>Duane,
> unfortunately, once I get into a 2d environment, I'm not sure
>that "!exists 3d" is meaningful, though it might be in a meta-world
>embedding the 2-d world.
>
>Sean Barker
>0117 302 8184
> (01)
This message, and indeed this sub-thread,
illustrate perfectly what seems to me to be the
key advantage of using a 'context ontology' (as
IKL does: that is, treating contexts as objects
and making non-contextual assertions about them)
as opposed to a 'context logic' (that is, a logic
in which assertions are understood as being made
in a context and interpreted there using
contextually local criteria). In a word, contexts
in a context logic make meaningful things
meaningless. (02)
Ask yourself: does it make sense to talk of 3-d
things? Yes, of course it does. Are 3-d things of
interest when talking of 2-d things? Yes, of
course they are: they are often the things that
have 2-d surfaces or 2-d projections, for
example. An adequate description of a knife
cutting a block of cheese involves entities of
all dimensions from 4 down (the cutting process
is 4-d; the block is 3-d; the newly revealed
surface of fresh cheese is 2-d and the location
of where the knife edge meets the cheese, where
the action is, is 1-d.) So what advantage or
utility is there is a framework which, when it
talks of 2-d things, makes it incoherent to also
talk of 3-d things? True, we might want to
consider a 'local universe' of purely 2-d
entities: but we can do that (or perhaps, if one
is being a logical purist, can *model* it) by
simply talking about the set of 2-d things -
which amounts, in a classical logic, to having a
property of 2-dimensionality and predicating it
of things in our quantifiers:
(forall ((x 2-D-thing)) ... ) instead of (forall (x) .... )
- and then can make any local assertions about
the 'universe' of 2-d entities that we want.
Nothing is gained by pretending that when we are
"in" (whatever that means) a 2-d context, that
all non-2-d things have some how vanished or
become inaccessible. To think about 2-d entities
is not to enter Flatland: it is simply to be able
to make assertions about a subset of the universe
of discourse. (03)
Pat (04)
>
>> -----Original Message-----
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
>> Duane Nickull
>> Sent: 31 May 2007 17:10
>> To: [ontolog-forum]
>> Subject: Re: [ontolog-forum] Ontology,Information Models and
>> the 'Real World': Contexts
>>
>> Sean:
>>
>> Assuming you have modeled correctly, there should logically
>> !exists 3d entity in a 2d environment, should there?
>>
>> Duane
>>
>>
>> On 5/31/07 1:35 AM, "Barker, Sean (UK)"
>> <Sean.Barker@xxxxxxxxxxxxxx> wrote:
>>
>> >
>> > What happens if a context/possible world is such that the
>> proposition
>> > ceases to be a proposition? That is, it ceases to evaluate
>> to true or
>> > false? For example, "the volume of a cube is the cube of
>> the length of
>> > its side" is meaningless in a 2-D world, since there is no
>> concept of
>> > volume. Similarly (A/B > 1) is meaningless in a context
>> where A and B
>> > are both zero.
>> > The tricky part is that there is no order of evaluation in
>> classical
>> > logic, so, in the latter case, adding guards on the
>> context, such as
>> > (A != 0) AND (B != 0), still leaves the combined
>> proposition meaningless.
>> >
>> > Sean Barker
>> > 0117 302 8184
>> >
>> >
>> >> -----Original Message-----
>> >> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> >> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf
>> Of John F.
>> >> Sowa
>> >> Sent: 31 May 2007 02:54
>> >> To: [ontolog-forum]
>> >> Subject: Re: [ontolog-forum] Ontology,Information Models and the
>> >> 'Real World': Contexts
>> >>
>> >>
>> >> *** WARNING ***
>> >>
>> >> This mail has originated outside your organization, either from an
>> >> external partner or the Global Internet.
>> >> Keep this in mind if you answer this message.
> > >>
>> >> Wacek, Ken, Pat, Ingvar, et al.,
>> >>
>> >> I agree that one should use technical terms in a way that stays
>> >> fairly close to traditional usage. But the tradition has a lot of
>> >> branches. In some branches, a proposition is fairly close to a
>> >> sentence, but with the option of considering a restatement in a
>> >> different language to be "the same" proposition.
>> >>
>> >> I take that to mean that a proposition is the language-independent
>> >> "meaning" or "intension" of a sentence, and that the truth
>> value is
>> >> evaluated in terms of some "extension" or universe of discourse.
>> >> If somebody changes the extension or universe of
>> discourse, then the
>> >> truth value may change. But the intension remains fixed.
>> >>
>> >> That interpretation is consistent with most 20th-century work on
>> >> modal and other kinds of intensional logics. Montague,
>> for example,
>> >> defined the intension of a sentence to be a function that maps
>> >> possible worlds to truth values.
>> >> Different possible worlds are different extensions, but
>> the function
>> >> (intension) remains fixed.
>> >>
>> >> Although I prefer Dunn's semantics of laws and facts to a
>> >> Kripke-Montague version with possible worlds, Dunn's approach
>> >> produces exactly the same truth values for the same sentences.
>> >> That implies that the same sentence with the same intension
>> >> (proposition) may have different truth values in different
>> >> circumstances. (I don't care whether anyone chooses to
> > use the terms
>> >> 'possible worlds', 'universes of discourse', or 'contexts'
>> for those
>> >> circumstances.)
>> >>
>> >> As Ingvar pointed out, Quine requires propositions to have fixed
>> >> truth values. But that follows from the fact that he does
>> not allow
>> >> different possible worlds or contexts.
>> >>
>> >> Although I do not like the notion of possible world, I would agree
>> >> with the modal logicians that any theory of modal logic
>> should permit
>> >> the same intension (proposition) to have different truth values in
>> >> different extensions (universes of discourse).
>> >>
>> >> I also agree with Pat that the word 'context' has been used in too
>> >> many confused and confusing ways. But I don't like either of the
>> >> following ways of talking:
>> >>
>> >> KC>> In that sense, a change in context BECOMES a
>> >>>> change in meaning of a proposition
>> >>
>> >> PH> No, that is muddled. That is exactly what does NOT happen.
>> >>> A proposition never changes its meaning. The SENTENCE >
>> >> expresses different propositions.
>> >>
>> >> I wouldn't say that a proposition changes its meaning
>> because I would
>> >> prefer to say that a proposition *is* the meaning of a
>> sentence. I
>> >> also would not say that a sentence whose indexicals were
>> resolved to
>> >> specific referents could express two or more different
>> propositions.
>> >>
>> >> I'm sure that one can find logicians such as Quine who
>> would disagree
>> >> with this interpretation. But I believe that it is
>> consistent with
>> >> those logicians who are more tolerant of modal logic. And since I
>> >> want to represent modal sentences in NL, I prefer to accommodate
>> >> their usage (even though I use Dunn's semantics rather than
>> >> Kripke's).
>> >>
>> >> John
>> >>
>> >>
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