Is the familiarity of recognition a matter of seeing something as something? If A shows B a stick that he then pulls apart to reveal as a cap and pencil, B might say, "Oh, this is a pencil," recognizing the object as a pencil. If A simply shows B a pencil and says, "what's this?" and B replies, "oh, this is a pencil," we are tempted to say that B recognized the object as a pencil just as he did in the first case. But in the second case there was no moment of recognizing the object as a pencil, because there was never any question of what it was.

When we use the same word in two different expressions—e.g. "looking for a word in my memory" versus "looking for my friend in the park"—we are tempted to say that there must be some similarity between the two situations described. Whether we can identify the similarity or not, we think it must exist, of the same word would not apply to both situations. This is like saying that someone must understand an order before carrying it out. This is not the case, for sometimes people carry out orders without any distinctive act of understanding.

Even the word "similar" is not always used in the same way. For instance, the similarity between a pale blue and a dark blue is different from the similarity between a mental strain and a physical strain. The similarity we identify between two things often depends on the context.

Suppose we ask someone to arrange the vowels in order from lightest to darkest, and he writes "i, e, a, o, u." It does not follow that the person saw some similarity between each letter and a color, or even had any colors in mind when he arranged the vowels. There is not one paradigmatic use of "darker" to which we must compare all unorthodox uses of "darker." We can talk about a deep sound, a deep sadness, or a deep well without comparing these different uses with one another or with some ultimate definition of "deep."

Suppose we teach someone the rule "Add one," by building the series 1, 2, 3, 4, etc., all the way to 85. Suppose we urge him to go on, and after he reaches 100 he writes 102, 104, 106, etc., claiming this is what he thought we meant by the rule "Add 1." If we reply, "I meant for you to write 101 after 100," we cannot mean that "101 follows 100" was somehow in our minds when we laid down the rule "Add 1." Nor is an act of insight or intuition necessary at every stage in order to follow a rule correctly. Wittgenstein explains, "We need have no reason to follow the rule as we do. The chain of reasons has an end" (Wittgenstein, 143). There is not necessarily an insight or mental act that should tell us to follow 100 with 101. This is just what we would normally do.


Wittgenstein's discussion of "darker" has an interesting reflection on the nature of metaphor. We say a usage is metaphorical if it suggests something other than the literal usage of the word. In these passages, Wittgenstein challenges the idea that we even have a clear sense of what the literal usage is. When we talk about a "deep sound," a "deep well," or a "deep sorrow," which of these uses is literal and which is metaphorical? Historically, we could point out that the "deep" of "deep well" is older than the other uses of "deep," but we don't think of a deep well when we refer to deep sounds or deep sorrows, nor are we even aware of using words figuratively.

Wittgenstein gives us an example of someone interpreting the instructions "Add one" to mean "Add one up to 100, and add two beyond 100." Wittgenstein uses this example to challenge us to make a convincing argument that this person is not following the instructions correctly. We cannot simply say "he's adding two when we explicitly said, 'Add one,'" because we gave only an ostensive teaching of what "Add one" means. That is, the person following our instructions only knows what "Add one" means because we showed him how we can add one successively to every number up to 85. All he knows for certain is that the first 85 terms in the series "Add one" are the first 85 cardinal numbers. Beyond that point, we expect him to have inferred the formation rule of the series and go on by himself. We never explicitly instructed him to continue adding one beyond the number 85.

It is difficult to prove that this person is wrong, because the first 85 terms of the series that we would call "Add one up to 100, and add two beyond 100" are also the first 85 cardinal numbers. The ostensive teaching we gave this person is equally applicable to the series as he writes it as it is to the series as we write it. We might argue that the person is wrong because in teaching the series "Add one," I meant that he should follow "100" with "101." "I meant" can be interpreted in one of two ways. The first, which Wittgenstein has been criticizing throughout the Blue and Brown Books, is that what I meant was somehow in my mind, that in teaching the rule "Add one," I had a mental image of the series that included "101" following "100." One problem with this argument is that I would have to claim that not only was "101" in my mind in teaching the series, but also "5679," "104,756," and so on. I could also argue that in saying "I meant that 101 should follow 100," I meant that if someone asked me what term follows "100," I would have said "101." But the person who writes "102" after "100" cannot be faulted for failing to continue the series as I meant it, because I did not tell him specifically "what I meant."

If we accept that we cannot prove this person followed the instructions incorrectly, we might be tempted to say that to follow the instructions correctly, insight or intuition must be present at every step. However, there is no reason to suppose that intuition would necessarily suggest adding one forever. The ostensive teaching that I gave of "Add one," applies equally well to the rule "Add one up to 100, and add two beyond 100," or to "Add one up to eighty-five, add two up to ninety-one, add three up to 100, and then add 6.5 thereafter." Our ostensive teaching has not taught the student a general rule that he can then apply successively to each term in the series. He will need a fresh insight for every term he writes down.

Wittgenstein's point is that explanations can only go so far. His example of the person following "100" with "102" is meant to show us that there is no underlying reason why we should automatically follow "100" with "101." We simply behave in this way without reason, without meaning, without interpretation; no intermediate step is necessary. If I gave a reason for why I follow the rule as I do, you could ask what reasons I have for this reason. We have not reached a rock-solid foundation of certainty by giving a reason for following the rule as we do, we have simply dug one level deeper and raised new questions of justification. Sometimes we do have obvious reasons for behaving as we do, but Wittgenstein urges us not to assume that there must also be reasons in less obvious cases.