|Date:||Tue, 26 Jul 2011 06:15:19 -0400 (EDT)|
I believe that the following point is the crux of the
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. 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. If your logic for stating laws and facts is FOL, you get quantified modal logic.
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.
In Kripke semantics, worlds are undefined elements of a set. Dunn just made the assumption that the undefined w can be replaced by a pair of sets of propositions (L,F). That implies that D's semantics subsumes K's semantics as a proper subset.
But D's semantics is *richer* than K's. In K's version, the accessibility relation is assumed as a given. But in D's semantics, the accessibility relation can be derived from the choice of laws and facts.
The converse is also true: Dunn's laws and facts can be derived from a primitive accessibility reation. But for both students who are learning modal logic and for professional philosophers, laws and facts are more intuitive and easier to explain than some abstract notion of accessibility.
Furthermore, D's semantics allows you to partition the laws into subsets with different levels of entrenchment. That enables you to define a hierarchy of multiple modalities. With K's semantics, you have to assume a partitioning of the accessibility relation -- it's equivalent, but not very intuitive for either students or professional philosophers.
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