On 8/8/2011 9:13 PM, Christopher Menzel wrote:
> I already suggested in my earlier post how one could probably provide > a
>classical quantification theory for Dunn's semantics by adapting
> a substitutional approach. (01)
Yes. You could have "counterparts" in multiple worlds, even uncountably
many of them. Just define a set C of counterpart labels. Then define
a function f(w,x) to C with the following properties: (02)
1. For any individual x in a world w, f(w,x) would be an element of C
called the identifier of x. (03)
2. No two individuals in the same world would have the same identifier: (04)
For any x1, x2 in world w, if x1 ≠ x2, then f(w,x1) ≠ f(w,x2). (05)
3. Any individuals in different worlds that have the same identifier
are said to be counterparts: (06)
For individuals x1 in world w1 and x2 in world w2,
if w1 ≠ w2 and f(w1,x1) = f(w2,x2), then counterpart(x1,x2). (07)
> it appeared clear to me it's not for nothing that Dunn suggested
> extending his semantics with a substitutional quantification theory; (08)
Dunn published papers about truth-value semantics and substitutional
theories for years. It's one of his main interests. (09)
> you can't just tack on a classical QT onto his semantics and go on
> your merry way the way you can with Kripke semantics. (010)
There is a one-to-one isomorphism between Kripke worlds and Dunn's
pairs. Every theorem that applies to one applies to the other. (011)
Could you please show me anything you can "tack on" to a K model
that you couldn't "tack on" to a D model with a line-by-line
translation from one formalism to the other. (012)
> But your complaint was exactly that: "if [Kripke] had used the
> term 'model' instead of 'possible world', he would have saved
> a lot of dead trees." (013)
I wasn't actually blaming Kripke for not adopting Hintikka's
terminology. I was just noting that the absence of the colorful
metaphor "possible world" would have led philosophers to focus
on something more useful -- the propositions that describe the
worlds -- instead of trying to find some mystical meaning in
the worlds that was not in the descriptions of those worlds. (014)
JFS
>> but about professors
>> who teach modal semantics with featureless points and ignore the fact
>> that people who implement possible worlds use sets of sentences. (015)
CM
> I'm not sure I see the problem with that. It is easy to move back
> and forth between the two. The model set corresponding to a
> "featureless" world is just the set of sentences true there. (016)
But that contradicts what you say later: (017)
JFS
>> It's fine to teach them K's method for historical reasons. But it's
>> even more important to show them that D's method is what they actually
>> use in their applications. (018)
CM
> I am not at all sure that that is true. Be that as it may, Kripke's
> methods are of far more than historical interest. They are used
> ubiquitously -- and compellingly -- in theoretical comp sci, AI, and
> linguistics, as you well know, so I really don't see how you can say this. (019)
But they are *not* using Kripke semantics for their implementations.
They are using sets of laws and facts. That is Dunn's semantics,
but their teachers erroneously told them that they were using
Kripke semantics. (020)
CM
> Readers might have been left with the impression that CSP's list
> was correct and exhaustive. (021)
Unfortunately, CSP never got a chance to produce a definitive statement
of his logical writings. He kept producing more and more variations,
each with different elaborations of the basic ideas. (022)
In 1902, he applied for a grant from the Carnegie Foundation to publish
a complete finished version of his logic. His application was endorsed
by William James, President Teddy Roosevelt, and even Andrew Carnegie
himself. (023)
But the head of the Carnegie committee was Peirce's nemesis, Simon
Newcomb, who turned down the application on the grounds that the
funding was for science, but logic was not a science. (024)
John (025)
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