John, (01)
> One quibble is about the phrase "the same" is problematical for both sets
and types. (02)
I can see the problem for types - which one does not escape by saying "the
same" could be replaced by "provably equivalent. (03)
However, I cannot see the problem for sets - and cannot see where you
explain this in your response (maybe I missed it).
Could you give us some idea what you mean. (04)
Regards,
Chris Partridge
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> -----Original Message-----
> From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx [mailto:uom-ontology-std-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: 07 October 2009 05:28
> To: uom-ontology-std
> Subject: Re: [uom-ontology-std] What is mass?
>
> Chris and Dave,
>
> One quibble is about the phrase "the same" is problematical
> for both sets and types.
>
> 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)?
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> John
>
>
>
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