Logic with a relative truth predicate and ?that?-terms

Abstract

In this paper we shall discuss and characterize an interpreted axiomatic system which can express the notion "relative to so-and-so, such-and such is true". The system features one non-extensional context, the name-former "that", which can enter into extensional contexts, such as "jc is necessary", "x believes y", and "x tries to bring about y" so as to form non-extensional compounds, such as "that such-and-such is the case is necessary", "jc believes that such-and-such is the case", and "jc tries to bring about that such-and-such is the case". Principles of interchange will be allowed to depend on content, rather than on uniform conditions of provability or necessity. While the system should provide for "intensional" phrases of English, no semantic use will be made of entities which are thought of as possible objects, possible worlds, or propositions. In particular, truth will be relativized to entities which are both formally and intuitively linguistic in nature. The paper begins with a presystematic statement of problems and desiderata, continues with an informal discussion of formal devices to be sub sequently employed, presents the semantics and axiomatics with brief informal sidelights, and ends with a completeness proof.