[FOM] Correction to Posting on Kaplan's Sentence
hdeutsch@ilstu.edu
hdeutsch at ilstu.edu
Mon May 19 11:21:11 EDT 2008
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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