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Re: [ontolog-forum] A different approach to ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 11 May 2008 17:27:32 -0500
Message-id: <25D36DEE-42DF-4630-AF14-BA6DA8B0DA99@xxxxxxxx>
On May 11, 2008, at 4:08 PM, Pat Hayes wrote:
> At 2:52 PM -0500 5/11/08, Christopher Menzel wrote:
>>> The papers I've seen on possible worlds seem to cover a wide  
>>> variety of other topics like, necessity, possibility, etc ...
>> Yes, worlds (re-)entered the philosophical lexicon to provide an  
>> intuitive underpinning to Kripke's formal semantics for modal  
>> logic.  Formally, the set of "possible worlds" in Kripke semantics  
>> is just a set W of featureless objects whose role is basically to  
>> index a collection of Tarski interpretations.  Since, in a Kripke  
>> model of a given modal language, every sentence of the language is  
>> true or false at any given element w of W, "possible world" is a  
>> reasonably natural and intuitive label, as a possible world is,  
>> intuitively, a complete "way things could be", a complete  
>> "alternative description" of reality.
> From which it also seems reasonable - still speaking intuitively -  
> to say that a Tarski interpretation is a complete "way things can  
> be" in the same sense, i.e. a (formal, mathematical object which  
> stands for a) world. Right?    (01)

For sure.  The trick behind possible world semantics is just to glue a  
bunch of them together to get an interpretation for modal languages.   
The real *insight*, though, was seeing (and proving) that different  
constraints on the accessibility relation on worlds correspond in a  
precise way to different systems of modal logic.  That was Kripke's  
chief contribution.    (02)

-chris    (03)

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