Logical presupposition : a re-appraisal of the concept and revision of the theory

Abstract

This dissertation is a defence of a logical approach to presupposition. In it (1) I enumerate, by way of apologia, some fundamental assumptions underlying both antagonistic and protagonistic treatments of such an approach, and argue that they are conceptually unnecessary, methodologically untoward, and/or logically contradictory. Most saliently, (a) I demonstrate the conceptual and logical contradiction in the view that presuppositional logic might be compatible with (or even imply) an ambiguity of natural language negation, (b) I provide a critique of the now traditional disassociation of the problems of presupposition-definition and presupposition- projection, (c) I provide a critique of the view that presuppositional logic -might be compatible with (or imply) logical trivalence. (2) In the light of a discussion of the conceptual distinction, I propose logical criteria for the distinction between a three-valued logic and a two-valued logic with truth-value gaps. (3) I demonstrate that, by these criteria, the standard (Strawsonian) Definition of Presupposition (SLDP) induces a trivalent logic.

(4) I present a distinct (but comparable) revised logical definition of presupposition (RLDP)showing that it induces a system that conforms to the proposed criteria for a two-valued logic with truth-value gaps. (5) By showing that the several problems associated with the SLDP do not arise (are 'solved') in the framework of the RLDP I show (a) that the problems encountered by the SLDP stem more or less directly from its trivalence and (b) that the facts of presupposition-projection are (and should be) immanent in the concept (and hence the definition) of presupposition itself, rather than represented as properties of logical functors. I also show that the revised definition reveals an unsuspected connection between compound counter-examples and simple counter-examples to the SLDP.