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Re: [ontolog-forum] Visual Complexity

To: Sergei Nirenburg <sergei@xxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 7 Feb 2007 15:47:17 -0600
Message-id: <p06230913c1eff76405c0@[]>
>On Feb 7, 2007, at 3:48 PM, 
>>I think you're missing the point.  Pat's (and I'm certain Chris') point is
>>that the term "model" used in the way they were discussing, is a
>>mathematical object that may be built up over things in the real world,
>>for example, such a model could contain a set containing you and I.  So,
>>standardly, you assign to terms in your language interpretations that are
>>picked from parts of that mathematical object.  Say the term 'funny' is
>>assigned the interpretation that is the set of you and I.  Now, all things
>>being equal, in FOL if we apply the term 'funny' to John Sowa (the real
>>John Sowa, not an abstraction of any kind) we get a big fat FALSE.  As
>>Chris and Pat have pointed out far better than I could hope to, there just
>>is no abstraction going on here of any kind.  If you're thinking that the
>>"model" is about 'funny' and not about sets containing you, I, or John
>>Sowa, then I could see how you might make that mistake -- things like
>>'funny' are the kinds of things that make their way into data models and
>>ontologies.  But that is not what Chris and Pat were talking about.
>Well, the set of you and Chuck is an abstraction, isn't it?    (01)

Reasonable, highly intelligent, articulate 
learned men disagree on the right answer to that 
question. But it is not really germane to this 
thread, since a (simple) Tarskian interpretation 
does not require that sets are in the universe, 
only that the universe itself is a set. There 
need be no expression in the language which 
refers to this set. The universe itself is part 
of the semantic meta-theory, not an entity of 
direct ontological significance. So calling it a 
set is only following normal good practice when 
we are building mathematical theories of 
semantics. It does not carry any ontological or 
even metaphysical weight. And even if one insists 
that the set {Bill, Chuck} is an abstraction, it 
does not follow that if you cut Bill, he will not 
bleed.    (02)

(If anyone here has taken a look at the CLIF 
model theory, I will admit that it *does* require 
that the universe contain some entities that some 
folk will consider to be abstractions, such as 
character strings and natural numbers; and IKL 
even requires propositions. But it is really hard 
to do without a few such sub-universes in any 
realistic ontology, so I will plead pragmatic 
convenience over philosophical qualms at this 
point.)    (03)

Pat Hayes    (04)

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