14 - Partiality

Abstract

Partiality is both complex and widespread. Aspects of it have been the object of intensive study in logic and mathematics. This chapter aims to survey issues in partiality of possible relevance to theoretical and computational linguistics. It also surveys various sources of partiality arising from grammatical form, structure of knowledge, complexities of rule following, and the paradoxical properties of self-referential possibilities in natural languages, and outlines a model for linguistic structure. The complexity of actual communication is too difficult for both the logician and the linguist; it is therefore, immediately abstracted from reality and starts from what is grammatically correct. But even in the domain of the “grammatically correct” there are issues of partiality. One aspect of partiality is connected with sortal incorrectness. Another source of grammatical partiality is associated with the use of indexicals. Sortal incorrectness and indexicals lead on to the broader topic of presuppositions which lives on the border line between grammatical form and semantical content, where partiality or truth-value gaps may enter.