Transparency : An Incremental Theory of Presupposition Projection

We sketch a theory in which presuppositions do not directly impose conditions on the context set, but rather on the contextual meaning of a sentence. Specifically, a part of an expression's meaning which is marked as presupposed should satisfy a principle of Transparency, according to which this part can be disregarded without affecting the contextual meaning of the sentence. We argue that if Transparency is checked incrementally, i.e. as soon as a clause is pronounced, it yields a predictive account of presupposition projection: unlike competing theories, it derives the projection behavior of connectives from their bivalent semantic contribution. We further speculate that Transparency originates from a more general pragmatic principle, Be Articulate!, which states that one should not say too much at the same time, i.e. express a meaning that is too complex with a single expression. Transparency is a way to satisfy Be Articulate! even when an expression with a complex meaning is uttered because it ensures that part of this meaning can be disregarded. 1. Programmatic Outline: Be Articulate! and Transparency Two main questions can be asked about presuppositions: (i) How are they triggered? (ii) How are they projected? In ground-breaking work, Heim 1983 gave a lexical answer to both questions (similar remarks apply to the DRT accounts of van der Sandt 1993 and Geurts 1999; these raise several problems for Heim's theory, which we fully inherit). Specifically, she made the following assumptions: (i) Presuppositions are triggered lexically, in a context-insensitive fashion (though accommodation is context-sensitive). Thus whenever John knows that p is uttered, p will be triggered as a presupposition. (ii) The projection behavior of connectives and operators is encoded in their lexical entry. For example, if C is a context set, it is stipulated that C[F and G]=(C[F])[G]. [For an atomic proposition F, we write F as pp' if F contributes a presupposition p and an assertion p'. In this case, Heim's theory specifies that the update of C with F is C[F]=C[pp']=# iff for some w∈C, p(w)≠1. If ≠#, C[F]=C[pp']={w∈C: p(w)=1}]. Assumptions (i) and (ii) both raise the same explanatory problem: (i') Why could there not be a verb know*, which has the same global (i.e. assertive + presuppositional) content as know, but a different presupposition? For instance we could imagine that John knows* that p has no presupposition but asserts that p and John believes that p. We rarely encounter words such as know* (but see Abusch 2002 for a different opinion). Why? Heim 1983 provides no answer. (ii') Why could there not be a word and* which had the same logical contribution as and but a different projection behavior? For instance we could imagine that C[p and* q]=(C[q])[p]. But there seems to be no word such as and*. Why? Here too Heim 1983 (criticized by Soames 1989 and Heim 1992) gives no answer. We will sketch a purely pragmatic account of presupposition triggering and presupposition projection. Our attempt is purely programmatic with respect to the Triggering Problem. On the other hand we offer a precise algorithm for the Projection Problem, one that is predictive, in the sense that it can be applied to any connective as soon as its bivalent semantic contribution is known (neither Heim 1983 nor DRT are predictive in this sense). Our account is stated within a fully classical (bivalent) framework, and it has the following structure (the two parts could well be separated, but the result would be conceptually less natural): 1. A general pragmatic principle, Be Articulate!, specifies that one should not say too much at the same time, in the sense that one should not express a complex meaning with a single expression. For instance, in John fell, the single word fell contributes -very roughlythe information that i) John was standing up (=u for short), ii) he underwent an involuntary motion (=i), and iii) He ended up lying down (=d). Unless one is explicitly interested in this complex conjunction uid, Be Articulate risks being violated: it would be better conversational practice to articulate the intended meaning in separate parts, e.g. as John was standing but he fell. 2. In case Be Articulate! might seem to be violated, there is a way to salvage the principle by assuming that part of the meaning of the offending term is transparent, in the sense that one can disregard it without changing the contextual meaning of what is said. Specifically, Transparency states that one can erase one of the conjuncts that make up the meaning of the offending term, and still obtain a sentence which, given the assumptions made by the conversation