Without naming Wittgenstein, the court has opted for a family resemblance understanding of the concept of “religion.” Perhaps closer to American jurisprudential tradition is the Harvard philosopher-psychologist William James. In a favorite book of Wittgenstein’s—The Varieties of Religious Experience, James set out a position in 1902 that Wittgenstein must have taken to heart:
Most books on the philosophy of religion try to begin with a precise definition of what its essence consists of. Some of these would-be definitions may possibly come before us in later portions of this course, and I shall not be pedantic enough to enumerate any of them to you now. Meanwhile, the very fact that they are so many and so different from one another is enough to prove that the word “religion” cannot stand for any single principle or essence, but is rather a collective name. The theorizing mind always tends to the over-simplification of its materials. This is the root of all that absolutism and one-sided dogmatism by which both philosophy and religion have been infested. Let us not fall immediately into a one-sided view of our subject, but let us rather admit freely at the outset that we may very likely find no one essence, but many characters which may alternately be equally important in religion.
The US Supreme Court has, on this issue, avoided the kind of theorizing, over-simplification, and dogmatism that Wittgenstein and James opposed.
Analysis
In the Tractatus, Wittgenstein held that familiar facts could be broken down—analyzed—into facts at the most basic level—“atomic” facts. The notion of an “atom” comes directly from the ancient Greeks. The Greek word atom means not-cut. (Notice that in English, an appendectomy is where they cut out your appendix.) What the ancient Greek philosopher Democritus called an atom was a minute bit of matter that could not be broken down any further. Everything else was built up out of arrangements of these atoms. Wittgenstein had been interested in the search for logical (not physical) atoms—he was sure they existed, and he called them “objects.”
It is an irony of history that during the Second World War, scientists in the United States figured out how to “split” the physical atom. To the ancient Greeks, that would have seemed to be a contradiction in terms. But it shows that what we might have supposed to be the most “basic” level turned out not to be basic after all. The atom was split into electrons, photons, protons and neutrons. And these, in turn, had been split into quarks. The search for “elementary” physical particles continues, but it is unclear if or where it will end.
In the Investigations, Wittgenstein took a much more pragmatic view of complexity. He no longer supposed that some things are inherently complex, or that there is some analysis that would reveal their true structure built up out of simple parts:
But what are the simple constituent parts of which reality is composed?—What are the simple constituent parts of a chair?—The bits of wood of which it is made? Or the molecules, or the atoms?—“Simple” means: not composite. And here the point is: in what sense ‘composite’? It makes no sense at all to speak absolutely of the ‘simple parts of a chair’. (PI §47)
For an event planner, the chairs themselves would be the simple parts out of which arrangements could be made. For a woodworker, the legs and arms and seats would be the simple parts from which a chair could be built. And for a chemist, the cellulose fibers would be the simple parts out of which a piece of wood is composed.
You can’t ask whether a particular object is composite or simple “outside a particular language game” (PI §47). The question only makes sense “if it is already established what kind of complexity—that is, what particular use of the word—is in question” (PI §47). The grammar of the language game tells us what counts or does not count as simple. So this is not a discovery so much as it is a stipulation. Wittgenstein now replied to a question about simplicity, in the abstract, apart from a purpose or context, by rejecting the question.
9-11 and the Twin Towers
On September 11, 2001, the twin towers of the World Trade Center in New York City were destroyed when they were hit by two Boeing 767 airliners piloted by suicide terrorists. In addition to the loss of thousands of lives, the material losses were in excess of $7 billion. The leaseholder for the World Trade Center sought insurance payment of this amount, but the insurance coverage was limited to $3.5 billion per insured “occurrence.” The leaseholder claimed the destruction was two events, in which American Airlines Flight 11 hit the North Tower at 8:46 am local time, and then United Airlines Flight 175 hit the South Tower at 9:03 am local time. The insurance company argued the destruction constituted only one event, a “coordinated” attack in which a terrorist cell destroyed the World Trade Center. It turns out to make a huge difference whether it was one event or two.
Who was right? Wittgenstein’s earlier account might have suggested that the leaseholder was right since the coordinated attack could be analyzed into two spatio-temporally separated crashes. But Wittgenstein’s account in the Investigations suggests that it is important to determine the language game in which the question is being asked. For the purpose of discussing terrorist strategy, the coordinated attack seems to be a focus of attention. For the purpose of determining the impact on Lower Manhattan, there are two events to consider. There is no right answer in the abstract.
A federal jury ruled that there were two occurrences “for insurance purposes,” siding with the leaseholder. Yet the finding by the U.S. District Court of Manhattan was that the leaseholder should collect $4.6 billion. Perhaps this was a sort of compromise to indicate the inherent indeterminacy of the issue. In any case, Wittgenstein showed why questions like this could not be answered without specifying the context and purpose for which the question is asked.
Meaning
In the Tractatus, Wittgenstein saw meaning as a matter of correspondence between language and the world. Language was about the world by being isomorphic with it. But even in the Tractatus Wittgenstein realized that there needed to be a way to indicate that something was meant to be a picture or a representation.
