Is subclassing "strict order" or is it reflexive? RE: [sc34wg3] New SAM PSIs

[Murray Altheim]

Anthony B. Coates wrote:
> ** Reply to message from Murray Altheim <m.altheim@open.ac.uk> on Fri, 14 Feb
> 2003 14:45:35 +0000
> 
>>On the one hand, and the error I think OWL is making, is that it
>>seems to be talking about *members* of sets. So, if we have a set A
>>and a set B whose members are all the same, they are identical sets.
>>Eg., if we have 100 hominids and 100 primates, and they are the same
>>100 individuals, we can consider the two sets identical. We cannot,
>>and I repeat, cannot, necessarily therefore consider the classes of
>>primates and hominids as identical. They are not.
> 
> A set of 100 hominids is not the set of all hominids, just a lousy subset.  If
> you cannot find any case of a being that is hominid or primate, but not both,
> then you have to conclude that hominids and primates are identical.

Uh, you are making my point for me. There is a concept of "set"
and a concept of "class". These are distinct notions. The
constitution of any specific set of members operates in a
different realm than the *definition* of a class, and indeed,
could not be used to prove anything at all about classes or
class membership, or of anything in the realm of class definition.
Any such proof would be anecdotal, and not in the realm of logic.

By way of your argument, one could say that if one had an
empty set called "hominids" that no hominids exist. Obviously,
this is not true. And as for "finding a case", this is hardly
a way to approach logic. If you can't find aliens on other
planets they don't exist?

Murray

......................................................................
Murray Altheim                  <http://kmi.open.ac.uk/people/murray/>
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK

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