On 25 Jan, at 10:03 Jan , John F. Sowa wrote:
> Leo,
>
> I think that we agree about the basic issues, but it is
> very hard to set any limits on the domain:
>
>> Indeed, I would say an ontology is a logical theory AND
>> purports to be about the real world. I can develop a
>> nonsensical logical theory, for example.
>
> For example, all mathematical theories are purely abstract,
> and they could be applied to the real world or anything else
> imaginable. And any plans for something that does not yet
> exist (e.g., the next new airplane by Boeing or Airbus) are
> about an imaginary entity that does not yet exist, but it might
> or might not exist at some indefinite time in the future.
>
> And once you allow ontologies for hypothetical devices, virtual
> worlds, arbitrary mathematical structures, and hypothetical
> scientific theories, it is hard to exclude anything else. (01)
I strongly agree with this. I have always thought Jerry Hobbs' idea
of "promiscuity" in ontology was right on the money: there should be
virtually no constraints whatever on the things one should be allowed
to quantify over in an ontology. Note that this is NOT to say that
it ontologies can be constructed willy-nilly, without regard for
internal coherence and without any sort of critical oversight; far
from it -- every ontological decision should undergo rigorous
inspection. Rather, the idea is that one shouldn't let antecedent
philosophical opinions about what does or does not exist prevent one
from introducing *whatever* ontological categories make for an
effective ontology. For example, following up on John's idea, one
might have philosophical scruples about introducing a category of
future or possible (but not presently existing). Fact is, however,
it is very convenient to be able to talk about, and quantify over,
such entities, and philosophical scruples should simply not get in
the way here. (02)
My concern, therefore, is that Leo's additional qualification that a
legitimate ontology should "purport to be about the real world" will
lead to pointless (and often confused and amateurish) philosophical
discussions about the nature of reality. I don't at all mean to
imply that this was Leo's intent -- I think rather he is only
concerned to try to keep silly, clearly incoherent logical theories
from counting as ontologies. I just don't think there is a useful
way to divide such theories from those that we want to countenance as
fully-fledged ontologies and so is best left out of any
characterization of what an ontology is. The test of an ontology is
its usefulness for its intended task, and that should suffice to
separate wheat from chaff. (03)
> Therefore, I would propose the following definition:
>
> A formal ontology is a consistent theory expressed in some version
> of logic that defines the types, relations, and functions that
> characterize the entities of some domain, which may be concrete
> or abstract, real or virtual.
>
> The requirement of a consistent theory rules out nonsense whose
> existence is impossible even in a virtual world, but it does
> allow worlds whose laws may be very different from what we
> currently consider "physics". (04)
I am general agreement with your definition, John, except for the
criterion of consistency -- not that it isn't a good idea, but the
consistency problem in propositional logic is NP-complete and it's
flat out undecidable in predicate logic (by Church's theorem, a
corollary to Gödel's incompleteness theorem). Hence, it is simply
theoretically impossible in general to enforce. (05)
Chris Menzel (06)
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