THE DYNAMICS OF LOOSE TALK.

In the positive component of this paper, I develop a hybrid semantics for loose talk on which expressions are assigned a static, ‘literal’ denotation and a dynamic ‘loose’ interpretation. A dynamic loose talk- (DLT-)model for L is a tuple ℳ=⟨𝒲,𝒟, ℛ, ⟦-⟧, [-]⟩ where 𝒲≠∅, 𝒟 is a set of typed entities, ℛ is a set of accessibility relations on 𝒲, ⟦-⟧ is a standard static interpretation function from L into 𝒟 and [-] is a dynamic interpretation function also defined on L.

The accessibility relations in a DLT-model are intuitively understood as functions from a world w to the set of worlds which are equivalent to w for present conversational purposes. For example if all that is important is when Lena arrived, to within margin of error of +/- 5 min, and Lena arrived at 9.02pm at w, then R(w)={w′: Lena arrived between 8.57pm-9.07pm in w′}.

Where φ is a sentence of L, ⟦φ⟧ℳ,w_{∈{01,}, as expected. In contrast, [φ]∈ℛ×ℛ, i.e., a relation} between accessibility relations in ℛ. Intuitively, the idea is that in addition to its literal, static content, each sentence in the language also has an effect on the accessibility relation representing conversationally-equivalent worlds. Expressions in L can be divided into those which are R-inert (i.e., have no non-standard effect on the accessibility relation) and those which are R-active. Where every constituent in φ is R-inert, [φ] acts as a test:

[φ]ℳ,w_{=λRλR′. R′(w)={w′: w′∈R(w) & ∃w′′∈R(w) ⟦φ⟧}w′′_=1}.

That is, given an accessibility relation R, [φ]ℳ,w _{returns the accessibility relation R′ which maps} each world to ∅ unless there is a world in R(w) in which φ is true. For example, if ⟨R,R′⟩∈[Lena arrived at 9pm]ℳ,w_{, then R′(w)=∅ unless there is some world w′ which is conversationally} equivalent to w according to R, and Lena arrived at 9pm at w′. We then say that φ is assertable at a an accessibility relation R and world w just in case for all ⟨R,R′⟩∈[φ]w _{R′(w)≠∅ (i.e., updating R} with [φ]w _{does not return the trivial accessibility relation on w). The communicated content of a} sentence, given a contextually supplied accessibility relation, is just the proposition p={w: φ is assertable at w}.

Given this framework, we can introduce dynamic meanings for loose talk operators, negation and conjunction which will be shown to capture the data introduced in §2.1-3. The relevant lexical entries in DLT are given below.

 [exactly]w_{= λFλx.λRλR′. ∀w R′(w)={w′: w′∈R(w) & ⟦Fx⟧}w_=⟦Fx⟧w′_=1}  [NEG]w_{= λφλR.λR′. ∀w R′(w)={w′: w′∈R(w) & ∀w′′∈R(w) ⟦¬φ⟧}w′′_=1}  [and]w_{=λφλψλRλR′. ∃R′′ R[φ]R′′ & R′′[ψ]R′.}

Finally, I conclude by demonstrating how DLT can give an account of the communicated content of utterances of interrogative sentences, by treating such expressions as propositional fragments.

Bibliography

Lasersohn, Peter. 1999. "Pragmatic Halos." Language 75: 522-551.

Lauer, Sven. 2012. "On the Pragmatics of Pragmatic Slack." In Proceedings of Sinn and Bedeutung Sperber, Dan, and Deidre Wilson. 1985. "Loose Talk." Proceedings of the Aristotelian Society 86.

Implicatures of modified numerals: quality or quantity? Elizabeth Coppock, Floris Roelofsen, and Ivano Ciardelli

Puzzle. Expressions of the form at least n, more than n, n or more, and plain n have been observed to di↵er with respect to their quantity and ignorance implicatures. None of the modified numerals in this group gives rise to a quantity implicature of ‘no more than n’, while plain n does. Furthermore, it is often held that more than n does not give rise to an ignorance implicature while at least n and n or more do, though as Westera & Brasoveanu (2014) show experimentally, the latter claim is too simplistic, as some explicit QUDs, in particular polar questions, eliminate the ignorance implicature of at least n. The assumed contrast is attested, however, with other QUDs, including how many questions, where more than n signals ignorance to a lesser degree. This finding, along with contrasts in out-of-the-blue contexts such as I grew up with{Xmore than,#at least} two parents, suggests that more than n triggers ignorance inferences of a di↵erent, less obligatory nature than at least n.

