Journal of Semantics Advance Access originally published online on May 3, 2005
Journal of Semantics 2005 22(3):281-305; doi:10.1093/jos/ffh026
| ||||||||||||||||||||||||||||||||||||||||||||||||||
© The Author 2005. Published by Oxford University Press. All rights reserved.
Articles-Special Issue |
A Modal Analysis of Presupposition and Modal Subordination
Institute for Logic, Language and Computation, University of Amsterdam
Correspondence: ROBERT VAN ROOIJ, Institute for Logic, Language and Computation (ILLC), University of Amsterdam, Nieuwe Doelenstraat 15, 1012 CP Amsterdam, The Netherlands. e-mail: R.A.M.vanRooij{at}uva.nl
In this paper I will give a modal two-dimensional analysis of presupposition and modal subordination. I will think of presupposition as a non-veridical propositional attitude. This allows me to evaluate what is presupposed and what is asserted at different dimensions without getting into the binding problem. What is presupposed will be represented by an accessibility relation between possible worlds. The major part of the paper consists of a proposal to account for the dependence of the interpretation of modal expressions, i.e. modal subordination, in terms of an accessibility relation as well. Moreover, I show how such an analysis can be extended from the propositional to the predicate logical level.
1 See Fernando (1995) for an analysis of context where full introspection is assumed as well.
2 Stalnaker (2002) suggests what is presupposed by an agent is what she believes is commonly believed by the discourse participants. This has as a result, however, that the attitude of presupposition does not obey negative introspection, because more things can be taken to be commonly believed than what is explicitly agreed upon.
3 Updating through the elimination of arrows instead of worlds has been used, among others, by Landman (1986a) and Veltman (1996). Its limitations for multi-agent settings are discussed in Gerbrandy (1999).
4 If we think of a world as representing everything that is the case, including some modal facts, a pointed model should be thought of as such a world.
5 A relation R is serial if 
x: 
y: xRy; transitive if 
and Euclidean if 
6 A presuppositional analysis can be ‘two-dimensional’ in two different ways. One is through the assumption that the presupposition and the assertion of the sentence can and must be determined relatively independently of each other. The analysis of what Karttunen & Peters (1979) call ‘conventional implicatures’ and the presuppositional analyses of Herzberger (1973), Gazdar (1979), Soames (1979), and Van der Sandt (1988) are all two-dimensional in this sense.
But there is also a less radical way in which an analysis of presuppositions might be called ‘two-dimensional’. On this reading it means only that at least some sentences in which a presupposition trigger occurs can be true even though the triggered presupposition is actually false. I believe that Stalnaker's analysis of presuppositions, just as my own analysis, should be thought of as two-dimensional in this more liberal sense.
7 Although I use a four-dimensional logic, I am not explicit about when a sentence is true or false, although its presupposition is not satisfied. But this is needed if we want to allow Even John was there to be true although it is not presupposed that John's being there was unlikely (thanks to Kai von Fintel for reminding me of this). However, there is no problem in principle of distinguishing those cases as well.
8 Though we will give a somewhat different analysis of possibility statements later.
9 Soames (1989) observed already that this is problematic for the standard way of accounting for presupposition satisfaction in dynamic semantics.
10 Throughout the paper I will assume the same for an aspectual verb like stop.
11 Our simple update function has limitations here: if we attributed to Sam attitudes about what the discourse participants presuppose, things would go wrong. I will ignore such attributions in this paper. See, among others, Gerbrandy (1999) for an analysis in which this problem is overcome.
12 Roberts' (1989) constraints are the following: (i) modal subordination ‘requires non-factual mood’ (p. 701); (ii) ‘it must be plausible that the modally subordinate utterance has a hypothetical common ground suggested by the immediately preceding context’ (p. 701); and (iii) modal subordination may not make antecedents available to anaphoric expressions that have no explicit representation in the given DRS (p. 705). For a critical discussion of these constraints, see Kibble (1994) and Geurts (1995).
13 Geurts (1995) claims that a modal presupposes its domain and assumes an exclusively anaphoric account of presupposition (satisfaction) for these cases. Given the important role that (non-global) accommodation plays in Geurts' (1995) analysis of presuppositions, this restriction is somewhat surprising.
14 Kaufmann (1997) discusses a similar example involving a conditional: (i) If John bought a book, he'll be home reading it by now. (ii) John works at a gas station. (iii) *It'll be a murder mystery.
15 As shown in Frank (1997), however, this problem can be overcome.
16 See, however, Fernando (1996) and Frank (1997) for less straightforward implementations of this idea within standard set theory.
17 That the proposed analysis is technically similar to Veltman's (1996) analysis of normally doesn't mean that the ordering relation represents the same kind of information.
18 This update rule is defined on the assumption that either w 
R(w) or w is not an A-world, because otherwise we would falsely predict that after the use of the possibility statement only other A-worlds would be accessible from w. In general we cannot make this assumption, of course. Fortunately, there are several ways to solve this problem. One way is to assume that w is the distinguished actual world, and that we change the update rule for possibility statements as follows: Upd(
A, R) = {
u, v
R| (if [[A]]R,u = 1, +, then [[A]]R,v = 1, +) or u = w}. In this paper I leave the update rule unchanged, and adopt a more tricky solution. Assume that if w R(w) and w is an A-world, we don't go to the new pointed model R', w, but rather to the pointed model R', w* with a new world w*. This new world is exactly like w of the original pointed model, except that w*R(w*) although w R(w*). Because our technical problem has a simple solution, I will ignore this complication in the main text. (Thanks to Frank Veltman and Henk Zeevat for discussion on this point.)
19 Notice that this analysis predicts that if A doesn't give rise to a presupposition, the sentence Would A can only be true if A is true in all accessible worlds. But the following sequence suggests that this is a wrong prediction: It might be rainy next week. The strawberries would rot in the garden. Here we seem to have modal subordination even though the embedded clause of the second sentence doesn't trigger a presupposition. One way in which this problem might be solved is to assume that the embedded clauses of would-sentences should be interpreted only with respect to accessible worlds v such that u R(v) : R(u) = R(v). In the above example, the embedded clause would now only be interpreted in worlds where it rains next week.
20 For a different analysis of modal subordination with questions, see van Rooy (1998).
21 For disagreement, see Geurts (1998).
22 For a discussion of some alternative analyses of desire attributions, see Van Rooy (1999).
23 So, with Kaufmann (2000) I agree that we need to keep previous contexts ‘in memory’. Accepting this—according to one reviewer—we give up the assumption that we can account for modal subordination in terms of a single accessibility relation. But I don't agree, for we still might think of R as a single accessibility relation for each time point. In systems that add to possible worlds a temporal dimension it is very normal to assume perfect memory: at each point in time you recall what you knew, believed, or presupposed before. To implement this assumption, we don't have to add to the model some extra accessibility relations, although the accessibility relation now has to represent more information. I won't go into the details of such a system here.
24 Based on the assumption that [[xrA]]R,i = 0, + only if 
25 Notice that because we think of worlds as a combined function from (i) propositional variables to truth values; (ii) discourse referents to individuals; and (iii) variables to individuals, the union of two worlds is well-defined. Notice also that after the update of a world with new information, this can have an effect only on the individuals it assigns to variables.
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  R. Van Rooij Strengthening Conditional Presuppositions J Semantics, August 1, 2007; 24(3): 289 - 304. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
N. Asher and E. McCready Were, Would, Might and a Compositional Account of Counterfactuals J Semantics, May 1, 2007; 24(2): 93 - 129. [Abstract] [Full Text] [PDF]
|
|