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. (01)
Sean Barker
0117 302 8184 (02)
> -----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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> (03)
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