Abstract

The basic goal of the dissertation is to provide a formalization of a metalinguistic approach to modality, wherein necessity is treated as a predicate attaching to names of expressions, rather than as an operator attaching directly to statements. Richard Montague has argued that the predicate interpretation of necessity is fundamentally inconsistent, and his view has gained widespread acceptance in the philosophical community. But even though Montague's negative conclusion is expressed in very general terms, his technical demonstration of inconsistency relies upon a constellation of very specific background assumptions. In the present work, several formal strategies are explored for altering these background assumptions, and thereby constructing consistent predicate systems of propositional and quantified modal logic which completely mirror the operator approach within a first-order setting. Since the modal device is interpreted completely in terms of first-order models, this shows that possible worlds semantics need not be invoked in order to do standard modal logic. ;Two primary techniques for altering Montague's background assumptions are explored: the use of structurally primitive terms for denoting syntactical objects, and using structural-descriptive terms as names of formulas, while limiting the scope of application of the modal axiom schemas. The first technique is employed through the use of simple quotation names as logical constants designating formulas, so that the diagonal lemma fails for the set of terms through which the modal logic is defined. In this manner, diagonalization is unable to formally mesh with the modal logic. ;The second strategy relies upon defining a hierarchical sublanguage as a proper subset of the overall predicate system, and restricting instantiations of the modal axiom schemas to members of this privileged subset. This strategy preserves consistency because the formulas which give rise to contradiction are fixed points of the modal predicate, and these 'self-referential' expressions have no natural analogues in the standard operator approach. Thus if such formulas are identified and excluded from the scope of the axiom schemas, then they are rendered modally inert, while the predicate system remains capable of proving the counterparts of all modal theorems expressible via an operator