Chris and Dave, (01)
One quibble is about the phrase "the same" is problematical
for both sets and types. (02)
CP> Would you be happy with a re-phrasing of 1 and 2) as:
>
> 1a Two sets are considered identical iff they have the same members.
>
> 2a But two types are considered identical iff they have the same
> definitions
>
> Surely 1) is correct, but what about 2)? (03)
As we have seen, one can argue about whether 1 is "the same" as 1.00.
For definitions, "the same" could be replaced by "provably equivalent"
but in some cases, the proof may be nontrivial. (04)
DM> But if we're talking about the set of employees of company x and
> the set of union members at company x, if they happen to be the
> same and we declare them equivalent, then I think we've said
> something different. (05)
That is a good reason why we need to distinguish sets and types.
The two sets are the same, but the type Employee has a very
different definition from the type UnionMember. (06)
Both of those are examples of role types. The base type would be
Person or HumanBeing. But a human being in the role of Employee
has different implied relationships than the same human being
in the role of union member. (07)
John (08)
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