There are a number of very different surface features that we might call manifestations of understanding a series like one, five, nine, eleven, nineteen, twenty-nine. A person may utter the algebraic formula for the series, or remark that the difference between each successive term increases by two, or simply say, "that's easy!" and write down the next five numbers. However, we will also be tempted to say that there must be something in common in all these cases. In each case, the person understands the series, but that understanding expresses itself in different ways. Because this commonality is not evident in the person's behavior in each of the three different cases, we will be tempted to say that the understanding is a hidden, mental phenomenon or state.

In discussing the mind, Wittgenstein frequently returns to the theme that when our grammar suggests that there must be something common in a number of unlike phenomena, we say that commonality exists in the mind. Because we call these three different reactions "understanding the series," we feel the compulsion of a "must": they must have something in common if we call them all by the same name. Because we cannot find any direct evidence for this assumed commonality, we conclude that it must be hidden in the complexities of the mind.

Psychological investigations begin after this assumption has been made. Firm in the knowledge that there must be a mental mechanism of some sort that constitutes understanding, a psychological investigation then probes the mind to identify exactly what this mechanism is and how it works.

Wittgenstein argues that there is no such mental mechanism. It is perfectly acceptable to talk about understanding as a state, and to say "Jane understands the series, but John does not." The problem arises when we take this talk of a state of understanding to point to some underlying psychological truth.

Wittgenstein tries to simplify the discussion to make his position clearer. For instance, people generally don't think that understanding a word consists of the word's summoning up a mental image, which is the point that Wittgenstein is trying to make with the cube example. However, if we want to talk about understanding as a mental state that somehow causes the different manifestations of understanding, a mental image is the clearest picture of such a cause. If the example of "cube" as a mental image does not work, then more complex theories will probably not work either.

The discussion of reading is a similar simplification. There are many complications in the discussion of understanding that do not come up in the case of reading. "Reading" covers a more limited range of phenomena. It is a distinctive act that we can recognize easily, and there is less of a distinction between reading and the various manifestations of reading. If, despite all these simplifications, we still cannot identify a single state or mechanism that we call "reading," we are unlikely to find one in the more complex case of "understanding."

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