Ed,
>
> And I don't think my intuition is very good with respect to this
> taxonomy. Ian said "types are identified by their members", which is a
> surprise. It seems to make Type a "set" or a "collection". I would
> have expected that a Type would be identified by its 'characteristics',
> i.e., the necessary and sufficient conditions specified by its axioms.
> So I don't presume that I understand any of what is listed.
> (01)
This may turn on different senses of identify. (02)
Pragmatically, one tends to use characteristics to identify a member of a
class/set - once these characteristics have been agreed - not always easy. (03)
Where the characteristics are not agreed, but people claim to know what the
set is then checking whether they agree on its members is a good way to
start to determine whether they are talking about the same set. So, for
example, in the IDEAS meeting we found it difficult (well impossible :-) )
to get people to agree on the characteristics, but when we compared putative
members, we soon found that they were not. (04)
The next step is to go extensional - and take the identity criterion for
Types (Sets) as their extension.
This resolves issues such as 'equilateral triangle' and 'equiangular
triangle' (where different "necessary and sufficient conditions specified by
its axioms" would seem to indicate different types. (05)
It seems to me that ISO standard writers like to identify a definition for
their types and that these should identify characteristics which are
"necessary and sufficient conditions". As I noted in an earlier email,
despite ardent support for this approach, it is not clear whether they
regard these "characteristics" as a criterion for identity. Most of the
people I have talked to have not really thought about it. Perhaps an
'equilateral triangle' and 'equiangular triangle' test would help here. (BTW
where do you stand on this?). (06)
Also, it seems to me that it is helpful to have some process in place to
discuss types where the "characteristics" have not been clarified, let alone
axiomatised. (07)
Best regards,
Chris (08)
PS Agree with LOTS of your other comments. (09)
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