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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