Sean: (01)
Assuming you have modeled correctly, there should logically !exists 3d
entity in a 2d environment, should there? (02)
Duane (03)
On 5/31/07 1:35 AM, "Barker, Sean (UK)" <Sean.Barker@xxxxxxxxxxxxxx> wrote: (04)
>
> 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
>>
>>
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>> 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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