The Investigations have a peculiar literary style that is difficult to characterize. Very little of Wittgenstein's writing even resembles standard philosophical argument. Instead, we get questions, hesitant hypotheses, doubts, temptations, and the like. Instead of giving us a monologue in which he lays out his position, Wittgenstein engages us in a dialogue with an interlocutor. The interlocutory voice, usually (but not always) found in quotation marks, is the driving force that propels the Investigations forward. The interlocutor voices the temptations that are liable to lead us into philosophical theorizing. In any given section of the text, the interlocutory voice raises objections to Wittgenstein's anti-metaphysical outlook, and Wittgenstein responds to these objections. By means of this dialogue, Wittgenstein does not bring us to any definite answers, but to an end to questioning.
One of the major themes in the early sections of the text (particularly sections 65–91) is that the meanings of words are not rigidly defined. Wittgenstein uses the example of "game," showing us that there is no catch-all definition that will include everything we call a game and exclude everything that we do not call a game. This conclusion can be, and is, extended to a wide range of terms that philosophers often try to include within a single definition: "language," "understanding," "meaning," "reading," "seeing," and so on. This position reflects Wittgenstein's remark at section 43 that the meaning of a word is determined by its use. Definition is not something prior to the use of a word that fixes its meaning and determines how it will be used. Rather, definition is a descriptive tool that reflects the various ways a word is used.
This criticism of the notion of fixity of meaning sets the stage for Wittgenstein's work in the later sections of the book to show that there is no mental state or process that corresponds to such concepts as "meaning," "understanding," "believing," and so on. If there is not one fixed meaning or use for these words, then they cannot possibly refer to a single, fixed concept.
The Investigations are difficult to understand not only because they introduce a number of unfamiliar themes and methods, but also because these themes and methods are introduced in the service of a new conception of what philosophy ought to do. The Investigations consist to a large extent of an extended criticism of old ways of philosophical thinking. Philosophy has generally concerned itself with metaphysical theories and deep explanations that cut to the core of the concepts that govern human life and reality. Wittgenstein suggests that this kind of theorizing can only lead us astray: there are no concepts or explanations hiding beneath the surface of everyday phenomena. These metaphysical theories are built upon unwarranted assumptions or generalizations, often born out of the structure of our grammar. The purpose of Wittgensteinian philosophy is to lead us to recognize these temptations toward metaphysical thinking, and to learn to subdue them.
This is not to say that we are better off not doing philosophy at all, or that Wittgenstein represents an end to philosophy. Wittgenstein's "therapeutic" method of identifying temptations and then showing them to be mistaken does not simply bring us back to where we were before we started thinking philosophically. Some philosophers have identified Wittgenstein's method as a method of self-knowledge. It brings us to a deeper understanding of ourselves, our thoughts, and our temptations. The kinds of temptations Wittgenstein identifies do not only crop up when we sit down to study philosophy; they are a general characteristic of abstract thinking. As long as we wish to think abstractly, we are liable to commit the sorts of errors Wittgenstein identifies. His concept of philosophy is a honed method by which we can avoid this sort of error.
We commonly think of the role of justification as providing a definite ground for holding the beliefs, claims, etc., which we are justifying. Wittgenstein's discussion of rule following in sections 185–242 is the foremost among a number of discussions that show us that justification plays no such role. If we accept that every rule is open to various possible interpretations (for instance, "—>" could mean "go left" or "go right"), then every rule will require a deeper level of justification— another rule—to fix which is the correct interpretation. But then, that further rule is also open to various interpretations. If any given rule is open to various possible interpretations, there is no ultimate ground of justification upon which the correct interpretation can be fixed.
Wittgenstein does not conclude that there is no ultimate justification or correct interpretation. Rather, he suggests that we are looking for the wrong thing when we look for ultimate grounds of correctness. The mistake we make is in accepting that every rule is open to various possible interpretations. The sign, "—>" is not open to various interpretations: we never stop to wonder if it means "go left" or "go right." Interpretation and justification are not applicable to everything, nor do they serve to determine correctness. They are only called upon in genuine cases of ambiguity where we do not know how to go on without a justified interpretation.
The theme of privacy is most explicitly discussed in sections 250–300, but it runs throughout the rest of the Investigations. It is difficult to articulate clearly what Wittgenstein is doing here, largely because he is dealing with ideas that he shows are largely inarticulate. Roughly speaking, he sets about deconstructing the mystification we feel when faced with peculiarities of the inner life.
Wittgenstein devotes a great deal of the Investgations to the peculiarities of talking about our inner sensations. On one hand, it seems an obvious truism that I have a kind of access to my own sensations that other people do not. On the other hand, Wittgenstein shows us that any attempt to formulate this truism as a substantial metaphysical fact is doomed. Though I uncontrovertibly experience my pains in a way that no one else does, I cannot talk about them in terms of "knowledge," because claims about knowledge presuppose that there is something to be known, and hence something that might not be known. My relationship to my inner sensations is not one of knowing, because I could not but experience them. We misunderstand this fact when we claim that other people have limited or only "indirect" knowledge of my inner sensations. Other people's knowledge seems limited in comparison to my own knowledge, but if we accept that what I have is not knowledge, then these limits disappear.
We find a great number of very strange examples in the Investgations. There is the tribe of section 2 who have a language of only four words; there is the student who thinks he has done nothing wrong when he follows out the order, "Add two," by writing "1004" after "1000"; there is the person who keeps a journal where he marks an "S" for everyday he feels a particular sensation; there are odd assertions like, "a rose has teeth in the mouth of a the beast," and "if a lion could speak, we would not understand him," and so on. One of the purposes of these examples is to lead us to reflect on how much of our ordinary life is simply taken for granted. We would not know how to correct a student who thinks he is following the rule correctly in writing "1004" after "1000," because if he thinks that is what "Add two" means, it is unclear what facts or arguments we could appeal to that he would understand. At a number of points in the Investigations, Wittgenstein emphasizes the importance of "forms of life." We are able to understand one another and communicate because we share a common understanding of what a rule is, what following a rule is, what count as criteria for inner sensations, what words mean, and so on. Such understanding is not fixed by any logical ground of justification, but simply because a different understanding never occurs to us. This appeal to a shared understanding enforces Wittgenstein's criticism of privacy: our words and what they mean are necessarily public matters.
Grammatical investigation is one of Wittgenstein's primary tools in sorting through a particular issue. We find a prime example of such investigation in sections 138–184 with regard to "understanding" and "reading." When asking what a particular word means, Wittgenstein insists that we look at how the word is used. Grammatical investigations then explore the variety of different uses certain words can be put to, and the variety of different contexts they appear in. Among other things, this sort of investigation highlights the fact that meanings are not fixed. There is no a single thing that is "meaning" or "understanding": rather, there is a wide variety of different, but related, uses these words can be put to.