Previous approaches. Two approaches have been explored in the literature to explain the observed empirical contrasts. One approach (e.g., Mayr, 2013;Schwarz, to appear a) tries to derive all the data from a particular way of computing quantity implicatures. Di↵erences between the various kinds of bare/modified numerals are accounted for on this approach by assuming that they activate di↵erent Horn alternatives. Another approach (Coppock & Brochhagen, 2013, henceforth C&B) is to derive the ignorance implicatures of at least n and n or more as quality implicatures. The standard Gricean quality maxim, however, does not suffice for this purpose. Rather, C&B invoke a quality maxim that is not only concerned with the informative content of the uttered sentence, but also with its inquisitive content, i.e., the semantic alternatives that it introduces. Di↵erences between the various kinds of bare/modified numerals are accounted for on this approach by assuming that they introduce di↵erent semantic alternatives. Note that in other empirical domains (e.g., free choice e↵ects of disjunction under modals or in the antecedent of a conditional), these two approaches have also both been pursued. We suggest that, in the domain of modified numerals, a combination of the two approaches is in fact needed. We develop such a combined account, and show that it improves on earlier proposals which placed the entire explanatory burden either on quantity or on quality.

Schwarz (to appear a) exemplifies the quantity-based approach. He assumes that the Horn alterna- tives for a sentence like Al hired at least two cooks result from two interacting Horn scales: _{h1, 2, 3, . . .i} and_{hat least, onlyi. The resulting set of alternatives A consists of the sentences [2], [3], [4], etc., as well as} [3, ...), [4, ...), [5, ...), etc, where [n] stands for ‘only n’ and [n, ...) for ‘at least n’. He adopts Fox’s Innocent Exclusion recipe for deriving scalar/ignorance implicatures, which starts with the quality assumption that the speaker believes p: 0p=_{{2p}. The primary implicatures are that the speaker does not have sufficent} evidence for any stronger alternative in A: 1p,A= 0p_{[{¬2q : q 2 A & q ⇢ p}. Secondary implicatures are} then computed as follows: 2p,A= 1p,A_{[{2¬q : ¬2q 2 1}p,A& q is innocently excludable relative to 1p,A} where p is innocently excludable relative to S i↵ 2¬p is an element of every maximal subset of {2¬q : ¬2q 2 S} consistent with S. When none of the alternatives is innocently excludable, an ignorance implicature is generated but no quantity implicature.

Under this view, it is unclear how to distinguish more than from at least. If numerals form a Horn scale, then something akin to what is done for at least needs to be done to block scalar implicatures here as well, but without creating an ignorance implicature. Furthermore, at least cannot always be grammatically replaced by its presumed Horn alternative only : He gave three people a raise,_{at least/*only_{}. Schwarz’s account predicts that a quantity implicature should arise in such configurations,} and no ignorance (here: the speaker believes that exactly three people got a raise), contrary to fact.

On C&B’s quality-based approach, the ignorance implicature of at least derives from the violation of a sincerity maxim akin to the Maxim of Inquisitive Sincerity, which militates against ‘raising an issue’ (expressing an inquisitive proposition) when the issue is already resolved in the speaker’s mind. C&B capture the fact that at least generates ignorance implicatures but no quantity implicatures, and the fact that bare numerals exhibit exactly the opposite pattern. They also predict the lack of ignorance implicatures for more than. However, they do not predict the lack of quantity implicatures for more than. Second, the e↵ects of the QUD documented byWestera & Brasoveanu (2014) are not accounted for. Third, as pointed out by Schwarz (to appear b), the ignorance implicature that C&B predict for at least n is too weak. In particular, it does not imply that the speaker should consider n itself a viable option. Finally, there is a framework issue: C&B formulate their account in ‘unrestricted’ inquisitive semantics, InqU, a modification of the basic inquisitive semantics framework, Inq_B. Technically, the di↵erence between the two is that Inq_B bans nested alternatives, while in Inq_U nested alternatives are allowed (hence the name ‘unrestricted’). While Inq_Uis richer in expressive power

1

than Inq_B, it is less well-behaved from a logical point of view. In particular, it does not come with a suitable notion of entailment. As a consequence, it does not provide the usual algebraic operations on meanings, like meet and join, either. One question, then, is whether an account of scalar modifiers along the lines of C&B really needs the full expressive power of InqU, or whether such a theory could also be formulated in Inq_B.

