From a Modal Point of View: a Logical Investigation into Modalities De Dicto and De Re
Paul Harrenstein
Abstract:
From a Modal Point of View:
A Logical Investigation into Modalities De Dicto and De Re.
Paul Harrenstein
Philosophical conundrums regarding the reference of 'each man' in 'each man
is mortal' in traditional logic were rendered irrelevant by the
introduction of the quantifiers.
In this paper comparable Fregean and Quinean issues concerning the
reference of terms in modal contexts are bypassed in similar fashion
by conceiving of modal operators as being capable of binding terms in their
scope. Intensional phenomena such as the failure of substitution salva
veritate of coreferential terms are then accounted for by pointing out that
terms bound by a modal operator cannot be substituted. Moreover, the
calamitous conclusion of an infamous argument due to Quine that modal
distinctions are liable to collapse in quantified modal logics, is thus
avoided in an elegant, be it somewhat unorthodox, way. (The more orthodox
solution is to impose a division between referential terms, such as proper
names and variables, on the one hand and general terms, which may describe
the object they denote, on the other).
These ideas constitute the philosophical background of the modal predicate
logic PLuM, in which the formal investigations of the paper are executed.
In the modal predicate logical languages for PLuM each modal operator is
indexed with the terms it does not bind. The languages for PLuM will be
semantically dealt with by interpreting them in a possible worlds
framework. When a term is bound by a modal operator it will obtain a de
dicto reading, otherwise it will get a de re reading. An axiomatization is
provided for the most general system of PLuM.
There are some striking resemblances between the semantics of PLuM and
Kaplan's views on direct reference. In particular, the framework of PLuM
offers prospects for a semantics for indexical referring expressions. These
and related issues are dealt with in the penultimate chapter.
The final chapter revolves around issues concerning quantification and
other referential devices. The quantifiers behave in predicate logical
structures in a similar fashion as a special kind of indexed modal
operators do in a special class of possible world models. Accordingly, any
quantified modal logic could be treated as a bi-modal logic. No miracles,
however, are to be expected to result from this. The intention behind the
development of PLuM, however, is rather to outline another way of doing
modal predicate logic. The advantages of this approach are mainly of a
philosophical nature:. Issues concerning the reference of terms in modal
contexts are avoided. Moreover, one need no longer impose a once and for
all division between referring and general terms.