The Investigations open with a quote from St. Augustine's Confessions, which describes the process of learning language in terms of learning the names of objects. It appears that there is nothing wrong with saying that words name things and that we teach people the meanings of words by pointing to the objects that they name. The trouble arises when we take this connection between word and thing as the fundamental relationship that fixes language to the world. This relationship can only be seen to exist once a great deal of the machinery of language, context, and usage are already in place. We would not say the words in a four-word language between builders, consisting of "block!" "pillar!" "slab!" and "beam!" are names of objects, because they can only be understood as such in contrast to names of colors, prepositions, adjectives, and the like. Meaning is not fixed by the relationship between words and things, but by how words are used.
Talking about "the meaning of a word" misleads us into thinking that there are fixed boundaries and strict definitions that determine our use of a word. If we examine how words are used, we will see this is not the case. No definition of the word "game" can include everything that is a game and exclude everything that is not a game. The relationship between various uses of the word "game" is like the relationship between various members of a family: a resemblance exists, but we cannot give this resemblance any rigid definition. The boundaries that determine the meanings of words are not sharp.
Wittgenstein says that the purpose of these investigations is not to bring to light any complex or hidden theories that underlie and explain the surface features of language. Instead, Wittgenstein wants us to recognize that there is nothing beneath this surface. The correct method in philosophy is to assemble reminders of how language is actually used so that people who are tempted to develop this or that metaphysical theory will recognize that they are misusing language.
For instance, we are tempted to think of understanding, thinking, meaning, intending, and so on, as distinctly mental processes. According to this idea, if I can speak with or without thinking, the thinking must be an intangible mental act that underlies the speech. Wittgenstein sets about demolishing this notion, first with a grammatical investigation of the words "understanding" and "reading." Our criteria for determining whether someone has understood something or is reading something are not based on inner states or processes. We judge that people have understood or are reading based on their outward behavior.
Wittgenstein gives an example. He asks, what justifies my assumption that in the series, "Add two," "1002" should follow "1000"? If someone wrote "1004" after "1000" and claimed he thought that was what I meant by "Add two," how could I show him he was wrong? Any rule or justification I provide is just as liable to be misunderstood as the initial order, "Add 2." There is nothing grounding our rule following behavior any more than there is anything that fixes absolutely how we should follow a signpost or an arrow. This is not to say that we choose randomly or that rules fall apart. For the most part, we do not think of "interpreting" rules; we simply follow them. Our understanding of one another is not fixed by any ultimate ground of justification, but by our shared participation in certain forms of life.
Because the functioning of language relies on shared practices and forms of life, the concept of a private language is nonsensical. There would be no use in forming a private language that described inner sensations in a way that only one person could understand them, because there would be no criteria fixing the proper use of the words. Talk about inner sensations is not parallel to talk about outer things, except that with inner sensations, the objects referred to are not open to public view. The notions of knowledge, doubt, and justification function in an entirely different way. Other people can know I am in pain by observing my behavior: the fact that they cannot feel the pain themselves is no block to their knowledge. On the other hand, I do not "know" I am in pain, because my pain is something I feel, not an object of knowledge.
The final three hundred sections of Part I deal with a number of issues related to inner sensations and mental states. The approach is manifold, but there are two general thrusts. First, beliefs, expectations, and intentions are defined by the outward circumstances surrounding them and not by the mental state of the subject. Second, inner sensations are not objects that are known only to the subject and surmised by others.
Part II treats a number of related themes. It plays heavily on the grammar of the word "to see," attacking the view that what we see are only sense data, which we then interpret as objects in the world around us. When we see something as something we may be interpreting what we see, but when I say, "I see a fork," I am not interpreting what I see as a fork: I could not see it as anything but a fork.