Wittgenstein gives an example. I teach someone the series "Add two," that runs two, four, six, 8 , and he writes it to my satisfaction up to 1000, but beyond 1000 he begins writing 1004, 1008, 1012 . On what grounds can we say he is following th e rule incorrectly? When I said, "Add two," I meant that he should write "1002" after "1000," but I surely did not have those two numbers specifically in mind when I gave the rule. I simply assumed that that is what I would do at that stage.
We want to say that even if "'1002' follows '1000'" is not directly on my mind, something in what I say or mean determines all the steps in advance. The algebraic formula for a series determines every step in advance insofar as people have been trained in such a way that everyone will normally write down the same series given that algebraic formula. There is nothing in the formula itself (nothing in what I say or mean) that determines the steps. Without training, the formula is meaningless.
The idea that a formula determines every subsequent step is like the idea that a machine at rest contains in it the possibilities of its movement. The possibility of its movement is not an observation of past experience or a prediction of future movement: it would seem to be something in the present state of the machine. But there is nothing in the machine that we could call its "possibility of movement." this is just an expression that tells us the kinds of movement we anticipate in the machine.
If we cannot prove that following "1000" with "1004" is incorrect, we might conclude that any interpretation of a rule can be correct, and that at every step, a new interpretation is needed. Wittgenstein counters this conclusion by suggesting that followi ng a rule does not usually consist of interpretation at all. If I follow a sign-post, I am not interpreting the sign-post; I am according myself with the custom or institution of sign-post-following that is a common practice in my community. There cannot be a society in which there was only one rule that was obeyed only once, because rules can only exist as public practices.
Following a rule correctly is not guided by guessing the rule-giver's intention, hearing an inner voice, or finding some logical justification. When I teach a rule, I am teaching a certain practice, and when I follow a rule I am obeying that practice. The practice need not rely on any further justification. This absence of justification does not mean that I am free to interpret and then follow a rule however I choose. The question of interpretation or choice does not occur to me when I obey a rule.
Though there is no ultimate justification for following rules as we do, we do not dispute how to follow a signpost or follow the order "Add 2." These practices of rule following are forms of life that are prior to questions of justification and interp retation. If we could not agree on how to follow these rules, there would be little point in disputing them because the level of our misunderstanding would be so deep as to render any meaningful communication impossible.