Proposal. Like C&B, we assume two Quality maxims: informative sincerity says that if a speaker utters a sentence ', her information state s should be contained in the informative content of '; inquisitive sincerity says that if a speaker utters a sentence ' that is inquisitive, then her information state should not already resolve it, i.e., it should not be included in any alternative for the sentence.

Like Schwarz, we adopt an Innocent Exclusion based recipe for deriving quantity implicatures, but now: (i) the Gricean Quality requirement, 2', is replaced by sincere('), which requires both infor- mative and inquisitive sincerity; (ii) we do not let 1',A include 0', ensuring that only primary quantity implicatures—and not quality implicatures—can be strengthened into secondary quantity implicatures in the final step. So we have:

0'={sincere(')}

1',A ={¬sincere( ) : 2 A & info( ) ✓ info(')}

2',A ={2¬ : 2 A & 1',A|= ¬2 & is innocently excludable given 0'[ 1',A} We make the further assumption that the QUD constrains the set of Horn alternatives A.

For more than, we propose an account that is very close to Schwarz’s proposal for at least. The only di↵erence is that we assume that the pragmatic alternatives that are taken into account when computing quantity implicatures are partly determined by the question under discussion. In the context of a how many question, the pragmatic alternatives that are taken into account are the ones obtained by replacing (i) the numeral n with some other numeral and/or (ii) more than with exactly. In the context of a polar question, these pragmatic alternatives are not activated/deemed relevant. Semantically, more than n is interpreted as having [n+1,...) as its unique alternative; exactly n is of course interpreted as having [n] as its unique alternative. Using the standard innocent exclusion mechanism, then, we derive: (i) in the context of a how many question: ignorance implicatures, and lack of quantity implicatures (because of symmetry of Horn alternatives); (ii) in the context of a polar question: lack of ignorance implicatures, and lack of quantity implicatures (since there are no relevant Horn alternatives).

For at least n (and similarly for n or more) we assume a semantics involving two alternatives, namely, [n] and [n + 1, ...). This di↵ers from C&B in that it does not require nested alternatives, and is therefore compatible with Inq_B. On the other hand, the Horn alternatives for at least n in the context of a how many question are_{{at least m | m 2 N}; in the context of a polar question these alternatives} are not activated. This di↵ers from Schwarz’s proposal in that only is not needed as a Horn alternative for at least, and in that the activation of Horn alternatives is QUD sensitive.

For instance, the semantics of John ate at least three apples is{[3], [4, ...)}. The Horn alternatives are John ate at least four apples (with denotation{[4], [5, ...)}), John ate at least five apples (with denotation {[5], [6, ...)}), and so forth. An ignorance implicature is predicted in virtue of the inquisitive sincerity maxim: the speaker’s information state cannot be included in [3] or in [4, ...). On the other hand, we correctly predict the lack of a quantity implicature, because there is no Horn alternative such that 1',A _{|= ¬2 . Finally, since the ignorance implicature already arises at the Quality level rather than} at the Quantity level (as in the case of more than), we account for the observation that the ignorance inference generated by at least is of a more obligatory nature than the one generated by more than.

This proposal allows us to: (i) predict ignorance with respect to the prejacent of at least (cf. Schwarz’s critique of C&B); (ii) get a three-way contrast between superlative modifiers, comparative modifiers, and numerals (in contrast to both Schwarz and C&B); and (iii) avoid the prediction that at least should pro- duce quantity implicatures and no ignorance implicatures when only is not a grammatical alternative (in contrast to Schwarz). With it, we reconcile Westera & Brasoveanu’s findings with the conceptual core of the C&B account, bring that work in line with recent theorizing on inquisitive semantics, avoiding nested alternatives, and show that inquisitive sincerity can interact with Horn-based quantity implicatures in a non-trivial way, something that may be fruitful to consider in other empirical domains as well.

