Nov. 10, 2013
First lecture on Wittgenstein: rule-following
THE RULE-FOLLOWING PROBLEM
The passages of Wittgenstein that provide the inspiration for the argument appear, in typically
compressed and gnomic form, in Wittgenstein 1953, ¶138–242, and Wittgenstein 1978 §VI.
Kripke’s account was published in its final form in Kripke 1980, having been widely presented
and discussed before; a similar interpretation was given independently in Fogelin 1987 (first
edition 1976). There has been some controversy as to how accurate Kripke’s presentation of
Wittgenstein’s views are; a number of authors have embraced the term ‘Kripkenstein’ to refer
to the imaginary proponent of the views discussed by Kripke. The exegetical issue will not be of
concern here. The concern will be only with the argument presented by Kripke. (For discussion
of the exegetical issues see Boghossian, 1991)
The central idea is easily put. Imagine an individual who makes statements using the sign ‘+’.
For instance, they say ‘14 + 7 = 21’, ‘3 +23 = 26’. It might be thought that they are following the
rule that ‘+’ denotes the plus function. But consider the sums using ‘+’ that they have never
performed before (there must be infinitely many of these, since they can only have performed
finitely many sums). Suppose that ‘68 + 57’ is one such. Now consider the quus function, which
is stipulated to be just like the plus function, except that 68 quus 57 is 5. What is it about the
individual that makes it true that they have been using ‘=’ to denote the plus function rather
than the quus function? By hypothesis it cannot be that they have returned the answer ‘125’ to
the question ‘What is 68 + 57?’, since they have never performed that sum before.
The immediate response is that the individual meant plus in virtue of having mastered some
further rule: for instance, the rule that, to obtain the answer to the question ‘What is 68 + 57?’
one counts out a heap of 68 marbles, counts out another of 57, combines the two heaps, and
then counts the result. But now reapply the worry. How can it be known that by ‘count’ the
individual did not mean ‘quount’, where, of course, this means the same as ‘count’ except
when applied to a heap constructed from two piles, one containing 68 objects, the other
containing 57, in which case one correctly quounts the pile if one simply returns the answer 5?
One might try to fix the meaning of ‘count’ by some further rule; but this will just invite further
worries about what is meant by the words occurring in that rule. Clearly there is a regress. Any
rule that is offered to fix the interpretation of a rule will always be open to further
At this point it might be suggested th