A Solution To Karttunen’s Problem

In document Two indefinite pronouns in Catalan Sign Language (LSC) (Page 151-157)

Matthew Mandelkern, mandelk@mit.edu Abstract for Sinn und Bedeutung 21

1 Overview

I present (1) a new empirical characterization of the difference in felicity conditions between an epistemic necessity claim of the form pMust ϕq versus a claim of non-modal ϕ alone, and (2) a pragmatic explanation of this difference.

2 The Difference

The main claim in the literature1 is that a ‘must’-claim is licensed only when the speaker’s

evidence for its prejacent is indirect, whereas its bare prejacent can be asserted whether the speaker’s evidence is direct or indirect. I endorse this constraint, which I call Indirectness, and which has been well motivated in the literature.

But is Indirectness the end of the story? Most of the literature suggests the answer is ‘yes’. I argue this is wrong. Following Stone (1994), I argue that a ‘must’-claim is only felicitous if an argument for its prejacent is salient, whereas its bare prejacent can be asserted whether or not there is a salient argument. Call this claim Support. To see the motivation for Support, consider the five variants of the following case, adapted from Murray (2014): (1) On her way to a meeting in a windowless building, Sarah sees Jim come in with a wet

umbrella. Sarah concludes it’s raining. When she goes into the meeting, Thomas, who didn’t see Jim carrying a wet umbrella, asks, ‘How’s the weather?’ Sarah responds: a. It must be raining out.

b. It’s raining out.

c. It must be raining out; I just saw Jim come in with a soaking wet umbrella. d. It’s raining out; I just saw Jim come in with a soaking wet umbrella.

e. Apparently it’s raining out.

Now suppose Thomas replies: ‘Too bad. Ok, let’s talk about the agenda for this meeting.’ In this context, there is something odd about the ‘must’-claim alone, without an argument, as in (1-a). Sarah seems obligated to give reasons in support of the claim that it’s raining out before the conversation moves on. By contrast, a ‘must’-claim with an argument (as in (1-b)) or a non-modal claim with or without an argument (as in (1-c), (1-d)) are all fine. This confirms Support. An indirectness marker like ‘apparently’ (in (1-e)) is also fine without an argument, which brings out the distinctness of Support from Indirectness.

Intuitions here are not altogether clearcut. This is to be expected, though. First, judging whether speakers comply with Support is a matter of judging discourses as a whole, not

1Karttunen (1972), Kratzer (1991), von Fintel and Gillies (2010), Lassiter (2016), a.o.

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individual assertions. Second, in many cases an argument can be accommodated, so that Support is met even though nothing is said explicitly. Nonetheless, there is strong evidence in favor of Support. I present a wide variety of cases which elicit judgments confirming Support. I find similar judgments in a wide range of languages, suggesting cross-linguistic robustness. Finally, I present experimental results which confirm these judgments. 153 Amazon Turk subjects were given either example (1) or a similar case and asked to rate the first four variants (+/− ‘must’, +/− argument) for weirdness. We found an interaction (F(1,584) = 3.849, p = 0.05) between whether the statement included ‘must’ and whether there was an argument proffered. This interaction was primarily driven by the difference in perceived weirdness between ‘must’-claims with an argument (mean=1.926, SD=1.33) and those without one (mean=3.3423, SD=1.89; t(265.43) = 7.49, p<0.001, d = 0.868). These results thus provide further confirmation of Support.

3 Explaining Indirectness

The provenance of Indirectness has puzzled researchers. Much recent work follows von Fintel and Gillies (2010) in stipulating it lexically, but − as vF&G acknowledge − this does not provide a compelling explanation of the constraint, which is robust across modals with the meaning of ‘must’. I will argue instead that we can give an explanatorily and empirically compelling pragmatic derivation of Indirectness by way of Support.

There are two ingredients to this derivation. First, note that there is a general require- ment that, when speakers give evidence for a claim, they give their strongest evidence (a familiar Gricean idea; see Faller (2012) for a careful exposition). Second, note that certain arguments strike us as redundant: in general, if JϕKc follows from Γ in a way mutually rec- ognized to be obvious, then proposing to update the common ground with JϕKc on the basis of an argument Γ strikes us as redundant (see Stalnaker (1974) a.o. for this general idea).

It follows from Support that a speaker of pMust ϕq must give evidence forJϕK

c. It follows

from the first observation just made that it must moreover be her strongest evidence forJϕKc.

It follows from the second observation that JϕKc cannot follow from her strongest evidence

in a way mutually recognized to be obvious. A speaker may thus assert pMust ϕq only ifJϕK

c

does not follow from her strongest evidence in a mutually obvious way.

This provides a derivation of Indirectness which is explanatorily more satisfying than a lexical approach. It is also empirically more satisfying. In particular, this approach predicts that intuitions about indirectness for ‘must’ and intuitions about redundancy track together. I argue that this prediction is borne out. Two cases illustrate this. First, reliable testimony for JϕKc is intuitively indirect evidence for JϕKc, but does not generally count as indirect when it comes to Indirectness; thus (2-b) is marked:

(2) a. What time is the movie?

b. ??Google says that it’s at 7:30, so it must be at 7:30.

