John,
Answers my question and makes sense to me. Thanks,
Doug (01)
On Jan 25, 2007, at 10:23 AM, John F. Sowa wrote: (02)
> Leo, Steve, and Doug,
>
> To start with Leo's concluding comment,
>
> LO> So I am not convinced that (ontology = logical theory) only.
>
> The relevant clause of the definition specifies that an ontology
> is a theory that
>
> characterizes the entities of some domain, which may be
> concrete or abstract, real or virtual.
>
> That distinguishes an ontology from a theory that just states
> some arbitrary facts about some entities that may be defined,
> specified, or identified elsewhere.
>
> LO> Although mathematical theories are abstract, are they not
>> a part of the world? By part of the world, I don't necessarily
>> mean empirically determinable (though even this can beg the
>> question).
>
> That gets into philosophical issues that can be left to other
> discussions. My short answer is that a pure (i.e., unapplied)
> mathematical theory defines abstract entities that are outside
> any kind of space-time coordinates. Therefore, it would be odd
> or unusual to say that they were "part" of anything physical,
> but they might be "applied" to something physical.
>
> The next two comments are closely related:
>
> SR> We were trying to come up with a categorization scheme into
>> which we could place everything that anyone calls an ontology,
>> whether it is computer processable or not, consistent or not,
>> correct or not.
>
> DH> So, then what should said about folksonomies, topic maps,
>> lots of schema that were devised without a theory in mind, and
>> all those others that seem to be used "like" these theories?
>> In my view, at least, we were trying to understand and somehow
>> characterize the common ground that links all these things.
>
> Several points:
>
> 1. I explicitly said "formal ontology", but I agree that a more
> general definition should say how the other kinds of things
> are related to a formal ontology.
>
> 2. My definition of logic includes natural languages as supersets
> of any or all of the formal logics that have ever been invented.
> Therefore, definitions in natural languages are also acceptable
> for an ontology, although a machine might not be able to
> interpret
> them. I would call them informal ontologies.
>
> 3. My definition of theory is also very general: Any set of axioms
> stated in any version of logic, which would include natural
> languages for the informal theories.
>
> 4. Re folksonomies: I hate that term because it sounds disparaging.
> I have nothing against informal classifications, many of which
> are superior to some of the so-called formal ones.
>
> 5. Re topic maps: I consider them a form of logic, and some
> versions
> of TMs have been formally specified, but other versions are used
> in a way that would put them in the informal category.
>
> 6. Re "lots of schema that were devised without a theory in mind":
> The fact that a theory has not been formally specified does not
> imply that the author has "no theory in mind". On the contrary,
> people have lots of theories in their minds, which for better
> or worse have major impacts on what they do. As my favorite
> philosopher C. S. Peirce said, "Every man of us has a
> metaphysics,
> and has to have one; and it will influence his life greatly.
> Far better, then, that that metaphysics should be criticized
> and not be allowed to run loose."
>
> 7. Re common ground: If we generalize the definition by deleting
> the word "formal", we get a definition that includes all of the
> other proposals.
>
> Following is my previous definition, but generalized to include
> informal as well as formal theories:
>
> An ontology is a theory expressed in some language, natural or
> artificial, that defines the types, relations, and functions
> that characterize the entities of some domain, which may be
> concrete or abstract, real or virtual.
>
> If you add the word "formal", then the language must be some
> version of formal logic, which could be stated in a formalized
> or controlled natural language. Aristotle's original syllogisms,
> for example, are a version of formal logic stated in a controlled
> dialect of Greek.
>
> John Sowa
>
>
>
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