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.