We must distinguish between what one might call a “process” being in accordance with a rule”, and, “a process involving a rule” (in the above sense).

20.

Take an example. Some one teaches me to square cardinal numbers; he writes down the row

1 2 3 4,

and asks me to square them. (I will, in this case, again, replace any processes happening “in the mind” by processes of calculation on the paper). Suppose, underneath the first row of numbers, I then write:–

1 4 9 16.

What I wrote is in accordance with the general rule of squaring; but it obviously is in accordance with any number of other rules also; and amongst these it is not more in accordance with one than with another. In the sense in which before we talked about a rule being involved in a process, no rule was involved in this. Supposing that in order to get to my results, I calculated 1 × 1, 2 × 2, 3 × 3, 4 × 4 (that is, in this case, wrote down the calculations); these would again be in accordance with any number of rules. Supposing, on the other hand, in order to get to my results, I had written down what you may call “the rule of squaring”, say, algebraically. In this case this rule was involved in a sense in which no other rule was.

(2015–) Wittgenstein Source Bergen Nachlass Edition (WS-BNE). Edited by the Wittgenstein Archives at the University of Bergen under the direction of Alois Pichler. In: Wittgenstein Source, curated by Alois Pichler (2009–) and Joseph Wang-Kathrein (2020–). (N) Bergen: WAB.