[FOM] Correction to Posting on Kaplan's Sentence

[hdeutsch@ilstu.edu]

In a recent posting I mentioned that Kaplan has argued in "A Problem  
for Possible Worlds Semantics" that possible worlds semantics is  
wanting in that it excludes certain "possibilities."  Kaplan works in  
a extension of sentential modal logic which allows for quantification  
over propositions (sets of worlds).  He gives an example of a sentence  
that is not satisfiable in this system, but that Kaplan thinks should  
be satisfiable in a correct semantics of modality.

In both Kaplan's paper and in my posting, the relevant sentence is  
misstated. (There is a typo in Kaplan's formulation that I did not  
correct in my posting.)  The correct version is as follows:

For all p, it is possible that, for all q ( Qq < > p = q), where Q is  
a sentential operator, < > is material implication, and p and q range  
over sets of worlds.

The sentence seems to require that there be a one to one  
correspondence between worlds and propositions (sets of worlds), and  
hence is not satisfiable in Kaplan's extension of modal logic.

I asked in my posting whether the existence of this sentence had any  
wider significance. It seems interesting that this idea (that there is  
a one to one correspondence, etc.) could be formulated in the language  
of modal logic. hd

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