Ambiguity and the Principle of Idiosyncratic Interpretation

This paper discusses logics whose premisses and/or conclusions can contain ambiguous material. Two diierent kinds of applications are sketched for these logics. First, the paper discusses how logics with ambiguous expressions can shed light on the way in which human hearers or readers understand certain`paradoxical' logical arguments, in which crucial use is made of ambiguous material. Second, the paper discusses how diierent types of practical applications can restrict the choice of which logics may be used to reason about ambiguous material. Here a key role is played by the Principle of Idiosyncratic Interpretation, which states that, in a given context of occurrence, a human interpreter may be unaware of the fact that, in that context, a given utterance may have diierent legitimate interpretations. 1 INTRODUCTION Natural language is known for the ambiguity of its expressions. Whereas artiicial forms of communication tend to be designed in such a way that ambiguity is reduced to a minimum, natural language is ambiguous at variousìevels' of interpretation. At a low (e.g., speech recognition) level, a signal can be ambiguous between various utterances; at a higher (semantic) level, a fully recognized utterance can be used to express various diierent propositions; and at an even higher (pragmatic) level, a proposition may be used for various diierent purposes. Ambiguity, conceived in this broad way, is the main problem that confronts interpreters of natural language. We will, in this paper, focus on ambiguities of the second kind, which are sometimes called semantic ambiguities, or also just ambiguities, when there is no likelihood of confusion. Semantic ambiguity can arise from various diierent sources. For example, the source of an ambiguity may be lexical (as in cases of lexical homonymy and polysemy), syntactic (when an expression has more than one possible syntactic derivation), or contextual (as in anaphoric ambiguities). Combinations of such diierent sources occur as well.