On Jul 22, 2011, at 6:44 PM, sowa@xxxxxxxxxxx wrote:
> I view talk about possible worlds as a kind of Gedanken experiment. Such
>discussions can be very helpful in discussing the issues in an informal way.
>They are useful heuristics, and I encourage people to use whatever heuristics
>they find helpful. (01)
Again, that is a reasonable philosophical position. But it is not an argument
and does not address Lewis's arguments for the existence of worlds. (02)
> But the end result in physics is based on the formalism and its predictions
>about observable quantities. (03)
Worlds are postulated to solve certain philosophical and semantical problems.
They are not postulated to enable us to make better empirical predictions. (04)
> I believe that the same criteria are appropriate for any other field: use
>whatever heuristics are helpful, but the only concrete results are in the
>formal or formalizable statements. (05)
Well, it's not clear what a "concrete result" is supposed to be, but Lewis
would argue that belief in the existence of worlds is justified insofar as they
enable us to solve philosophical and semantical problems. I think that is a
reasonable philosophical methodology (although I do not in the end find Lewis's
views tenable). (06)
> JFS
> >> Could you please give one example of a problem that can be solved by
> >> Lewis's approach, but not by Dunn's laws and facts.
>
> CM
> > You set the bar too high; I can't give an example that CANNOT be solved by
> > Dunn's approach. All I can say is that Lewis provided world-based
> > solutions to, e.g., the analysis of modality, the analysis of intensional
> > entities, and the problem of mental content, among others, and that, to my
> > knowledge, no solutions to those problems exist in terms of laws and
> > facts.
>
> I haven't studied all of Lewis's writings, but what I have read sound very
>much like Gedanken experiments. (07)
They are not. (08)
> They're interesting heuristics. But I wouldn't call them solutions unless
>they were stated in logic or in some very clear NL that could be translated to
>logic. (09)
I'm not sure what you mean. His world theory and his counterpart theory are all
clearly expressible in first-order logic. Lewis himself provided an early
axiomatization in "Counterpart Theory and Quantified Modal Logic." (010)
> > (For another thing, I don't think there has been any detailed
> > philosophical account of what laws and facts even ARE in anything other
> > than a purely formal sense. It is thus not even clear how one would
> > develop Dunn's account to metaphysical ends.)
>
> The general method for mapping a Kripke model to a Dunn model is to treat any
>statement that is true about a world w as a fact, and any statement that is
>necessarily true as a law. That method could be applied to anything that
>Lewis considers true or necessary in any of his discussions. But the primary
>argument for Dunn's method is not merely that it's isomorphic to Kripke's, but
>that it opens up completely new topics for development.
>
> In particular, Dunn's method allows any insights about laws of any kind to be
>put in the set of laws. You can even have different levels of entrenchment
>among the laws: laws of logic, laws of nature, the US Constitution, the laws
>passed by Congress, the laws of New York State, ... down to the laws asserted
>by your mommy. (011)
The notion of a law in Dunn's semantics is very formal; the set of laws of a
world is simply a subset of the sentences that are mapped to the truth value
TRUE (subject to the usual boolean constraints). There is a rather huge gap
from this very formal notion to the sorts of workaday applications you suggest.
I know of nothing in the literature that attempts to close this gap. (012)
> Dunn's method opens up very flexible ways of talking about multiple
>modalities within the same framework. For example, the word 'must' is
>usually considered ambiguous. But in Dunn's method, it is univocal: it is
>defined in terms of some law, which could be at any level from a law by your
>mommy up to a law of nature or logic. (013)
I don't see anything that makes Dunn's method more flexible than Kripke
semantics in this regard. (014)
> As far as metaphysics goes, I believe that Dunn's method is far more fruitful
>and clearer than anything I've read in Lewis's writings. (015)
That could be, but I have to wonder how. Dunn's semantics is only a semantics
for propositional modal logic. It is far from obvious how it generalizes to
quantified modal logic, which would be essential if the framework is going to
applicable to the issues that Lewis addresses. (016)
> I tried to discuss some of those issues in my worlds.pdf and laws.htm
>articles. (017)
I'll have a look, but my recollection from earlier readings is that you build
off the nice metaphors of laws and facts but don't really develop Dunn's actual
semantics to the point that it could serve as an actual formal foundation to
the stuff you are doing. (018)
I have to say that your animus toward worlds strikes me as a bit too
ideologically driven. Isn't the only interesting question whether worlds are
useful for representing the kinds of information that ontological engineers
want to represent? (019)
-chris (020)
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