>On Feb 7, 2007, at 3:48 PM,
><mailto:andersen@xxxxxxxxxxxxxxxxx>andersen@xxxxxxxxxxxxxxxxx
>wrote:
>
>>Chuck,
>>
>>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)
>
>Cheers
>
>Sergei
>
>
>
>
>_________________________________________________________________
>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
> (05)
--
---------------------------------------------------------------------
IHMC (850)434 8903 or (650)494 3973 home
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 cell
phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes (06)
_________________________________________________________________
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 (07)
|