The Proviso Problem: A Note*

Several theories of presupposition projection predict that some sentences which intuitively yield unconditional presuppositions should have weaker, conditional ones. For instance, If John is realistic, he knows that he is incompetent is predicted to have the presupposition that if John is realistic, he is incompetent, whereas one certainly infers that John is in fact incompetent. We summarize some difficulties faced by three solutions, DRT, Singh’s ‘Formal Alternatives’, and Singh’s ‘Interacting Alternatives’; we then offer a new analysis which is compatible with several semantic theories of projection, and which does not require the addition of a new representational module. In essence, we obtain unconditional inferences by assuming that speakers may ignore certain parts of a sentence when they accommodate a presupposition – presumably to simplify their computational work. They do so by adding to the context an assumption that would satisfy the presupposition of the sentence no matter which meaning some of its elements have. Depending on which elements are ignored in this way, a variety of strengthened presuppositions are obtained. We speculate on a possible mechanism (which follows some of Singh’s earlier ideas) to determine which of these strengthened inferences are in fact obtained. The analysis correctly predicts some new instances of the Proviso Problem in quantificational examples. Dynamic semantics (Heim 1983, Beaver 2001) and several other theories (e.g. Schlenker 2008, 2009, George 2008a, b, Fox 2008, Chemla 2008) predict that sentences that intuitively yield unconditional presuppositions should have weaker, conditional ones. This problem has been dubbed by Geurts (1996, 1999) the ‘Proviso Problem’. With the convention that we write as qq’ a clause with a presupposition q and an assertive component q’, the problematic prediction is that (p and qq’) and (if p, qq’) presuppose if p, q whereas in many cases they just presuppose q. This issue was raised by van der Sandt 1992 and Geurts 1996, 1999 as an argument against Heim 1983 and in favor of their own account of presupposition, DRT (‘Discourse Representation Theory’; see also Gazdar 1979 and Karttunen and Peters 1979 for earlier incarnations of the Proviso Problem); the criticism applies in identical form against more recent theories that also predict conditional presuppositions in these cases. There are two main approaches to the problem. (i) Proponents of DRT (van der Sandt 1992, Geurts 1996, 1999) take these facts to argue in favor of a representational theory of presupposition projection, one in which in many cases presuppositions ‘percolate up’ to take wide scope – which directly yields unconditional inferences. (ii) Proponents of dynamic accounts (e.g. Heim 1983, Beaver 2001) stick to the semantic analysis of Heim 1983, but supplement it with a strengthening mechanism to explain why unconditional presuppositions are sometimes obtained in lieu of conditional ones. There are two types of strengthening mechanisms. (iia) For some authors, it is purely pragmatic (e.g. Beaver 2001). (iib) For others, it crucially involves a representational component (Singh 2007, 2008, 2009). We will defend a new version of (iib). Bart Geurts gave an important argument for the view that a representational component must be involved somewhere as is assumed by accounts (i) and (iia). As he notes (Geurts 1996, 1999), it is very difficult for proponents of fully non-representational theories to explain the contrast between (1)a, which displays the conditional presupposition predicted by dynamic semantics, and (1)b, which typically yields a stronger (unconditional) inference. 1 Gazdar 1979, which will not be further discussed here, can be seen as a semantic account which generates unconditional presuppositions