Formal philosophy: Selected papers of Richard Montague

Abstract

Natural language syntax, semantics, and pragmatics are mathematical disciplines rather than psychological ones, susceptible to the same rigorous metamathematical treatment as artificial formal languages. A comprehensive semiotic program develops this thesis by defining disambiguated languages as algebraic structures and constructing model-theoretic semantics based on intensional logic. This framework interprets linguistic meaning through intensions—functions from possible worlds and contexts of use to extensions—thereby addressing classical puzzles involving indexicality, modality, and non-extensional verbs. By formalizing fragments of English through universal grammar, it demonstrates that quantificational scope, definite descriptions, and prepositional modifiers can be analyzed using higher-order logic without sacrificing rigorous truth conditions. Furthermore, this approach extends formal analysis to epistemological and metaphysical entities such as events, tasks, and obligations, treating them as predicates within an intensional system. Logical paradoxes, including the “Knower” and the “Hangman,” are reformulated in syntactical terms to demonstrate the boundaries of formalized theories of knowledge. Ultimately, this program provides a unified methodology for translating natural language into formal symbolic logic, proving that the structural and semantic complexity of ordinary speech is fully compatible with the precision of mathematical logic. – AI-generated abstract.