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Ok, let me see if I can summarize, as it appears to me, the
philosophical difference between your, my (and Marshall?),
and Dmitry's viewpoints.
Let us call OD = O - OA 'derived' operations. And let us call a subset OS of OD 'scoped' operations which are operations that are currently "in scope".
3a) I (and Marshall?) say that S + OA defines a data type T. 3b) You (Bob) say that S + O defines a data type T. 3c) Dmitry says that S + OA + OS defines a data type T.
Do you Bob, Marshall, and Dmitry find this summary accurate?
> > > What is important is not which operations we consider
> > > fundamental and which we consider auxiliary. What is
> > > important is all of those operations exist and we can
> > > communicate them to each other.
> >
> > Not important? Well that is a large part of mathematics,
> > finding sets of operations (the smaller the better) we
> > consider fundamental and from which we can derive other
> > operations.
>
> Axiomatization is arbitrary. Mathematicians also spend
> time trying to find completely different sets of axioms
> for the same things and then trying to prove the
> equivalence between them.
It may be arbitrary (if by arbitrary you meant the "subject to judgment" and not "without reason") but it is obviously valuable. No?