>His position is only that we should teach that although these two operations of multiplication and repeated addition get the same results, that does not mean therefore that they are the same operation.
The action that the term "repeated addition" refers to, is a computable procedure. Multiplication on integers is typically defined by such a procedure. In that sense they most assuredly *are* the same. If you want to take things from certain axiomatic viewpoints, and avoid "defining" multiplication from more primitive notions, then mult. is just a function, a mapping from pairs of integers to integers. In that view it has no "action" at all, it just is. That's fine too - but its misleading even in that view to compare an abstract function against a computable procedure as if they were comparable. If one wanted to be clear about these matters, they would lay out the options, not go (to paraphrase Kirby) "kicking down other peoples sandcastles, while insisting their own was inviolable."
No, Devlin's writing is clearly misleading - he wants people to think "repeated addition" is one kind of action, and "multiplication" is a comparable that is another kind of "action" (stretching a rubber band). Its all plain to see. Stretching is fine as mental imagery, but if you want to turn that mental imagery into a computable procedure, you will need to rely on iteration or recursion one way or another.
