NEGATION, AMBIGUITY, AND THE IDENTITY TEST

Abstract

Negation has been closely tied to semantic presupposition since the concept was first discussed. In most accounts there is a definition or a theorem to the effect that A presupposes B if and only if A and the negation of A, in one sense of negation, both entail B. The multiple senses of negation assumed by such principles have been criticized and along with it the concept of presupposition. Indeed one of the most interesting arguments against semantic presupposition is the joint claim that many-valued semantics for presupposition require ambiguous negation and that negation as found in English is not ambiguous. In this essay I propose to discuss quite generally the idea of ambiguity and the role of negation in presupposition theory. Along the way I shall argue that it is quite difficult to explain precisely how the usual identity test for ambiguity employed by linguists should apply to a logical connective like negation, and that most versions of the test when clarified do not yield the result that negation in English is ambiguous. I argue for these conclusions by attempting to clarify what the theoretical properties of language would have to be if this critique of semantic presupposition were right. The kind of syntax and formal semantics needed to support the identity test when combined with the relevant data about natural language usage does not yield the result that negation is ambiguous. The argument is based on details that are of some interest in themselves. An effort is made to formulate precisely what the identity test is, and in particular what the conditions are that must be met before a meaningful conjunctive abbreviation is permissible. Two different sorts of conditions are distinguished which really amount to two quite different versions of the test. Only one of these is really relevant to the issue of negation. This variety is also of interest because failure in this sense amounts to what philosophers have called zeugma. Both sorts are distinguished from a third version of the test, probably the most common, in which it establishes syntactic but not semantic ambiguity