All the questions considered here link up with this problem:
Suppose you had taught someone to write down series of numbers
according to rules of the form: Always write down a number
n greater than the preceding.
(This rule is abbreviated to “Add
n”).
The numerals in this game are to be groups of dashes
-,
--,
---, etc.
What I call teaching this game of course consisted in giving general
explanations and doing examples. ‒ ‒
These examples are taken from the range, say, between 1 and 85.
We now give the pupil the order, “Add 1”.
After some time we observe that after passing 100 he did what we should
call
100.
adding 2; after
passing 300 he does what we should call adding 3.
We have him up for this: “Didn't I tell you
always to add 1?
Look what you have done before you got to 100!” ‒ ‒
Suppose the pupil said, pointing to the numbers 102, 104,
etc. “Well, didn't I do the same
here?
I thought this was what you wanted me to do”. ‒ ‒
You see that it would get us no further here again to say,
“But don't you see … ?”,
pointing out to him again the rules and examples we had given to
him.
We might in such a case, say that this person naturally understands
(interprets) the rule (and examples) we have given as we
should understand the rule (and examples) telling us:
“Add 1 up to 100, then 2 up to 200,
etc.”