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Re: [ontolog-forum] Ontological Assumptions of FOL

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, Chris Partridge <mail@xxxxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Kathryn Blackmond Laskey <klaskey@xxxxxxx>
Date: Sat, 17 Mar 2007 15:32:17 -0400
Message-id: <p06110426c221e61b9bb9@[]>
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 ....    (01)

More precisely, one can represent it as a set for purposes of 
defining truth-conditions for sentences.    (02)

>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:    (03)

This is a very serious ontological commitment.    (04)

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.
  - 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.    (05)

Tarski showed that one can define a precise set-theoretic semantics 
for such a universe.    (06)

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.    (07)

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.  The universe is real.    (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)

If we go around saying the universe "is" a set, we are in danger of 
confusing a representation of the world with the world we are 
representing.  Tarskian semantics accords well with the Western 
scientific worldview. It is quite useful for mathematical 
formalization of the meaning of statements that can be given definite 
truth-values.  Formal ontology is most usefully applied to problems 
that can be described in terms of statements that can be given 
definite truth-values.    (010)

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.    (011)

I apologize for getting a bit metaphysical, but I think this is an 
important point.    (012)

Kathy    (013)

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