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Re: [ontolog-forum] Ontological Assumptions of FOL

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Sat, 17 Mar 2007 18:31:11 -0500
Message-id: <20070317233111.GA92165@xxxxxxxx>
On 17 Mar, at 2:32 , Kathryn Blackmond Laskey wrote:
> At 10:36 AM -0500 3/16/07, Pat Hayes wrote:
> > ...the *only*, repeat ONLY, assumption that FOL makes about its
> > universe is that is is a nonempty set ....
> More precisely, one can represent it as a set for purposes of defining
> truth-conditions for sentences.
> > All other logics seem to impose extra conditions on their
> > universes...  Now, it is hard for me to image what could possibly be
> > *less* of an ontological commitment than that the elements of the
> > universe can be viewed as members of a set:
> This is a very serious ontological commitment.
> FOL makes the ontological commitments that: 
>   - The universe of discourse is made up of elements or constituents.  
>   - These elements or constituents have properties and stand in 
>     relationship to one another.    (01)

I'm not sure what the upshot of "serious" is here, but it is indeed the
case that FOL assumes that any given domain we are capable of
representing contains "things", or "objects" -- though, mind you, with
utterly no presuppositions as to their nature -- and that these things
have properties and stand in relationships to one another.  However
serious these commitments might be, they are simply inescapable by
anyone who has any hope of representing some aspect of the world in a
computer, hence by anyone with any intention of doing ontological
engineering.  I myself think these commitments are exceedingly minimal,
as they presuppose only the most basic categories in terms of which we
conceptualize the world.  Not a single *specific* object, property, or
relation is assumed to exist.    (02)

>   - One can make statements about these properties and
>     relationships (e.g, that all, or some, elements have a 
>     given property or stand in a given relationship)
>   - Any such statement has a definite truth-value.    (03)

These are not ontological commitments.  The first is the assumption that
we are capable of representing the world -- also inescapable for anyone
doing ontological engineering.  The second is a convenient semantic
assumption that, for most domains, is perfectly well warranted.    (04)

> That doesn't mean the universe "is" a set.  To say that something can
> be represented as a set for purposes of defining truth-values of
> sentences is a very different thing from saying it IS a set.    (05)

Certainly true.  Tarski interpretations can serve as models of the world
but are not identical to it.  However, those models are often capable of
capturing all of the relevant structure of some piece of the world that
we're interested in representing.  To ensure that our chosen
representation language is *capable* of expressing that structure is the
point of developing a model theory for it.    (06)

> The universe is what it is.  For many purposes, it is useful to
> describe it as a set with elements that have properties and bear
> relationships to each other.  But sets, elements, properties and
> relationships are mathematical abstractions.     (07)

This is, in part at least, a very dubious claim.  I'll grant you that
sets are mathematical abstractions (though there is no reason not to
count them as real for all that), but the smell of coffee, the colors of
the rainbow, and the shape of the Sydney opera house are all properties.
Do you think they are mathematical abstractions?  While they are in some
sense abstract, perhaps, they don't seem mathematical in nature to me at
all, and moreover they seem to me to be intimately connected to the real
world.    (08)

> There was a comment in another recent post about the Chinese language,
> and how it appears to be based on a fundamentally different
> metaphysics as Western languages.    (09)

Perhaps with regard to the *specific* things, properties and relations
it assumes to exist (though I frankly find this *exceedingly* doubtful)
but *not* with regard to the basic logical categories -- unless perhaps
one hews to some sort of 19th century anthropological myth about the
Inscrutable East.    (010)

> If we go around saying the universe "is" a set,     (011)

I don't believe anyone has gone around saying this.    (012)

> we are in danger of confusing a representation of the world with the
> world we are representing.     (013)

I don't think anyone here is in any such danger.    (014)

> Tarskian semantics accords well with the Western scientific worldview.     (015)

And most any other an ontological engineer might be interested in, I'd
venture.  (Note that this is not at all to say that an ontological
engineer wouldn't be interested in other semantic theories, notably
those that might have computational benefits of some sort.)    (016)

> It is quite useful for mathematical formalization of the meaning of
> statements that can be given definite truth-values.    (017)

And a lot more besides.  For purposes of ontological engineering, model
theory's function is primarily theoretical -- to ensure that one's
representation language has (among other desirable properties) the
expressive powers one desires.  It is also useful, e.g., for ensuring
that one's ontological axioms adequately characterize one's intended
domain.  (The NIST Process Specification Language is an especially
cogent example of this use of model theory.)  But having done its job,
model theory sort of falls away -- in ontology, axioms are where the
action is.  They are what constitute our ontologies and are what we
exchange and reason upon.  Model theory simply helps to ensure that out
axioms express (as far as possible) what they are intended to express.    (018)

> Formal ontology is most usefully applied to problems that can be
> described in terms of statements that can be given definite
> truth-values.    (019)

I don't know why.  Though many ontologists as a matter of fact stick to
representation languages that assume a classical 2-valued semantics,
there is no reason whatever that one couldn't use a language with a
non-classical semantics (e.g., the semantics of fuzzy logic where
"partial" truth values are allowed or a 3-valued semantics in which a
sentence can fail to be true or false.).    (020)

> But that doesn't mean nothing exists except that which can be
> described in terms of properties of or relationships among elements of
> a set.    (021)

Hm, well, that might be true, but if you seriously don't think you can
describe some domain in terms of propertied objects -- objects, perhaps,
of a very complex sort -- then that domain, while perhaps of vital
interest to mystics and shamans, is utterly irrelevant to ontological
engineering, as it is incapable of being axiomatized.    (022)

> I apologize for getting a bit metaphysical, but I think this is an
> important point.    (023)

I certainly can't disagree with you about that.    (024)

Chris Menzel    (025)

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