It is standard to describe the topic of §§185-242 as “rule-following.” These remarks expand on the discussion of §§143-155, and the continuation of a series again often serves as a paradigm. But Wittgenstein’s concern now is less to question the picture of a mental act or event of grasping the continuation of a series than it is to question a related picture, one of there being something present in us or to us which determines the correct continuation of the series. In a slightly earlier work, Wittgenstein responds to this as follows:

The fault which in all our reasoning about these matters we are inclined to make is to think that images and experiences of all sorts, which are in some sense closely connected with each other, must be present in our mind at the same time. If we sing a tune we know by heart, or say the alphabet, the notes or letters seem to hang together, and each seems to draw the next after it, as though they were a string of pearls in a box, and by pulling out one pearl I pulled out the one following it.

Now there is no doubt that, having the visual image of a string of beads being pulled out of a box through a hole in the lid, we should be inclined to say: “These beads must all have been together in the box before”. But it is easy to see that this is making a hypothesis. I should have had the same image if the beads had gradually come into existence in the hole of the lid. We easily overlook the distinction between stating a conscious mental event, and making a hypothesis about what one might call the mechanism of the mind. All the more as such hypotheses or pictures of the working of our mind are embodied in many of the forms of expression of our everyday language. [The Blue Book, pp. 39f.]

The most direct response in the Investigations is perhaps the idea of a new decision at every stage (§186).

• §§185-188. The idea of an act of meaning. Since the initial steps of a series might be continued in an unexpected way (§185), what determines what the series was meant to be (§186)? The steps are not all considered individually (§187) so we are inclined to suppose that a special act of meaning determines them all (§188). Focus on §186; the idea of a new decision at every stage first appeared in Wittgenstein’s thinking when he addressed the question of how mathematicians can be creative if mathematics consists solely of tautologies.

• §§189-197. A machine as a symbol. We can be led to think that a formula for a series determines the steps in a way that is more direct than what is indicated by the normal use of the formula—e.g., that we have been trained so as to act in a regular way in applying it (§§189-192). This is like regarding a machine as a symbol for its normal operation and supposing the basis for this symbolism to lie in some shadowy feature of the machine (§§193-196). (Notice that you’ve seen remarks that recall Wittgenstein’s background both as an elementary school teacher and as a mechanical engineer.) The real connection between a formula and the steps of a series in which it is applied is to be found in ordinary places—lists of rules, teaching, day-to-day practice (§197). Focus on §§191-192, 194 , and 197.

• §§198-207. Rule-following as a practice. In general, we will speak of someone following a rule only in the context of a general practice of rule-following, a practice sustained by the common behavior of humanity. Focus on §§199, 202, 206. The second is a preview of the topics for next week; think how it fits in here.

• §§208-216. The centrality of examples. The regularity embodied in a custom is taught by examples and practice. Practitioners of the custom know no more than can be given in this way. At some point they just go on to act—and do so in complete confidence. Compare this to Wittgenstein’s earlier discussion of our knowledge of concepts like the concept of a game (e.g., in §69). Focus on §§208 and 211-212.

• §§217-231. Running out of reasons. When we look for an understanding of our behavior (as opposed to external explanations of it), reasons eventually give out, and the picture of determination by a rule symbolizes this. Focus on §§217, 219-221, and 230.

• §§232-239. Some curious examples. We can imagine various combinations of the usual criteria for rule-following (e.g., a feeling of determination, or behavior in accordance with the rule), and these have various consequences for our attribution of rule-following. Focus on §§234 and 236-237; with regard to the first, think of the figure of the string of pearls.

• §§240-242. Agreement in a form of life. Language is based on an agreement in a form of life and this includes judgments as well as definitions. Recall §§198-207; Wittgenstein will turn to the issue raised in §202 again in §243. And, in regard to the last sentence of §242, recall §§80 and 142.