The Rule-Following Problem Problem and Its Solution

Abstract

The problem of how to follow a rule is logically speaking a question about dependence: What should one choose to do at each stage (say stage number n) depending on n? This question has the same logical form as an experimental question: How does the value y = f(x) of the observed variable y depend on the controlled variable x? Nature’s direct response, i.e. the outcome of the experiment, is a correlation of the values of x and y, as it were a curve on graph paper. But this “reply” does not answer the dependence question unless and until the inquirer knows what the function f is that the curve represents. Thus answering any dependence question involves two conceptually different tasks, not only to find the correlation but also to identify the function that the correlation is determined by. These tasks are largely independent of each other. Even knowing the precise curve does not automatically mean identifying the function whose graph it is. In the rule-following case, one can act in accordance with the rule in each case without being aware of the rule itself. Wittgenstein’s original problem about rules is that of identifying the function rather than acting in accordance with it. The solution lies in recognizing how we identify in actual conceptual (including mathematical) practice different functions (rules).