I suddenly feel sane again. I always assumed that the word type, by
definition, was intensional. So I have been wondering what this smart
new method is that uses extensional ontology and what I am missing. (01)
I notice that OWL allows extensional as well as intensional definitions
of classes, but I presume that is done by defining a number of OWL
Individuals and making these a member of that class. I don't use that
mechanism in my work. (02)
When I am describing the ontology, as a simple engineer talking to
simple banking folks, I describe it in terms of set theory, but the sets
are intensional not extensional (though of course I don't use words that
people would have to look up). So for example if a thing in your
universe of discourse (another term I don't inflict on them) walks like
a duck, swims like a duck, quacks like a duck and flies like a duck,
then it belongs in the class or set of things in the ontology that is
defined as having those facts about it. That class, for ease of
labelling, would be called Duck. (03)
Mike (04)
John F. Sowa wrote:
> Dear Matthew and Pat,
>
> I strongly disagree with that point:
>
> MW> Types are sets, OK. Why not just call them 'sets', then?
> > I suspect the reason is that while all types are sets, not
> > all sets are types.
>
> For every type t and every domain d (or possible world, if
> you want to use that metaphor) there exists a set of all
> entities of type t in the domain d.
>
> In the terminology of worlds, a common term for that set
> is the *denotation* of the type t in the world w.
>
> PH> Then I REALLY don't understand why you don't just use the
> > word "set", which is about as common and as thoroughly described
> > as any concept has ever been in the history of mankind.
>
> I agree with Pat. If you have a purely extensional approach,
> you don't need any notion other than 'set'. To avoid confusion,
> you should just use the word 'set'. A set is uniquely defined
> by its members, and two sets with the same members are identical.
>
> On the other hand, there are good reasons for using the word 'type'
> for intensional distinctions:
>
> - Since the empty set is a subset of every set (including itself),
> the set of all unicorns is a subset of the set of all cows.
>
> - But the type Unicorn, according to traditional descriptions,
> is definitely not a subtype of Cow. It is possible that somebody
> could genetically engineer a kind of mammal with a single horn,
> which would conform to the usual descriptions of unicorns. In
> that world or domain, the set of unicorns would not be empty,
> and it would not be a subset of the cows.
>
> There are many other reasons for types, but they all treat types
> intensionally: two types can have different definitions (Unicorn
> and Griffin, for example) but have the same extensions in the
> real world.
>
> John
>
>
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> (05)
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