[topicmapmail] Getty Art and Architecture Thesaurus On Line

[Murray Altheim]

Thomas B. Passin wrote:
> [Kal Ahmed
> 
>>Is instanceOf really a transitive relation ? I don't believe it is.
>>
>>Kal instanceOf Homo Sapiens
>>
>>Homo Sapiens instanceOf Species
>>
>>Kal instanceOf Species ?
>>
>>Subclass/superclass *is* transitive, but not instanceOf. Unless you mean
>>something different to a class-instance relationship by 'instanceOf'
> 
> I do not think that this illustrates anything about transitivity.  Rather,
> this is the class/instance conundrum.  Is an "instance" of a class supposed
> to be a class or an individual?  If it is supposed to be an individual, you
> would not say "Homo Sapiens instanceOf Species".  If it is allowed to be a
> class, how do you know how to distinguish an instance as a class form an
> instance as an individual?
> 
> This has been discussed before, in this and other lists, but I confess that
> I am still not clear on how to deal with the issue except to rule that an
> "instance" by definition means an individual member of some class.  I gather
> that this is not altogether satisfactory because sometimes one does want the
> individual to be a class - although this is getting into the dangerous
> waters of the class of all classes

Actually, while it seems much has been written on the subject, the
answer is not typically made clear. The idea of class membership
involves definition of what constitutes the class in question, which
in mathematics is one thing, in the phenomenological world another.

I think in this instance the answer comes from Peirce: class-instance
is a dyadic relation, and what we need is Thirdness, triadic relations.
I.e., class-instance relations should [usually] be stated within a
specific context. Something can be considered an instance of a class
in one context, but may be used as a class in another. In Topic Maps
one could scope the associations.

So in the example provided, "Homo sapiens" is an instance of the
class of "species" (and would appear as such in a Topic Map describing
the zoological taxonomy), but may be used as a classifier itself (e.g.,
a character in my authoring ontology can be an instance of "Homo sapiens".

This is how I'm approaching this in Ceryle, anyway.

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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