Anatomy of a proposition

Abstract

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions (mappings). Instead they are higher-order, fine-grained structures. I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed $$\lambda $$ -calculus, whose $$\lambda $$ -terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context.