Presupposition Projection as Anaphora Resolution

The present paper presents an anaphoric account of presupposition. It is argued that presuppositional expressions should not be seen as referring expressions, nor is presupposition to be explicated in terms of some non-standard logic. The notion of presupposition should not be relegated to a pragmatic theory either. Instead presuppositional expressions are claimed to be anaphoric expressions which have internal structure and semantic content. In fact they only differ from pronouns and other semantically less loaded anaphors in that they have more descriptive content. It is this fact which enables them to create an antecedent in case discourse does not provide one. If their capacity to accommodate is taken into account they can be treated by basically the same mechanism which handles the resolution of pronouns. The theory is elaborated in the framework of discourse representation theory. It is shown that pragmatic factors interfere in the resolution of presuppositional anaphors. The resulting account can neither be classified as wholly semantic nor wholly pragmatic. Section 1 presents a survey of standing problems in the theory of presupposition projection and discusses the major competing approaches. An argumentation for a purely anaphoric account of presupposition is given in section 2. Section 3 presents a coding of presuppositional expressions in an extension of discourse representation theory. The final section is devoted to a discussion of the constraints which govern the resolution of presuppositional anaphors. 1 REFERENCE, BINDING, AND PRESUPPOSITIONAL EXPRESSIONS The traditional view on presupposition has it that presuppositions are referring expressions. When we use a sentence containing a proper name or definite description, we do not state that some object has a certain property, as the Russellian analysis implies. A proper use of such a sentence rather requires that the referring expression pick out some given object. Only if it does may we check for a particular property whether it holds of this object. If it does not, the sentence will not get an interpretation or, as Strawson phrased it, 'the question of truth or falsity simply does not arise'. This view originally derives from Frege's philosophy of language. For Frege it is referring expressions that give rise to presuppositions. Frege also insists that the reference of a complex expression is a function of the references of its parts. Thus, if one component expression of a complex expression lacks a reference, the whole expression will lack a at Lund U nirsity Lrary on F ebuary 6, 2011 jos.oxfjournals.org D ow nladed fom 334 Presupposition Projection as Anaphora Resolution reference. Given his doctrine that the reference of a sentence is its truth value, it is thus predicted that no sentence in which a non-referring expression figures as a part can have a truth-value. This consequence automatically carries over to any extensional compound. Presupposition failure is infectious. If one of the component sentences of a complex sentence suffers from presupposition failure and thus lacks a truth-value, any compound in which it figures as a proper part will lack a truth-value as well. However, as is shown by the standard examples from the literature on presupposition projection, this view gives rise to many counterintuitive predictions. Obviously, all of the following sentences can have a determinate value, even if John doesn't have any children. It is also clear that none of them inherits the presupposition that he has children as is predicted under a purely Fregean account: (ia) John has children and his children are bald. (ib) If John has children, his children are bald. (ic) Either John does not have any children or his children are bald. A second problem with the view that presuppositional expressions are referring expressions has been observed as early as 1973 by Mates. Presuppositional expressions may contain anaphors and these may be bound by external antecedents. This may seem innocuous with respect to the examples in (1), for in these sentences the pronoun depends on an antecedent which is a proper name and thus a referring expression itself. It does, however, give rise to serious problems as soon as a pronoun in a presuppositional expression is bound by an external quantifier: (2a) Someone had a child and his child was bald. (2b) If a man gets angry, his children get frightened. (2c) Every man kissed the girl who loved him. In all these cases the description contains a pronoun which is bound by and thus depends on an external quantifier. Consequently there is no uniquely identifiable object on which the 'presuppositional' expression depends and this in turn means that there is no way to analyse these descriptions as referring expressions. Strawson's revival of presupposition theory in the 1950s gave rise to two different explications of the semantic notion of presupposition. The first explication is very close to Frege's. A sentence presupposes another sentencejust in case the latter must be true for the first to have a truth-value. On this view presuppositional expressions are referring expressions. It is thus vulnerable to the objection stated above. The second explication takes preservation under negation to be the defining characteristic. Presuppositions are defined as those inferences which are entailed both by their carrier sentence and its negation. Let us call this the inference view on presupposition. According to this view a at Lund U nirsity Lrary on F ebuary 6, 2011 jos.oxfjournals.org D ow nladed fom Rob A. van der Sandt 335 sentence cp presupposes a sentence rp just in case q> 1= ip and -><ptrp. This explication actually requires a trivalent or other non-standard logic. However, on its standard definition the notion of entailment adopted is the classic one. This makes it easy to show that this strategy, like any attempt to define presupposition in terms of the classic notion of entailment, cannot succeed. For the entailment relation adopted is a monotonic one and presuppositions generally display a non-monotonic behaviour. Note that in the a-sentence the possessive phrase Harry's child induces the presupposition that Harry has a child: (3a) It is possible that Harry's child is on holiday. (3b) It is not possible that Harry's child is on holiday. (3c) It is possible that Harry does not have a child, but it is also possible that [he/Harry's child} is on holiday. (3d) Harry does not have a child. So {he/Harry's child) cannot be on holiday. Note