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

Ts-310,100

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.”