A Philosophical Conception of Propositional Modal Logic
Edward N. Zalta
Philosophical Topics, 21/2, Fall 1993,
The author revises the formulation of propositional modal logic by
interposing a domain of structured propositions between the modal
language and the models. Interpretations of the language (i.e., ways
of mapping the language into the domain of propositions) are
distinguished from models of the domain of propositions (i.e., ways of
assigning truth values to propositions at each world), and this
contrasts with the traditional formulation. Truth and logical
consequence are defined, in the first instance, as properties of, and
relations among, propositions.
These definitions have certain interesting consequences. One is
that they resolve a question that cannot be answered by the traditional
analysis, in which Kripke models directly interpret modal language.
The question is, is the reason a modal sentence has a different truth
value at other possible worlds due to the fact that the sentence has a
different meaning at that world or due to a change in the world? The
philosophical conception elaborates the second answer. Another
interesting consequence is that modal language, properly speaking, is
not intensional, at least according to the classic tests for, and
definitions of, intensionality.
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