References: Buring, D. 2008. The least at least can do. In Proceedings of the 26th West Coast Conference on Formal Linguistics, 114–120. Coppock, E. & T. Brochhagen. 2013. Raising and resolving issues with scalar modifiers. Semantics and Pragmatics 6(3). 1–57. Mayr, C. 2013. Implicatures of modified numerals. In Ivano Caponigro & Carlo Cecchetto (eds.), From grammar to meaning: The spontaneous logicality of language, 139–171. Cambridge: Cambridge University Press. Schwarz, B. to appear a. Consistency preservation in quantity implicature: the case of at least. Semantics & Pragmatics. Schwarz, B. to appear b. At least and ignorance: a reply to Coppock & Brochhagen (2013). Semantics and Pragmatics. Westera, M. & A. Brasoveanu. 2014. Ignorance in context: The interaction of modified numerals and QUDs. In Semantics and Linguistic Theory (SALT), vol. 24, 414–431.

Biscuit conditionals and past tense Eva Csipak Universität Konstanz

This talk presents novel data regarding biscuit conditionals, namely the fact that only some are acceptable with past tense, while others are not. We propose to explain this contrast by analyzing a subset of biscuit conditionals as performative utterances. This allows us to maintain a unified analysis of all types of conditionals. Biscuit conditionals (BCs) such as (1) differ from hypothetical conditionals in that the speaker is taken to be committed to the truth of the consequent, i.e., the speaker of (1) is taken to believe that there are biscuits on the sideboard in the actual world. This has caused much debate over whether BCs are in fact conditionals, and if so, whether a unified analysis is possible (arguing against a unified analysis e.g. Iatridou 1994, Siegel 2006, Scheffler 2008; arguing for it Franke 2009, and to some extent Ebert et al. 2014). (1) a. There are biscuits on the sideboard if you want them.

b. There were biscuits on the sideboard if you wanted them yesterday.

Since many languages (e.g. English, German, Romance, Slavic, Standard Arabic, Japanese) use the same form to express both hypothetical conditionals and BCs, it is attractive to see how far we can push for a unified analysis. Such an analysis predicts BCs to have the same properties as hypothetical conditionals; in particular regarding the interpretation of tense in the antecedent. At first glance this seems to be borne out, witness (1-b) which is simply a BC which references past time. The interaction of BCs with tense has consequently not received much attention, but cf. Swanson 2013. However, certain BCs are odd with past tense, see (2-b). Günthner 1999 calls these meta-communicative or ‘discourse-structuring’, a label I will adopt (note she does not consider tense).

(2) a. If I am being frank, you look awful.

b. #If I was being frank yesterday, you looked awful.

The puzzle, then, is this: can we maintain a uniform semantics for conditionals like (1), (2), and hypothetical conditionals, and if so, how can we explain the oddness of (2-b)?

We propose that a uniform semantics is possible if we analyze discourse-structuring BCs as performative utterances. It is suggestive that discourse-structuring BCs but not others can be paraphrased by more obviously performative means.

(3) a. If I may be frank ∼ frankly ∼ to be honest

b. If you want biscuits 6∼ wanting biscuits 6∼ to want biscuits

Ingredients • We adopt a Kratzerian semantics for (indicative) conditionals if p, q as given in (4), ignoring the tense operator scoping over the whole conditional (but see Ippolito 2013). (4) _{Jif p, qK= 1 iff ∀ w’ ∈ Opt}g(Tf (w)∪p), q(w’)=1

Next, we follow Franke 2009 who assumes that BCs receive their ‘biscuit’ interpretation via pragmatic reasoning: their antecedent and consequent are conditionally independent, i.e., chang- ing the belief about the truth of one will not cause a change of belief about the other; because this is known to both speaker and hearer, the hearer will infer that the speaker must have inde- pendent evidence for the truth of the consequent.

Finally, we assume that performative utterances are self-verifying, i.e., they become true by virtue of being uttered (e.g. Searle 1989, Condoravdi & Lauer 2011, Eckardt 2012). Thus, I am using a verb becomes true by virtue of being uttered, since am using is a verb. Performatives have to predicate something about the utterance context, not a past situation (cf. I was using a verb, see discussion below).

