Philosophical Investigations, reading it together. Since I'm currently working on a theory of knowledge involving Wittgenstein's thinking, I thought it appropriate to include some of these ideas as they apply to language-games and rule-following. This is central to understanding the implications of the PI.
It's very important to juxtapose private rule-following with language-games, because one or more people can participate in a language-game, that has as its basis for meaning a privately held meaning. This of course goes against Wittgenstein's notion that it's logically impossible to have such a meaning, i.e., it has no foothold in terms of what it means to be correct or incorrect. This is also Wittgenstein's stance in On Certainty as he responds to Moore's propositions, viz., "I know this is a hand." The point is that people can establish language-games that reflect a lack of understanding in terms of what gives meaning to words. It follows from this that not all language-games reflect the correct use of words. So if you think that all uses in terms of language-games, are correct uses, then you would be wrong. The correct notion of rule-following must be linked to the language-game, or you will miss an important part of what Wittgenstein is telling you.
For example, some people use the word know in a way that reflects some private access, which then allows them to assert that X is true, or that X is justified. People do this all the time, even philosophers do it based on particular theories of knowledge. To further illustrate the point, I'll use a religious example. If I say that "I know X," and you ask, "What is your justification for knowing X," and I reply, "The Holy Spirit revealed it to me," then you would be falling prey to the private notion of meaning. However, if Wittgenstein is correct, and it seems obvious (at least to me and others) that he is, then this way of giving meaning to a word, be it knowledge or some other concept, is faulty, to say the least. Why? First, because there is no way of resolving what would count as being incorrect about such knowledge. Second, and this is closely related to the first point, rules cannot be privately established, i.e., totally isolated from social contexts. It's just not possible. Every notion of correct or incorrect, knowing and not knowing is part of a social construct, viz., a linguistic construct. There is no meaning to be had privately. Again, because it's logically impossible.
Finally, Kripke's skeptical argument about rule-following, which in some ways reminds me of the Gettier dilemma. Basically it's the idea that there is no way to know if Mary understands addition beyond a certain point, i.e., there is no way to know if she understand the rules as they are acted upon in public over time. Let' say that Mary has been doing addition as we understand addition up to 1000, but that after 1000 Mary does something much different, viz., she randomly adds 5 to every answer above 1000. It would seem to follow from this that there is no way for us to know that anyone is following any rule correctly, because at some point their actions may reveal something very different than what we normally mean by a word/concept.
So the skeptical rejoinder is that we can never be sure that anyone is following a rule correctly, since at a given point in the future, a person's actions may reveal that what they understand as addition, doesn't conform to what we publicly understand as addition. Thus, the notion of rule-following collapses as an essential part of our understanding of concepts. Why? Again, because there is no way to know if someone really understand a rule or not.
But, there is something very wrong with Kripke's skeptical argument, i.e., it assumes the very thing it's arguing against. It's circular. Here's the crux of the problem. In order for Kripke's argument to work, he has to be able to compare Mary's understanding of addition up to 1000, with that of Mary's understanding of addition after 1000. However, if there is no way to know, according to Kripke's skeptical argument that we are following a rule in terms of any concept (addition in the e.g.), then there is no way for Kripke to know if he is following the rules of sameness correctly. When he compares what Mary did at point X, with what Mary did at point Y along the time line, how does he know that he is applying the rule of sameness in the correct way? If what his argument is claiming is true, then it would apply to all concepts, even the very words used to express his argument. This is what Wittgenstein meant when he said that a doubt that doubts everything, is not a doubt, which is what Kripke's argument boils down to.
Why was Kripke's argument circular, because it assumes an understanding over time of the concept sameness. So it assumes the very thing he is arguing against. However, it's more than circular, it's contradictory.