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## Re: [ontolog-forum] Ontological Assumptions of FOL

 To: "[ontolog-forum] " , Chris Partridge "[ontolog-forum] " Kathryn Blackmond Laskey Sat, 17 Mar 2007 15:32:17 -0400
 ```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) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (014) ```
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