the extent that they succeed, can be called logical (functional) descriptions. But the very form of the absolute statement precludes its being a logical (functional) description. And when a description is of a small enough fragment of reality, and it reflects neither the internal workings of what it is describing nor the external workings, it can be said to be an emblem — or, if it is made up of a string of words, a slogan. And it is the slogan’s pretension to logical (functional) description that makes it so undesirable. When trying to establish a coherent system, such as a coherent anthropological discipline (as Lévi- Strauss is attemping), we want logical models that can also be used as part of a logical context. Such models as the ones above, as they pass into context, yield situation after situation where abuse is almost inevitable:
If a woman objects to being exchanged or refuses to be exchanged, for example, by the above model she can be described as opposing society’s workings. But if a man objects to or refuses to be exchanged, he can be described as objecting to being treated as a woman! And on and on and on ad (in the manner of context models) infinitum.
38
Such translation into an artificial language may at first seem suspect. But is it really any more dubious than the translation Russell suggests in his theory of singular descriptions which so facilitates the untangling of