Our approach, however, predicts this, since reliable testimony for JϕKc is a redundant argu-

ment for JϕKc, as in (3-b):

(3) a. What time is the movie?

b. ??Google says that it’s at 7:30, so it’s at 7:30.

Second, we predict that whether an argument counts as indirect for the purpose of judging either redundancy or Indirectness depends on whether we are treating the inference in ques- tion as mutually obvious, a context sensitive affair. This prediction is again borne out: the following variants on (3) are fine, with or without the ‘must’, since in these cases we are not treating the inference from pGoogle says ϕq to ϕ as mutually obvious:

(4) Google says that the movie is at 7:30. Websites listing movie times are generally unreliable. Google is reliable, though, so the movie [must be/is] indeed at 7:30.

4 Explaining Support

This explanation of Indirectness reduces it to Support plus general conversational consider- ations about sharing evidence and redundancy. What explains Support ? I criticize existing derivations from lexical stipulations (Stone 1994) or from an underlying premise semantics for modals (Kratzer (1981), Swanson (2015)) on the basis that these approaches predict that the dual of ‘must’ will likewise carry a Support constraint. I show this is wrong: ‘might/can’ is fine without an argument. And giving up on the duality of ‘might/can’ and ‘must’ wouldn’t help, since Support does arise for ‘can’t’, which we could not explain on that approach. In- stead, I propose that Support arises as a manner implicature, as follows. pMust ϕq and ϕ have the same basic update effect: adding JϕKc to the common ground. But pMust ϕq

is structurally more complex than ϕ, so the speaker must have good reason to use pMust ϕq rather than ϕ alone. Finally, I assume pMust ϕq means, roughly, pϕ will be commonly accepted after this claim is madeq (Stalnaker (2014), Mandelkern (2016)), and thus calls attention to the group’s doxastic relation to JϕKc. The interlocutors therefore reason that, since she chose a more complex alternative that makes reference to the group’s doxastic relation, the speaker is proposing to update with JϕKc on the basis of a shared argument for

JϕK

c, and thus she must ensure such an argument is salient.

References: von Fintel, K. and Gillies, A.(2010)Must. . . stay. . . strong! Faller, M.(2012)Evidential scalar implicatures. Kart- tunen, L.(1972)Possible and must. Kratzer, A.(1981)The Notional Category of Modality. Kratzer, A.(1991)Modality. Lassiter, D.(2016)Must, knowledge, and(in)directness. Mandelkern, M.(2016)How to do things with modals. Murray, S.(2014)Varieties of update. Stalnaker, R.(1974)Pragmatic presuppositions. Stalnaker, R.(2014)Context. Stone, M.(1994)The reference argument of epistemic must. Swanson, E.(2015)The application of constraint semantics to the language of subjective uncertainty.

3

Parsing, Presuppositions, and Structure in the Calculation of Local Contexts Matt Mandelkern and Jacopo Romoli

We use data from antecedent final conditionals to pose a challenge to parsing-based ap- proaches to presupposition projection and triviality (Schlenker 2008, 2009, Fox 2008, George 2008, Chemla 2010), and sketch two solutions to the puzzle: one that maintains the parsing- based framework, and one that rejects it in favor of a structure-based framework.

1 Presupposition and Triviality Data

(1) presupposes that John is in France, and intuitively, this doesn’t change if we post-pose the antecedent, as in (2).

(1) If John regrets being in France, he isn’t in Paris. (2) John isn’t in Paris, if he regrets being in France.

Analogously, (3) strikes us as felicitous and so does its antecedent-final counterpart in (4). (3) If John is in France and Mary’s with him, John isn’t in Paris.

(4) John isn’t in Paris, if he’s in France and Mary’s with him.

2 The Puzzle

In contrast with the intuitions above, parsing-based approaches to presupposition projection and triviality predict that post-posing the antecedent of conditionals like these changes their status. In particular, they predict that (1) presupposes that John is in France but that (2) doesn’t, and that (4) will be infelicitously redundant, while (3) will not.

We show that the problem is general to all parsing-based approaches, in particular for both incremental and symmetric algorithms. For concreteness, we make use of Schlenker (2009)’s algorithm, which posits that at any stage in processing, we restrict our attention to the elements of the context whose truth value is unsettled by the material processed so far. In particular, when we are processing a conditional ‘B, if A’, by the time we arrive at ‘A’, we need only consider ¬B-worlds from the context, since we already know that any B-world will verify the conditional (following Schlenker’s assumption for the moment that the conditional is the material conditional). Thus the predicted local context of the antecedent entails the negation of its consequent.

