The reflexive ceiling of philosophical semantics:

A study of internal tensions within semantic theory and its limitations to account for Ideal conditions of assertability

Abstract

It is a consensus to locate the origin of the reflexive foundations of modern semantics in Frege's work. Since Frege's distinction between two components of meaning (sense and reference), however, semantics has been forced to lead a double life. Among its first receptions, in Russell's famous article (1905), the first unresolved criticism of this solution was that: It is not possible to split semantics into a theory about two classes of objects without their yielding one and the same thing under lower and higher conditions of instantiation (depending on the function used to identify it). But even Russell could not avoid a crisis. It is not possible to reconcile semantic coordination for a set of non-classical extension of instantiation and encoding (possible instances, counterfactual truth values, etc.) while preserving the classical properties of signification. This article covers these moments with a rough diagnosis: modern semantics has a reflexive ceiling. It is unable to model the contingent features of an "object" without oversizing itself to deal with various constraints on that object adapted to various strategies of intensional and modal specification. In order to model idealized conditions of assertability (Putnam), one must filter the sentences that pass Tarskian test using non-sematic parameters – like the parameter of coherence of a scientific paradigm. It cannot keep that model without stopping being semantic. We conclude with a response to attempts to give semantic status to complex scientific reasoning, and a suggestion as to how to locate the philosophical origin of this claim.