Recent philosophical literature has debated the question of how much context-relativity needs to be countenanced in precise semantic theories for natural languages and has displayed different conceptions of the way in which it might be accommodated. This article presents reasons to think that context-relativity is a phenomenon that semantic theory must accommodate and identifies some of the issues concerning how it ought to be accommodated.

It is commonly supposed that an utterance of a demonstrative, such as “that”, refers to a given object only if the speaker intends to refer to that object. This paper poses three challenges to this theory. First, the theory threatens to beg the question by defining the content of the speaker’s intention in terms of reference. Second, the theory makes psychologically implausible demands on the speaker. Third, the theory entails that there can be no demonstratives in thought.

This document presents a Gentzen-style deductive calculus and proves that it is complete with respect to a 3-valued semantics for a language with quantifiers. The semantics resembles the strong Kleene semantics with respect to conjunction, disjunction and negation. The completeness proof for the sentential fragment fills in the details of a proof sketched in Arnon Avron (2003). The extension to quantifiers is original but uses standard techniques.

It is often assumed that, though we may speak in sentences that express propositions only inexplicitly, our thoughts must express their propositional contents explicitly. This paper argues that, on the contrary, thoughts too may be inexplicit. Inexplicit thoughts may effectively drive behavior inasmuch as they rest on a foundation of imagistic cognition. The paper also sketches an approach to semantic theory that accommodates inexplicitness in mental representations as well as in spoken sentences.