What does a word or phrase mean? Here is an answer offered by Humpty-Dumpty in Chapter VI of Lewis Carroll’s “Through the Looking Glass”:
“…there are three hundred and sixty-four days when you might get un-birthday presents—”
“Certainly,” said Alice.
“And only ONE for birthday presents, you know. There’s glory for you!”
“I don’t know what you mean by ‘glory’,” Alice said.
Humpty Dumpty smiled contemptuously. “Of course you don’t—till I tell you. I meant ‘there’s a nice knock-down argument for you!’”
“But ‘glory’ doesn’t mean ‘a nice knock-down argument’,” Alice objected.
“When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
“The question is,” said Alice, “whether you CAN make words mean so many different things.”
“The question is,” said Humpty Dumpty, “which is to be master—that’s all.”
We might call this the “intention” theory of meaning. A word or phrase means whatever I intend it to mean. The above passage makes fun of the intention theory of meaning. If Alice had been thinking harder she would have asked Humpty Dumpty what he meant by “a nice knock-down argument,” for this intention theory leads to an endless regress, and it can’t be the whole story. But the moral here is that we can’t make a word mean something just by intending it to.
Wittgenstein raised this issue in a similar way: “Can I say ‘bububu’ [this is a baby sound made by running your index finger up and down over your lips as you make a B sound] and mean ‘If it doesn’t rain I shall go for a walk’?” (PI, p. 22). You can certainly imagine that scenario or think that thought while you make that sound. But imagining it while you make the sound is not the same as meaning it by that sound. Wittgenstein continued: “It is only in a language that I can mean something by something. This shows c
learly that the grammar of ‘to mean’ does not resemble that of the expression ‘to imagine’ and the like.” In fact, when I mean or understand something, there may be all kinds of things going on in my mind at the time—I may even form pictures, but it is a mistake to suppose they constitute the meaning or understanding of the word or phrase.
What does constitute the meaning? In the Tractatus, Wittgenstein offered a theory of meaning. But in the Investigations, he wrote: “And we may not advance any kind of theory” (PI §109). He did bring up things designed to help loosen the hold misguided theories have on us. The Humpty-Dumpty story serves that purpose nicely. Wittgenstein wanted to remind us that we judge whether someone understands something not by how they feel about it inside, but by what they can do with it in practice—how the person can use it. Wittgenstein acknowledged both these aspects: the inner or subjective aspect of meaning—what he called grasping it “at a stroke” or “in a flash,” and the outer or objective aspect of meaning—how it is used or applied (PI §138). Wittgenstein emphasized the outer aspect, while not entirely discounting the inner one because he did not offer an objective theory of meaning either. He put the point carefully: “For a large class of cases of the employment of the word ‘meaning’—though not for all—this word can be explained in this way: the meaning of a word is its use in the language” (PI §43).
Flags and Mascots
In the United States, there has been a decades-long debate about the acceptability of displaying the Confederate battle flag. People whose ancestors fought in the Civil War on the side of the Confederacy (and their sympathizers) argue that the flag represents the values of historical commemoration, Southern or rural culture, and conservative politics. Yet, historically the flag has also been associated with the defense of slavery, racism, and White supremacy. Because of its negative associations, many people find the flag to be offensive, but its defenders have insisted that they do not mean to offend, but only to emphasize the flag’s positive values.
To a certain extent, these are legal matters that involve the interpretation of free speech. The fact that these symbols are seen as “speech” confirms Wittgenstein’s view of language games as not just language in the narrow sense. The relevant issue here is one of meaning—what does the flag mean or represent? Its advocates seem to be offering an intention theory of meaning—we don’t intend any offense, therefore, the flag does not mean anything offensive. But is that an acceptable theory of meaning? According to Wittgenstein, meaning is something more than and apart from, what one has in mind.
On the other hand, opponents of the flag’s display seem to be offering an interpretation theory of meaning—the flag is offensive because I take offense. Is that any better as a theory of meaning? When people complain about “political correctness,” what bothers them is that too much weight is given to how something is perceived and to those who take offense.
This interpretation theory of meaning seems equally flawed. Several years ago, there were a few incidents in the United States in which some people were offended by the use of the word “niggardly.” The word sounds like “nigger,” which is almost universally agreed to be offensive, but in fact, it means “stingy” or “miserly,” and has nothing to do with the racial slur. The fact that some people interpreted the word as a racial slur does not make it one.
It seems that meaning is not a matter of the intention of the user, and equally it is not a matter of the interpretation of the hearer. What is it then? If one thinks that meaning depends on use, then the issue is more complicated. It cannot be denied that the flag has been used for offensive purposes over many decades. Can it be “separated” from the offensive uses by contemporary attempts to use it in other ways? There has been a recent discussion of these issues in Europe surrounding the swastika. The symbol had a positive use for thousands of years before the Nazis appropriated it for evil use. Can that symbol ever be reclaimed?