Schlenker then uses these predictions about local contexts to generate theories of pre- supposition and triviality. First, we say that a presupposition must be entailed by its local context. Then we predict that in a conditional of the form ‘B, if A,’ any presupposition of A will not project if it is entailed by the negation of B. But this is precisely what happens in (2): the negation of the consequent (i.e. John is in Paris) entails the presupposition of the

antecedent (i.e. John is in France), and so Schlenker’s approach predicts the presupposition of the antecedent will be satisfied in its local context and therefore will not project, contrary to intuitions. By contrast, the local context for A in ‘if A, B’ is just the global context, and thus the presupposition that John is in France is predicted to project from (1). Schlenker’s approach thus gets (1) right, but wrongly predicts that post-posing the antecedent will block projection in (2). Second, Schlenker proposes that a sentence is trivial if any part of it is entailed by or incompatible with its local context. Then we predict that a conditional of the form ‘A if (B&C)’ will be trivial if material in B is entailed by the negation of A. But this is just what happens in (4): the negation of the consequent entails the first conjunct in the antecedent. Therefore, the sentence should thus strike us as infelicitous. But it does not. By contrast, Schlenker’s algorithm rightly predicts that (3) will be felicitous, since the local context for B in ‘if (B&C) then A’ is the global context. Again, the algorithm predicts a contrast for antecedent-final conditionals where intuitions suggest there is not one.

3 A Parsing-Based Solution

It is natural to think that the culprit here is the simplifying assumption that the conditional is the material conditional. But switching to a variably strict or strict analysis doesn’t immediately help. We do, however, argue that changing our assumptions about the semantics of the conditional lets us avoid these problems. The key additional assumption we must make is that conditionals presuppose that their antecedent is compatible with the context set. It doesn’t matter what underlying semantic theory we adopt as long as this presupposition falls out (though it is most naturally seen as a corollary of a strict conditional analysis). Given this assumption, consider Schlenker’s algorithm for an antecedent final conditional ‘B if A’. When we arrive at the antecedent, we cannot ignore all the B-worlds, since to see if the conditional is true, we must check not only that none of the ¬B-worlds are A-worlds, but also that there is some A-world in the context. And the A world in the context may be a B-world. Therefore we need to consider both B and ¬B-worlds of c in evaluating A. We regiment these intuitions, proving that applying Schlenker’s incremental algorithm to an antecedent final conditional predicts that the local context for the antecedent is just the global context, provided the conditional presupposes that its antecedent is compatible with the context. We can thus predict, correctly, that (2) presuppose that John is in France and that (4) is not trivial.

This approach thus allows us to preserve a parsing-based derivation of local contexts. It requires a substantial change of perspective, however. These cases show that presuppo- sitions must be part of the input to the parsing-based algorithm. This is consistent with Schlenker’s incremental algorithm, but it runs counter to his formulation of his symmetric algorithm, which ignores the presuppositions of the input material. We must therefore mod- ify Schlenker’s symmetric algorithm so that it does not ignore presupposed material. This is, however, challenging, since Rothschild (2008) and Beaver (2008) point out that this version of Schlenker’s algorithm wrongly predicts that if the same material is presupposed on both

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sides of a conjunction, as in (5), the presupposition will not project. (5) The King of France isn’t tall and the King of France isn’t bald.

We discuss a possible response to this worry, along the following lines: distinguish local con- tent which is ‘main’-content from local content which is ‘not-at-issue’, and then formulate the theory of projection in terms of main local content: a presupposition must be entailed by main local content. This approach avoids both our objection and the Rothschild/Beaver ob- jection, but requires countenancing multi-dimensional local contents. Finally, we show that the present solution to our puzzles does not extend to trivalent parsing-based frameworks, which make the same predictions as Schlenker about antecedent-final conditionals.

4 Structure Based Solutions

We close by surveying the prospects for responding to our puzzles by abandoning parsing- based theories in favor of structural derivations of local contexts. Traditional dynamic the- ories like Heim (1983)’s have no trouble with the cases in question, but they depend on an entirely stipulative account of local contexts (see Schlenker 2009 a.o.). Rothschild (2011)’s approach is more explanatory, and avoids our objection, but it, too, relies on a stipula- tive mapping of sentences to a formal language which washes out the difference between antecedent-initial and antecedent-final conditionals by stipulation. We explore a solution based on Chierchia (2009), which posits that local contexts depend on the order of func- tional composition. This approach avoids our objections; but, as we discuss, it requires a revisionary approach to the semantics and syntax of connectives.

References:

• Beaver, D. (2008) As brief as possible but not briefer.

• Chemla, E. (2010) Similarity: towards a unified account of scalar implicatures, free choice permission and presupposition projection.

• Chierchia, G. (2009) On the explanatory power of dynamic semantics.

• Fox, D. (2008) Two short notes on Schlenker’s theory of presupposition projection.

• George, B. (2008) Presupposition repairs: a static, trivalent approach to predicting projection. • Heim, I. (1983) On the projection problem for presuppositions.

• Rothschild, D. (2008) Transparency theory and its dynamic alternatives.

• Rothschild, D. (2011) Explaining presupposition projection with dynamic semantics. • Schlenker, P. (2008) Be articulate: A pragmatic theory of presupposition projection. • Schlenker, P. (2009) Local contexts.

In document Two indefinite pronouns in Catalan Sign Language (LSC) (Page 151-157)