furthermore that we intuitively infer from both (3a) and its negation (3b) that Harry has a child. If we take this inference to be an instance of semantic entailment, the definition of semantic presupposition predicts that Harry has a child is presupposed by both (3a) and (3b). Since the entailment relation employed is a monotonic one, it is simultaneously predicted that this inference is preserved under growth of information. But this last prediction is clearly wrong. If we add the information that Harry may not have a child as in (3c) or that he does not have one as in (3d), the presuppositional inference disappears without a trace. It follows that under its standard definition the inference view of presuppositions is simply wrong. It also follows that any attempt to account for the full range of presuppositional phenomena in terms of the classic notion of entailment is doomed to failure. Two remarks should be made at this point. Firstly, the phenomena just discussed are known from the literature on presupposition projection under the name of presupposition cancellation. This phenomenon actually gave rise to a third view on the nature of presupposition, the pragmatic paradigm. Presuppositional expressions are not taken to be referring expressions, nor are presuppositions viewed as semantic inferences which should be accounted for in terms of truth and entailment. They are instead taken to be purely pragmatic and context-dependent and have one central feature in common with Gricean conversational implicatures: when they conflict with contradictory information they will not give rise to inconsistency. Instead conversational presumptions will be lifted or altered in some way and die original inferences will not be computed with respect to this new situation. It is then important to notice that it need not be conflicting information which is responsible for the removal of presupposirional inferences. In (3 c) we added the information that Harry may not have children. This does not conflict with the presupposition that he has one, but nevertheless defeats the inference. at Lund U nirsity Lrary on F ebuary 6, 2011 jos.oxfjournals.org D ow nladed fom 336 Presupposition Projection as Anaphora Resolution Secondly, but most importantly, it should be pointed out that the claim that presuppositional inferences can be defeated by the addition of extra information simply is another way of saying that presuppositional inferences behave in a non-monotonic way. Cancellability or defeasibility is just non-monotonicity and it is this simple fact which precludes a definition and treatment of presupposition by means of a logic which relies on the classic notion of entailment. The alternative approach we just alluded to and which dominated presupposition theory during the 1970s is to treat presupposition as an essentially pragmatic phenomenon. Inspired by the work of Grice, the informational content of natural language utterances was taken to consist of two parts: the proposition expressed in view of the semantic rules of the language and further information conveyed by pragmatic means. The basic tenet of this view is that semantic and pragmatic information constitute two different types of content. Propositional content captures only part of what is intuitively conceived as the meaning of an utterance. Presuppositions and implicatures equally contribute to our understanding of natural language sentences. But the latter are computed in a different way. They are not part of the truthconditional content, but computed on the basis of the propositional content of the sentence uttered, contextual information, and pragmatic principles of a Gricean nature. They are thus computed and represented separately and merged only afterwards into a more substantial proposition. Contextual update will take place both with respect to the propositional content and information which is conveyed by other means. It is the sum of both which will be incremented into the next context. The general picture derives from Stalnaker's work: utterances are construed as context-sentence pairs. A discourse is conceived as a sequence of utterances. Given an utterance of a sentence cp in a context c we first compute [ cp\c, the proposition expressed by cp in c. Only then is further pragmatic information computed on the basis of contextual information and the propositional content of the sentence uttered. The proposition expressed and the pragmatic information invoked give, when taken together, the information conveyed by this utterance in this context. Now both the proposition expressed and the information conveyed may be constructed as formal objects of a similar kind. Just take them to be sets of possible worlds. Their intersection will then give us a new and more informative proposition. Let us call this object IC {cp, c), the informative content of the sentence cp in the context c. It is this object which will be incremented into the next context. The next context will thus comprise all the previously accumulated information + all the semantic and pragmatic information which is conveyed by the utterance itself. The following utterance will be interpreted with respect to this information. The view just sketched has a number of non-trivial implications. Firstly, it at Lund U nirsity Lrary on F ebuary 6, 2011 jos.oxfjournals.org D ow nladed fom Rob A. van der Sandt 337 means that it is utterances not sentences which are the primary information carrying units. Secondly, it implies that in processing a sentence cp its semantic content should be determined before any pragmatic information can be computed and this in turn implies that pragmatic information is to be represented separately from semantic content. The first of these claims is uncontroversial. The second and third, however, turn out to be wrong. In fact, the postulation of priority of semantic content over implicatures and presuppositions and the representation of semantic and pragmatic information by separate expression give rise to three interconnected problems. We get a notion of propositional content which is rather counterintuitive with respect to extensional contexts and plainly wrong with respect to intensional ones. We run into binding problems when presuppositions and implicatures enter into scope relations with quantified expressions and, finally, we blur the distinction between accommodation as a procedure which adjusts contextual parameters with respect to which the current utterance is to be processed and contextual incrementation as a mapping of the adjusted context