Simply Wittgenstein

Some Complications

The big picture of structured facts and sentences, discussed in the previous chapter, leaves a number of details to be clarified. For example, many sentences seem to make sense but do not obviously fit this model, such as sentences about morality or mathematics. How are these instances to be handled? Wittgenstein proposed two options—either demonstrate that a problematic kind of sentence does actually fit the model, or argue that the sentence in question does not make sense after all. We will see that he resorts to each of these options in various cases.

Fiction and Directions

Consider a sentence like “The white kitten had been having its face washed by the old cat for the last quarter of an hour,” from the opening of Through the Looking Glass. What are we to make of this? It is not exactly true, as it does not seem to correspond to any fact in the world. But it is not exactly false either, since it is not meant to correspond to any such fact. Lewis Carroll meant it to create a world of make-believe, but we can’t tell that just from hearing or reading the sentence. 

In the Tractatus, Wittgenstein does not consider sentences that are fictional. He just assumes that descriptive-sounding sentences are meant to be about the world, and pictures are intended to represent the world. 

But how do we know when a sentence is meant to be about the world? You might say that this sentence about the kitten is in a novel or a work of fiction, so it’s not about the real world. Yet, the very same sentence could have appeared in someone’s diary. 

The same questions could be raised about a drawing—is it meant to be a representation of a portion of reality, or does it come from the artist’s imagination? Or, for that matter, couldn’t it be a sort of blueprint—a plan for what the draftsman intends to build? You can’t tell which it is just by looking at the drawing alone. 

While Wittgenstein did not address this problem directly, he did provide some relevant information: “A proposition is true if we use it to say that things stand in a certain way, and they do” (TLP 4.062). How would we use it to say things stand in a certain way? We could, for example, check the facts to see if the proposition is accurate. If we take a sentence to be fictional—say from a novel or fantasy—then we do not investigate any further. But if we take it to be part of a factual biography or documentary, then we may. And if we take the sentence to be part of the stage directions for a set, then we might go on to create the set that will make them be true.

On November 13, 1926, Wittgenstein and an architect named Paul Engelmann applied for a building permit for a house to be constructed in Vienna for Wittgenstein’s sister Gretl. The application contained a site plan and a number of drawings of floors and elevations. The fact that the drawings were part of this application indicated that they were plans for something to be constructed, rather than descriptions of something already in existence. There were also conventions, such as the use of blue paper and certain drawing styles, to indicate the use to which the drawings would be put.

Gottlob Frege thought he could sort out the problem of fiction vs. reality by prefixing an assertion sign “” to a proposition, so that “The cat is on the mat” indicated that the proposition was meant to be a representation. Similarly, one might prefix a “directive sign,” say, an exclamation mark, to indicate a sentence is to be made true: “!—The cat is on the mat.” Then the sentence would be part of stage directions, or an order: Put the cat on the mat! However, a novel can claim to be a work of history, in effect placing an assertion sign in front of each of its sentences, even though this does not make it so.

Recall the controversy over James Frey’s 2003 book, A Million Little Pieces, which he claimed was a memoir. In 2005, it was picked for Oprah Winfrey’s Book Club and became a best-seller. Yet based on an independent investigation, Oprah later got him to admit that large parts of it were made up. Or a movie can present itself as a documentary, and yet still be fiction, as with “The Blair Witch Project.”

In these sorts of difficult cases, the key is not in the nature of the proposition, or in what the proposition claims for itself, but in how we use or treat the proposition. As Wittgenstein phrased it, “What signs fail to express, their application shows” (TLP 3.262). Investigators looked into whether the events Frey described had happened—thus treating the book as history. But Frey’s confession on Oprah’s TV show made that sort of investigation no longer relevant.

In the case of a book, it is, presumably, up to the Library of Congress to classify it as “Fiction” (any call-number beginning with P) or “Non-fiction”—in effect, deciding whether to prefix the book with an assertion sign. In Frey’s case, the book was originally classified as HV (Social Pathology, Social and Public Welfare, and Criminology) and never officially reclassified to indicate its fictional nature. Nevertheless, the Brooklyn Public Library chose to re-shelve it with Fiction.

Consider some painting hanging on the wall. Is it meant to represent a real or imaginary scene? How would you tell?

Generalizations

When describing the world, we can make specific claims, such as “Socrates is mortal,” or “Kofi is smart.” But sometimes we wish to make generalizations, for instance, “All men are mortal,” or “All the people in this room are smart.” It seems as though generalizations correspond to complex facts, so that the latter assertion would really just amount to: “Juan is smart AND Betty is smart AND Kofi is smart.” If we can list all the specific cases that are covered, we can treat the generalization as a logical conjunction of all the specific cases. Even if we would have trouble coming up with all the specific cases, as in “All men are mortal,” as long as we suppose that the number of specific cases is finite, we can imagine treating it in the same way. 

This would seem to be the way Wittgenstein should have handled generalizations. However, in the Tractatus he did not. In fact, he rejected it: “I dissociate the concept all from truth-functions” (TLP 5.521). Still, it is not clear how he did wish to handle them. When he looked back on the Tractatus in lectures he gave a dozen years later, he said that he had taken the logical conjunction view, however mistakenly (PO, pp. 89-90). He noted that he had, at the time he wrote the Tractatus, failed to realize that the logical conjunction would amount to the generalization only in circumstances in which there are a finite number of cases. But it will not do so where there is an infinite number of cases, such as the Goldbach Conjecture, which states that every even integer greater than 2 can be expressed as the sum of two primes. In such a case, we can write: “4 is the sum of two primes AND 6 is the sum of two primes AND 8 is the sum of two primes AND….” But the catch is in the ellipsis (which we read as “and so on”). And even in cases like “All men are mortal,” where we don’t suppose there is an infinite number of men, if we mean to apply the assertion even to the future cases of those yet to be born, then we have an indefinite set, which encounters the same problem. There is no complete logical conjunction that can be equated to the generalization.

Russell had also foreseen problems with the logical conjunction view (PLA, Lecture V). Even if we could list all the cases, our work would still not be done until we had added “…and those are all the cases.” But that is not itself an elementary proposition or a truth-function of elementary propositions, so we haven’t gotten what we wanted in any case.

Generalizations that cover an indefinite number of cases, then, remain a problem for Wittgenstein in the Tractatus.

Showing

Semantics is the study of how language relates to the world. It is concerned with how we can talk about something. Wittgenstein’s model for language is language that is about the world. But can’t language also talk about itself? Can’t language talk about how it relates to the world? Not according to Wittgenstein: “Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it—logical form” (TLP 4.12). 

So too, one might hold that pictures can portray anything in reality, but they cannot portray what they must have in common with reality in order to be able to portray it. Yet, as soon as we spell this out, it seems questionable. Consider René Magritte’s 1933 painting entitled “The Human Condition” (see illustration). It is a painting of a painting and the scene it depicts. Wittgenstein holds that: “A picture represents its subject from a position outside it…. A picture cannot, however, place itself outside its representational form” (TLP 2.173-2.174). While it is true that a picture cannot place itself outside its own representational form, it seems possible, as Magritte showed, to stand outside the representational form of another picture.