partners, is equivalent to the original one. Transparency is checked in two steps: a. Selection (=Triggering Problem): First, one divides up the meaning of the offending term into two parts, and chooses (on pragmatic grounds to be determined) which one should be transparent; we write this part as underlined. How this selection process is performed may depend on the context. For instance, He didn't fall typically presupposes that the agent was standing up; we have in this case an analysis of the sentence as not f = not(uid). But one may utter the sentence felicitously to reassure a concerned mother who just saw that her son is lying on the floor crying (Don't worry, he didn't fall); here one seems to be presupposing that the little boy is lying on the floor, not that he was standing up right before [not f = not(uid)]. To see a third kind of situation, suppose that we saw someone come off a cliff. If I say that he didn't fall, I am probably presupposing that he was standing up and is now lying down, and denying that the motion was involuntary. Thus depending on the context, John didn't fall may be variably analyzed as not uid, not uid, not uid (or as uid if one is explicitly interested in the conjunction). b. Incremental Verification (=Projection Problem): Second, as soon as the offending clause is pronounced, one checks that, no matter what the end of the sentence will be, and no matter what the semantic content of the non-underlined part of the clause might be, Transparency will be satisfied. Suppose that John didn't fall is analyzed as not uid. In a context set C, we want to ensure that no matter what the end β of the sentence will be: (1) C |= ∀X [not(uX)β ↔ not(X)β) This will turn out to require that C |= u, as is desired. By contrast, if the sentence uttered is John was standing and he didn't fall, it can be understood with no presupposition whatsoever, because Transparency is automatically satisfied no matter what C is, we know that: (2) C |= ∀X [(u and not(uX))e ↔ (u and not(X) e)] We now develop in greater detail our account of the Projection Problem. Programmatic remarks on the Triggering Problem are included in the last section. 2. The Projection Problem I: Principles 2.1. Motivation: The Stalnaker/Heim Dilemma Unlike the standard Stalnaker/Heim account of presupposition projection, the present analysis does not take presuppositions to be constraints on the context, but rather on the contextual meaning of a sentence (specifically: a presupposition is a part of the meaning of a clause that one should be allowed to disregard without changing the truth conditions of the sentence). We take the Stalnaker/Heim analysis to have the following logic, which leads straight into a dilemma. 1. Assumption: When a clause pp' with presupposition p is uttered, it requires that p be taken for granted in the context (i.e. context set) of utterance . 2. Observation: In some cases, the Assumption seems to be violated, e.g. in It is raining and John knows that it is, which does not presuppose anything. 3. Conclusion: The notion of 'context' must be ramified. In the course of the evaluation of a sentence, there are a variety of local contexts, which are obtained as modifications of the initial context. In It is raining and John knows that it is, the local context obtained after the first conjunct is evaluated is one in which the presupposition that it is raining is indeed satisfied. Stalnaker and Heim differ in the way in which they set up the theory of local contexts. 1) In the case of conjunction, Stalnaker 1974 argues that presupposition projection can be explained in pragmatic terms: in p and q, q is evaluated in the initial context set as modified by the assertion of p. This is a plausible analysis, but only because a conjunction can be seen as a succession of two assertions. The account does not extend to other connectives, such as disjunction (p or q can certainly not be analyzed as a succession of assertions). 2) Heim 1983 abandons Stalnaker's pragmatic explanation, and posits that the way in which a connective modifies the context set is stipulated in its lexical entry. This account can extended to any connective, but it fails to be explanatory: it does not explain why the conjunction we find in natural language is and rather than and*. The dilemma is thus between a pragmatic and explanatory analysis that works for conjunction but not for all other connectives; and a lexical account that works for all connectives but is not explanatory. We conclude that a different course should be taken: the Observation should be seen as refuting the Assumption. Presuppositions do not directly impose something on the context, but rather on the (contextual) meaning of a sentence.