Unfortunately, even though Wittgenstein highlighted the importance of use to meaning, he did not say much about how to assess use. We might ask: Whose use? Wittgenstein seemed to treat the users of the language as a monolithic group, without attending to the varieties of use, either at a time or over time. But this gives readers of the Investigations an opportunity to do some philosophy themselves. How might we deal with issues such as this, using the tools that Wittgenstein provided?
I have described the flag issue in some detail so that it can serve as a model for similar topics, such as the use of Native American images as mascots. While they have disappeared gradually at the high school level, they continue to be occasionally used at the college and professional levels. The professional baseball team in the city where I grew up, Cleveland, is called the “Indians,” and the logo for the team is hard to look at. The professional football team that is close to where I live now, the Washington Redskins, has been strongly criticized for its name. The arguments over these matters have tended to follow the pattern of the flag arguments. Proponents of the name or logo emphasize the courage and honor of Native Americans; opponents see them as narrow caricatures of a legacy that was stolen from them. What would Wittgenstein say about these cases? How might they be discussed using Wittgenstein’s tools?
Understanding and Rules
Do you understand addition? I hope any reader of this book does. Wittgenstein used this simple case, but the points he made are equally applicable to the question of understanding calculus or quantum physics. The question in this context raises the philosophical issue of what it takes to understand something. Generally, if you are asked whether you understand something, you can think about it for a moment and answer. You may well have a feeling of confidence, which leads you to answer affirmatively, or a feeling of confusion, which leads you to answer negatively. But, as with the discussion of meaning, a feeling of confidence is not the same thing as understanding. After all, you can feel confident and get something consistently wrong (we all know people like that), or feel confused and yet manage to get it consistently right. Understanding something is a matter of whether you can get it right. Wittgenstein compared our use of “understand” with “can,” “is able to,” and “to have ‘mastered’ a technique” (PI §150).
So, in essence, understanding addition is a matter of whether you have mastered the technique of adding. And that isn’t something that we can necessarily take your word for. In general, whether we understand something is not a matter of our just saying so. What does it take to be able to add? What does it mean to get it right?
“Let us suppose that after some efforts on the teacher’s part [the pupil] continues the series correctly, that is, as we do it. So now we can say that he has mastered the system” (PI §145). “As we do it.” In writing this, Wittgenstein did not appeal to some transcendent numerical pattern to test our ability—it is tested by an appeal to how we do it. That might seem like a weak standard—couldn’t “we” be doing it wrong?
That’s a good question, and the answer depends on the case. But consider the case of understanding how to alphabetize a list. A student understands this process when she puts the list in alphabetical order—a, b, c, d….all the way to z. Yes, but couldn’t that be wrong? That question really doesn’t make sense. There is no “true” alphabetical order other than the one we use. Of course, we could have used a different order—but the order we use, the one we chose, couldn’t be wrong. Wrong in light of what? There isn’t anything further, any divinely ordained order, that it could be compared with.
But what about mathematics? Isn’t there something like a divinely ordained order there? The case Wittgenstein discussed is “adding 2”: 2, 4, 6, 8, 10….
Let’s suppose we have done exercises, and tested his understanding up to 1000.
Then we get the pupil to continue…beyond 1000—and he writes 1000, 1004, 1008, 1012.
We say to him, “Look what you’re doing!”—He doesn’t understand. We say, “You should have added two: look how you began the series!”—He answers, “Ye
s, isn’t it right? I thought that was how I had to do it.”—Or suppose he pointed to the series and said, “But I did go on in the same way.” (PI §185)
This is a hard scenario to wrap your head around. Clearly, the pupil has done it wrong. But (here’s the philosophical problem), what makes it wrong? It is not simply a case where the pupil has misremembered, as when he says, “2, 4, 8, 12….” That directly contradicts the teacher’s examples. We are supposed to imagine a case that goes beyond what has been explicitly taught. Even if the pupil was explicitly taught into the thousands, then we should imagine a scenario involving, say, 5-digit or 6-digit numbers. The point is that at some stage the student has to go on “in the same way,” but without having had explicit guidance.
Yet, our feeling is that this pupil doesn’t need explicit guidance because the initial guidance plus the nature of addition suffice to determine the next steps. It is as though the series of even numbers is laid out in heaven—visible to God, and to those who understand addition! How could the pupil go wrong in this way?
Let’s try to put more flesh into this scenario than Wittgenstein did. For example, recall how our base-10 number system involves moving from 1-digit numbers to 2-digit numbers, and then to 3-digit numbers, and so on. Although we get the hang of those transitions, they are not obvious when you think about it, and they come up increasingly rarely. At a certain point in the training, you may have to just say, “that’s how we do it—our number system is built to use only 10 different digits (i.e., it is base-10) and that is how we use it to count.” Hardly anyone fails to get this way of using numbers. This is what Wittgenstein called sharing a “form of life.”
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