Suppose A writes the series 1, 5, 11, 19, 29, and B says, "now I can go on," writing down the number 41. B might have calculated the formula a(sub)n = n^2 + n - 1 in his head, or he might simply have recognized a pattern in an intuitive fashion. In knowing how to continue the series 2, 4, 6, 8, we probably do not need to consult an algebraic formula in our heads. Knowing a formula seems a symptom of being able to go on, suggesting that there must be something explicable about the vague idea of "being able to go on."
The sentence "B can continue the series," can mean a number of things: that B knows the formula, that B has done this before, that B has not forgotten the formula, etc. While "B knows the formula" can often mean the same thing as "B can continue the series," under certain circumstances it might not. We should not conclude that "B can continue the series" describes a special state of affairs that stands behind the individual instances of knowing the formula, imagining further terms, and so on.
At the end of game sixty-four, Wittgenstein considers a variety of cases in which we say "I can " and then fail to do what we said we could, which he links with the various cases in which we talk about "forgetting" and "trying." Because "can" is in the present tense, we think of being able to do something as a mental mechanism that is present in us. This is similar to the notion that reading is a mental mechanism. Wittgenstein shows us that there is a family of different activities that we might refer to as "reading," ranging from skimming through a book silently, to painfully spelling out each letter. On the other hand, if the beginner has already memorized the passage he is being told to read, and then speaks the passage perfectly from memory, we say that he is not reading.
Suppose someone who is being trained to read occasionally pronounces random words, and sometimes these words are coincidentally the words on the page he is looking at. His teacher might claim he is not reading, because it is mere accident that he says the correct words. However, if the student goes on to pronounce some further words correctly, the teacher might slowly conclude that he has learned to read. However, we cannot point to any specific moment and say the student began reading there. There is no clear line between reading and not reading. Wittgenstein considers the suggestion that a person is reading if he derives spoken words from the page according to the rule provided by the alphabet. But suppose he reads a "b" for every "a," a "c" for every "b," and so on. He is still deriving a rule from the alphabet, and is still reading.
Wittgenstein stresses that these examples are not meant to show us the inessential features of reading, deriving, and so on, so that we can see through them and grasp the essential features. His method is purely descriptive: he is not suggesting there is something essential behind these inessential features.
Wittgenstein addresses the topic of reading precisely because it seems like a case in which there is a mental mechanism at work. We can think of humans as reading machines, analogous to a pianola, where there is an internal mechanism that turns written words into sounds. It even seems that the alphabet gives us a standard rule to transform these written symbols into sounds.
While Wittgenstein shows us there is a wide family of uses for the word "read," not all of which fit easily into this picture of reading as mental mechanism, he also argues that even in the most seemingly clear-cut cases, we are wrong to identify an internal mechanism. In game sixty-seven, he imagines a case of humans as "reading machines" that are simply trained to take written words from a page and pronounce them aloud. Untrained humans might occasionally guess a word by accident, but the trainer insists that they are not yet reading. Wittgenstein points out that a student who guesses one word correctly, then another, and slowly passes from a state of what the trainer would call "not reading" to one that the trainer would call "reading," does not make the transition from "not reading" to "reading" at any identifiable point.
This argument is not simply meant to show that we cannot know at what point the student stopped guessing and started reading, it is meant to show that no such point exists. This language game is based entirely on the behavior of the people reading. The game does not make any reference to their internal states. The trainer bases his judgment of whether or not someone is reading entirely on that person's response to written signs. "Read," in this language game, is defined by the trainer's observation of the students' behavior.
Suppose the word "table" was the first of a hundred that a student correctly pronounces in a row. When the student says "table," the trainer says the student is not reading, but one hundred words later, the trainer concludes that the student is now reading. We do not know whether or not the student read the word "table." We gather that the student is reading from his general behavior, because he correctly pronounces so many words in a row that we no longer call it an accident. When we say he is reading, we simply mean his behavior is of a certain general pattern. We are not pointing to an internal mechanism that might have been switched on when he looked at the word "table."
We should not mistake Wittgenstein as a behaviorist, however. Behaviorism is a psychological movement, popular in the middle of the twentieth century, which insists that all we can rightly claim about a person's psychology is based on that person's behavior. We cannot make any definite claims about people's internal structure or mechanisms, but can only observe the outward manifestations of their inner life. Wittgenstein differs significantly from this view in that he denies the necessity of an inner life to explain outward behavior. He is not simply saying that we can only observe the outward behavior of someone reading and cannot make any reasonable conjectures as to what sort of internal mechanism is at work. He is also saying that we have no good reason to suppose any kind of internal mechanism exists.
In game sixty-nine, Wittgenstein offers a possible general definition of reading, saying that reading is derived from the rule provided by the alphabet. This seems to be generally true of all instances of reading, which seems to refute Wittgenstein's insistence that there is no general definition for reading. However, as Wittgenstein has already shown, "following a rule" manifests itself in a wide variety of ways. Identifying reading as a form of rule-following gets us no closer to a general definition.
Wittgenstein concludes part I of the Brown Book by saying, "Our method is purely descriptive; the descriptions we give are not hints of explanations." He has given us numerous different examples of what "reading" is, how "can" is used, what "being able to go on" consists of, and so on. The point of these different examples is not to hint that there is some underlying commonality that all of these words share. The point is to show that there is a family of different uses for these expressions, and while some expressions share certain features with others, there is essential feature that make them what they are. In looking for internal mechanisms and other such secrets, we are barking up the wrong tree.