We can understand a word like "cube" without placing it in a sentence. We may, for instance, have a mental picture of a cube. But how do we apply that picture? There is no reason we shouldn't take it to be a picture of a prism, and yet we would say that one has misunderstood the word "cube" if one points to a triangular prism and says, "cube." We normally apply a picture of a cube only to what we call "cube" and not to what we call "prism," but this tells us only how we normally behave, and not how a certain picture must be applied.
Is understanding a mental state? We want to say someone has understood the series one, five, eleven, nineteen, twenty-nine because he has a certain mental state. We also want to say that writing down the next three terms of the series correctly or uttering the formula for the series are only manifestations of this mental state. But we do not say of understanding, as we would of other mental states like pain or depression, that it has been continuous for a few days, or that it went away yesterday evening. Understanding is determined by the particular circumstances in each case that justify us in saying we understand.
In this sense, "understanding" is much like "reading." There are a variety of activities we would call "reading," ranging from spelling out words letter by letter, to skimming entire paragraphs, and there is no distinctive mental state or mechanism that is common to all these different activities. In sections 156–178, Wittgenstein considers three possible general definitions of "reading." First, reading is accompanied by a distinctive set of sensations, different from when I am only pretending to read. Second, reading is a matter of deriving sounds from the rule provided by the alphabet. Third, sounds come to me, or my speech is guided when looking at words in a way that I am not when looking at random squiggles.
If, as in the first objection, reading were a matter of certain mental sensations, couldn't a drug make us simulate those sensations when we are not looking at a page? We would not call it reading unless these sensations were accompanied by certain forms of behavior. With regard to the second objection, there is more than one way we can interpret a rule, and it is not even clear when we are deriving from a rule and when acting at random. With regard to the third objection, there are just as many different uses of the phrase "being guided" as there are of "reading" or "understanding."
When we try to formulate definitions of "reading," we are generally trying to identify what differentiates reading from certain non-reading activities such as pretending to read or uttering sounds while looking at random squiggles. And indeed, these features that we identify are often characteristic of reading; but we cannot say these features alone define reading. What we call "reading" depends on a wider context of behavior and circumstances, and cannot be reduced to a particular sensation or mental state.
One of Wittgenstein's main preoccupations is to undercut commonly held ideas about the mind and mental states that are most present in so-called "scientific" theories of psychology. Just as physics takes as its object of study the workings of natural phenomena, psychology takes as its object of study the workings of mental phenomena. However, Wittgenstein suggests that psychology, unlike physics, bases its investigations on unwarranted assumptions that we take from everyday speech about the mind.