Re: Model != World?

Tegiri Nenashi says...

>Excuse me, but I have a basic question. What is the motivation for
>differentiating the concepts of "World" and "Model"?

You could think of each possible world as a different model of a theory. That works. (Although there may need to be certain constraints on what models of a theory are under consideration). But the philosophical discussion of what's possible, and what's necessary, and alternative possible worlds predates modern model theory.

One thing that is different about modal logics is that ability to refer to multiple possible worlds (any time you say that something is possible, you are implicitly quantifying over possible worlds). It's not usual in model theory to allow quantification over models in the object language (although such quantification may take place in the metalanguage). When you consider propositions involving modal operators, a single "possible world" is not a model for such propositions. It's the entire structure of all possible worlds that is being referred to by statements such as: "It is necessarily the case that X".

There is a discussion of the various uses of possible worlds here: http://www9.georgetown.edu/faculty/ap85/papers/PhilThesis.html but there is no mention of the fact that a possible world is a model of a theory.

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Daryl McCullough
Ithaca, NY