Semantics for Opaque Contexts

Kirk Ludwig and Greg Ray


We outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts.  Our starting point is the requirement that any semantics for a natural language be compositional, that is, that it provide an interpretation of each of the infinity of sentences in it on the basis of a finite primitive vocabulary and a finite number of rules.  At least since Frege, it has been recognized that sentences such as (1),

(1)               Galileo said that the earth moves,

present a prima facie difficulty for the project of providing a compositional semantics for natural languages.  A compositional semantics for a fragment of English which does not include sentences of indirect discourse, psychological attitude sentences (henceforth ‘attitude sentences), modal sentences, sentences about entailments, and similar constructions can be given straightforwardly in the form of a first-order interpretive truth theory for the language.  The approach breaks down when we turn to sentences such as (1), whose truth value is not a function of the truth value of the embedded sentence >the earth moves=.  In general, one term can be substituted for another in >that-clauses= salva veritate only if they are synonymous.  The most popular response exploits this fact by treating that-clauses as referring to intensional entities--entities (at least as) as finely individuated as the meanings of sentences.  We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts that does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts.  The account is inspired by Davidson’s paratactic account, but purged of the parataxis and other elements that spell trouble for it.  We treat complement clauses that do not contain bound variables as referring to the sentences following the complementizer, or the sentence from which the complement is derived.  Roughly speaking, a sentence of indirect discourse or an attitude sentence whose complement contains a complete sentence is treated as true just in case the complement sentence understood relative to context of utterance bears an appropriate sameness-of-content relation to an utterance or some appropriate psychological state, depending on the main verb.  However, we also hold that, though the only contribution to the truth conditions made by the complement of such sentences is exhausted by a metalinguistic reference, a speaker who uses such a sentence, and an auditor, must understand the complement sentence to understand the sentence (meaning in such cases outstrips truth conditions).  We show how to extend the basic approach to sentences in which there is quantification into the complement clause.  We also give a recursive characterization of the sameness-of-content relation required to meet certain objections founded on the Church-Langford translation test.  Finally, we show how to incorporate into the account the use of quotation marks in complement clauses and sketch extensions to some other opaque contexts.