The role of context in plural predicationGregory Scontras and Noah D. Goodman — Stanford University

Predicates like heavy or expensive admit both distributive and collective interpretations:The boxes are heavy can mean either that each member of some salient set of boxes is heavy(distributive), or that taken together the whole set counts as heavy (collective; Scha, 1984).Since Quine (1960, p.140), researchers have assumed that some predicates lack collectiveinterpretations: The boxes are big is said to communicate about individual, but not totalbox size. Other size and shape predicates behave similarly (e.g., long, round); Schwarzschild(2011) terms them “stubbornly distributive.” To address the issue of why (and whether)these predicates differ, we begin with the more basic question of how much the interpreta-tion of plural predication depends on context, and in what way. The answer may illuminateboth the semantics of plural predication and the pragmatic mechanisms of ambiguity reso-lution. We first establish a way of studying plural predication experimentally. In Expt. 1,we introduce and validate a new paraphrase methodology. We then explore the idea thatcontextual predictability of the relevant collective property is a critical factor in determiningwhich reading is used. Expt. 2 shows that less variable contexts make the collective moreacceptable for all of the predicates tested. Finally, we discuss the role of contextual pre-dictability under a pragmatic account of ambiguity resolution in plural predication, using aBayesian model to formalize the process.

(1) The boxes were big/heavy/tall.

(2) The boxes each were big/heavy/tall.

(3) The boxes together were big/heavy/tall.

Fig. 1: Sample trial from Expt. 1.

Fig. 2: Expt. 1 collective response rate.

Expt. 1 (N=50): One way to accessinterpretations of ostensibly ambiguous plu-ral predications is to elicit ratings of un-ambiguous paraphrases, for example rating(2) and (3) as paraphrases of (1). First,we must establish that these are in factunambiguous paraphrases. To do so, weused a reference task. Subjects were in-troduced to Cubert, an alien in a factoryworking with boxes. They were told thatafter receiving a shipment of boxes, Cuberttold his friend Dot about them. The taskwas to help Dot decide which boxes Cu-bert was referring to; subjects chose be-tween a collective interpretation-satisfyingreferent (Fig. 1, left) and a distributiveinterpretation-satisfying one (Fig. 1, right).Fig. 2 presents rates of collective referentchoice for each of the three predicates andtheir three variants. The disambiguatingparaphrases behave as expected: each re-sults in a distributive interpretation and to-gether results in collective. We also findthat the bare form of big patterns differentlyfrom heavy and tall – it is more distributive.This finding is expected with respect to bigvs. heavy, but surprising given the behavior

1

of tall : both tall and big are size and shape predicates, so what allows tall to more read-ily receive collective interpretations in our experimental context? To identify this factor,consider first the difference between potentially collective and stubbornly distributive pred-icates. Collective weight is a stable property of sets: regardless of the physical arrangementin which we encounter them, a set of boxes will have the same total weight. In other words,collective weight is contextually predictable. With collective height or size, these propertiesmay change depending on physical arrangement: stacking boxes on top of each other or liningthem up side by side, the total height of those boxes will change. With predicates of physi-cal extent, collective properties are less contextually predictable when physical arrangementstend to vary. To communicate effectively and avoid possible confusion, collective interpre-tations should therefore be avoided. In other words, the more potential noise inherent tothe collective interpretation of a predicate, the less useful and thus less likely that collectiveinterpretation. Reducing noise to make the collective property more predictable on the basisof context, we should see collective interpretations become more available. In Expt. 2, weuse the paraphrase methodology to investigate the role of contextual predictability.

Fig. 3: Example context priming scenarios.

Fig. 4: Example big trial from Expt. 2.

Fig. 5: Expt. 2 results.

Expt. 2 (N=80): If physical arrange-ments are less likely to change, collectivepredication becomes more predictable andstands a better chance of being informa-tive. It should therefore become more likely.We manipulated predictability through a se-ries of context scenarios. Subjects saw Cu-bert receive sets of boxes from a dispenser.Between subjects, the dispenser either dis-pensed boxes in random (Fig. 3, left) orregular physical arrangements (stacked ontop of each other; Fig. 3, right). Subjectsobserved the dispenser four times, then Cu-bert spoke to his friend, Dot. Subjects wereasked to help Dot understand Cubert’s ut-terance by rating distributive and collec-tive paraphrases on a sliding scale (Fig. 4).Fig. 5 presents average paraphrase endorse-ment rates for the three predicates tested.For each predicate, regular contexts hadhigher ratings for collective paraphrases andlower ratings for distributive. Tall was mostaffected by our contextual manipulation,which directly targeted the height dimen-sion, stacking boxes on top of each other.

Our results demonstrate the central role of context in plural predication: as collectiveproperties become more predictable, collective interpretations become more viable, regardlessof the predicate involved. We formalize this choice in a Bayesian RSA model (Frank andGoodman, 2012; Lassiter and Goodman, 2013): noisy interpretations are less useful becausethey require more coordination between speakers and listeners; they are therefore less likely.

2