Proposal • Assuming a Reichenbachian system with reference time R and speech time S, we analyze (5-a) as (5-b): In a sincere utterance situation e during which the speaker sends the mes-

sage m, (5-a) is judged as true because the speaker is sending a frank message to the addressee, namely m.

(5) a. I am being frank. b. ∃m.∃e.sp sends m to ad, &FRANK(e,m), & R⊆t(e) & S⊆R

Combining the conditional semantics in (4), the antecedent semantics in (5-b), and Franke’s pragmatic reasoning for BCs, we get the following meaning for (2-a).

(6) a. If I am being frank, you look awful.

b. ∀ w’ ∈ Optg(Tf (w)∪JI am being frankK), Jyou-look-awfulK(w’)=1

c. ∀ w’ ∈ Optg(Tf (w)∪(sp sends m to ad and FRANK(e,m) and R⊆t(e) and S⊆R)), AD-LOOKS-AWFUL(w’)=1

Because of conditional independence, the speaker is taken to be committed to the truth of you look awful(=q) in w0. Furthermore, she is sending a frank message at the utterance time in w0,

namely q. This in turn ensures that the antecedent proposition(=p) holds of w0. Thus since both

pand q are true in w0, then given (4), also the worlds closest to w0must be such that p and q are

true; thus the conditional self-verifies. More generally, discourse-structuring BCs are such that qserves to verify p, thus ensuring the truth of the conditional. Consider If we now turn to point 5, I have prepared a chart. Again the antecedent is made true by the consequent (assuming that the chart is listed under point 5 – then by virtue of uttering the consequent, the audience is turning to point 5).

Now it is easy to see why the past reference in (2-b) is odd. (7) a. If I was being frank yesterday, you looked awful.

b. ∀ w’ ∈ Optg(Tf (w)∪JI was being frankK), Jyou-looked-awfulK(w’)=1

c. ∀ w’ ∈ Optg(Tf (w)∪(sp sends m to ad and FRANK(e,m) and R⊆t(e) and R<S)), AD-LOOKED-AWFUL(w’)=1

Due to the past reference, it is no longer ensured that the antecedent p is true: p requires that a frank message was sent yesterday but the consequent only ensures that a frank message is sent at speech time S. Thus the conditional fails to function as a self-verifying, performative utterance, and therefore it fails to fulfill its discourse-structuring function. Its meaning cannot be repaired: because of conditional independence of antecedent and consequent, it cannot be interpreted as a hypothetical conditional, and a ‘problem-solving’ BC interpretation makes no sense. Thus (2-b) is odd.

Further evidence for the performative use of discourse-structuring BCs comes from an- other property of performative expressions: it is well known that such expressions can also be used reportatively; in those contexts restrictions regarding past tense etc. do not apply (cf. I was using a verb). The antecedent in (2-b) is not inherently prohibited from co-occurring with past reference; this is illustrated in (8).

(8) If I was being (too) frank one day, I apologized the next.

Here If I was being frank is used reportatively and (8) receives a hypothetical conditional inter- pretation; crucially the antecedent is compatible with past reference.

For reasons of space we omit showing how to extend this analysis to conditionals with modal verbs in the antecedent, such as If I may be frank, you look awful.

Thus even ‘discourse-structuring’ BCs which barely feel like conditionals at all can be part of a unified semantics for hypothetical and biscuit conditionals. Their unique restrictions regard- ing tense can be understood as part of the properties that performative expressions in general are known to have.

Selected references • R. Eckardt (2012): Hereby explained. L&P • M. Franke (2009): Signal to Act. • S. Günthner (1999): Wenn-Sätze im Vorfeld. Deutsche Sprache

Number marking and bare noun interpretation in Teotitlán del Valle Zapotec

Amy Rose Deal and Julia Nee• University of California, Berkeley

Overview. Bare nouns in languages lacking definite articles are often reported to freely func-

tion both as definites and as indefinites. If true, this would make bare nouns in such languages quite different from English bare plurals and bare mass nouns (Carlson, 1977). In this paper, we show that bare nouns in Teotitlán del Valle Zapotec (TdVZ) actually behave precisely as pre- dicted on the neo-Carlsonian theory developed by Dayal (2004), building on Chierchia (1998). Only definite and kind-level readings are freely available; all other readings are significantly re- stricted. We propose that anι type-shift is freely available in TdVZ, enabling definite readings,