On Presupposition Projection with Trivalent Connectives

Abstract

A basic puzzle about presuppositions concerns their projection from propositional constructions. This problem has regained much attention in the last decade since many of its prominent accounts, including variants of the trivalent Strong Kleene connectives, suffer from the so-called *proviso problem*.This paper argues that basic insights of the Strong Kleene system can be used without invoking the proviso problem. It is shown that the notion of *determinant value* that underlies the definition of the Strong Kleene connectives leads to a natural generalization of the filtering conditions proposed in Karttunen's article ``Presuppositions of compound sentences'' (LI, 1973). Incorporating this generalized condition into an incremental projection algorithm avoids the proviso problem as well as the derivation of conditional presuppositions. It is argued that the same effects that were previously modelled using conditional presuppositions may be viewed as effects of presupposition suspension and contextual inference on presupposition projection.

Presuppositional exhaustification

“…To see what is predicted for (13), we need to know how quantifiers handle presuppositions in their scope, because (13) features a presupposition triggerpex 2 -in the scope of the matrix quantifier (and it also features the same pex 2 at the level of the alternative that pex 1 negates; see below). Our analysis will henceforth rest on a specific-yet independently argued for-framework for presupposition projection: the Strong Kleene trivalent logic (George 2008, Fox 2013, Winter 2019. We show now that given this logic for presuppositions, the embedded pex will be semantically 'transparent' when it comes to evaluating the contribution of the higher pex, avoiding the conundrum faced by exh-based theories.…”