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Re: [ontolog-forum] intangibles (was RE: Why most classifications are fu

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 26 Jul 2011 14:21:25 -0700
Message-id: <CA78FA6C-D344-4C6B-B55C-DDB046D582ED@xxxxxxxx>
On Jul 26, 2011, at 3:15 AM, sowa@xxxxxxxxxxx wrote:
> Chris,
> 
> I believe that the following point is the crux of the misunderstanding:    (01)

Indeed, it seems to be. The question is, who is misunderstanding what? ;-)    (02)

> CM
> > 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.
> 
> On the contrary, Dunn's method defines the modal operators as an extension to 
>whatever logic is used to state the laws and facts.  I thought that point was 
>so obvious that I didn't mention it.    (03)

Not only is it not obvious, it is false.  Dunn's is a semantics for 
propositional modal logic.  Look in particular at the semantic clauses on pp. 
89-90 of Dunn's paper: one each for atomic sentences, negations, conjunctions, 
and modals.  There is no quantificational clause.    (04)

> But look at the formal definitions.  For any world w, a proposition p is 
>possible iff it is consistent with the laws of w, and p is necessary iff it is 
>provable from the laws of w.
> 
> That definition depends only on your logic and proof theory.      (05)

No, it doesn't.  The explicit context of the definition is a semantic theory 
for propositional modal languages.    (06)

> If your logic for stating laws and facts is FOL, you get quantified modal 
>logic.    (07)

Not so. It is in fact entirely non-trivial how you "get" QML from Dunn's 
semantics.  The foundational notions of laws and facts are based on an initial 
assignment of truth values to all the sentences of a language. To extend this 
idea to a language with predicates and quantifiers would mean that one would 
assign truth values to atomic and quantified sentences directly instead of 
deriving their truth values from an antecedent assignment of denotations to 
names/variables and extensions to predicates, as in classical semantics.  Dunn 
in fact notes in the last paragraph of his paper that such an extension of his 
framework to QML would require some sort of substitutional interpretation of 
the quantifiers  on the face of it, anyway, a rather radical departure from 
the objectual quantification of classical Kripke semantics for QML.  I can in 
fact imagine ways of doing this that would yield something equivalent to Kripke 
semantics for a quantified modal language L  notably, for a given 
interpretation I of L, by expressing the quantifier clause substitutionally 
with regard to an extension L' of L in which every one of the (perhaps 
uncountably many) objects in the domain of I has a name in L'. But, again, that 
is a long way from obvious and it is misleading to suggest otherwise.    (08)

> Another point:  I am not denying the value of any insight or proposal that 
>Lewis stated in terms of  possible worlds.  I'm just saying that replacing 
>each w with a pair (L,F) preserves every technical contribution that Lewis 
>made.    (09)

But I haven't been talking exclusively, or even primarily, about Lewis's 
technical contributions. I've been talking *applications* of his world theory 
to the solution of semantical and philosophical problems. My point has been 
that those applications do not map in any obvious way to Dunn's framework of 
laws and facts.    (010)

But look, this is a bit of a tempest in a teapot.  Both frameworks are rigorous 
and both have their own intuitive appeal; either might prove to be a useful 
framework for representing information in given context.  We should just follow 
Carnap's advice here and "let a thousand flowers bloom."  But we should also be 
clear about what each flower has to offer. :-)    (011)

-chris    (012)


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