Homophony, Validity, Modality

Abstract

Abstract A semantic theory for a language exhibiting a particular feature treats that feature homophonically when its treatment of sentences having that feature itself exhibits the feature in question.1 The features at issue here are semantically characterized properties of individual unstructured expressions (‘semantic primitives’) or of modes of construction (such as functional application, predication, quantification). Amongst semantic theories we have in mind particularly those in the style of model-theoretic semantics, and those in the style of truth-theoretic semantics. A model theory for a language describes a class of interpretations and defines inductively (possibly with the aid of ancillary notions) a notion of truth relative to an interpretation; a truth theory by contrast aims at an inductive definition of an absolute notion of truth. ‘Absolute’ here means ‘not interpretation-relative’ there may of course be a relativity to various parameters, such as moments of time, speakers, possible worlds … however, the sensitivity of assignments-for example, of denotations to indexical terms-to these parameters is thought of as part of articulating some one intended interpretation rather than as reflecting the model-theoretic concern with abstracting from any one such interpretation. Truth-theoretic semantics has accordingly flourished for interpreted languages, either formalized languages with an intended interpretation, or natural languages and fragments thereof.2