Numerical Discrepancies Between ‘Some’ and ‘A Few’ A Basis for Dutch Scalar Implicature Research Rien Debrouwer (Rien.Debrouwer@gmail.com) Department of Psychology, University of Leuven, Tiensestraat 102 B-3000 Leuven, Belgium Walter Schaeken (Walter.Schaeken@ppw.kuleuven.be) Department of Psychology, University of Leuven, Tiensestraat 102 B-3000 Leuven, Belgium Abstract messenger’s voice intonation, gestures, the general context and former experience in order to discern whether this Horn scales are a popular vehicle in the investigation of implicatures. Yet even this most user-friendly of implicature message was meant: ironically, sarcastically, in gest, social research categories is plagued by methodological and protocol, heartfelt, … . extrapolating difficulties. One of these difficulties is the possible existence of pungent semantic discrepancies that get (1) Could you crack a window? lost in translation. To form a basis for past and future Dutch (2) It is nice to meet you. scalar implicature research, we investigated the popular quantifier ‘some’. In an experiment we registered different Such information is not explicitly mentioned, though vital elements that make up its numerical description (i.e. minimal, for proper communication. It is part of the conventions that most likely and maximal value) and compared them to those make language more compact and manageable. It is not of other quantifiers from its Horn scale. The experiment showed that the parameter values for some are overall higher practical and opportune to repeat all this information with than those for a few. A scaling effect on some, however, every conveyed message: due to its sheer magnitude, and appears to blur some’s discrepancies with a few for lower because human beings tend to think faster than they can population sizes. articulate (Levinson, 2000). In attempting to resolve this laryngeal bottleneck, human language has developed certain Keywords: some; a few; scalar implicatures; numerical description; population size. pragmatic, culturally defined conventions or rules that provide linguistic messages with implied information for the Introduction receiver to infer. Grice (1989) introduced the name implicatures for these pragmatic, implied meanings of Communication consists of a process where: a sender messages. He discerned between Conventional Implicatures encodes his or her message into language, transmits the and Conversational Implicatures. Example (3) illustrates the message through a certain medium or channel (e.g., speech), former. The linguistic meaning of (3) is that someone and a receiver decodes and interprets the meaning of that named Paul had feelings of tiredness and satisfaction. An message (Levelt, 1989). A message does not merely consist implied message in (3) states that, out of its several lexical of the semantic value of a series of lexemes, ordered meanings (e.g., merely, yet, in spite of), the word ‘but’ is to according to grammatical convention (i.e. the linguistic be interpreted as ‘in spite of’. This pragmatic meaning of the meaning of the message). Most often, the receiver has to message stems from general linguistic convention on how attempt interpreting the pragmatic meaning of the message ‘but’ is to be interpreted given the grammatical build of the as well, i.e. the so-called implied subtext with all its relevant sentence. connotations. The message in (1), for example, is likely not actually an inquiry on someone’s aptitude at causing (3) Paul felt tired, but satisfied. fissures in windows. It refers to any nearby window, the context suggests a physical window (i.e. not a metaphorical Conversational Implicatures, on the other hand, cannot be one), the used syntax (i.e. “Could you …”) is common derived from such a secluded inspection of a sentence. practice for conveying a request for active behavior, in the Looking back at (1), the pragmatic meaning of “Could you current context the word “crack” is likely to be interpreted crack a window” is part of linguistic convention, i.e. a as the American English slang word for “open”, and the Conventional Implicature. The reason for this request could messenger’s posture and gestures might suggest that the only be detected from conversational cues (e.g., body goal for this request is to lower the indoor temperature. In language indicating feeling cold), i.e. a Conversational (2), the linguistic message may be at odds with the Implicature. While Conventional Implicatures rely on pragmatic one as well. The receiver has to inspect the convention, Conversational Implicatures depend on certain 205 rules of conversation known as Grice’s four maxims (Grice, subject of research. Previous research shows for example 1989). The messenger has to abide by these maxims for the that making a pragmatic inference is not the default pragmatic meaning of a message to get across properly, behavior, even though certain scalar inferences are found to otherwise Conversational Inferences cannot be correctly be made in high percentages of cases (e.g., cf. Table 1). made. Hence, conversational messages have to be: Children tend to interpret messages more as their linguistic meaning than as their pragmatic meaning (Noveck, 2001).  Informative (Maxim of Quantity), They respond more pragmatically as this behavior is more  Truthful (Maxim of Quality), saliently indicated to be the goal of the task (Guasti et al.,  Relevant to the conversation subject (Maxim of 2005), yet even then not as often as adults do (Guasti et al., Relation), 2005; Papafragou & Musolino, 2003). Children may also  And appropriately delivered (Maxim of Manner) to generate significantly more scalar inferences for one avoid for example ambiguity. quantifier (e.g., a few) compared to another (e.g., some) where this difference disappears towards adulthood Example (2) is informative if the correct intensity is phrased (Pouscoulous et al., 2007). One plausible explanation for (i.e., nice, not great or OK), truthful if the speaker means it, this difference between children and adults in interpreting relevant if said at an introduction, and appropriately implicative messages is that making scalar inferences delivered if spoken with a sincere demeanor. These four requires mental processing. Children don’t have as much of conditions being met, the listener may make the presumed these mental resources, resulting in fewer implicatures being correct pragmatic inference that the speaker indeed finds it produced, and even fewer for more complex quantifiers nice to meet them (in this case being the same as the (Pouscoulous et al., 2007). Yet, adults also require linguistic message). If, for example, the delivery was in a additional time (Bott & Noveck, 2004; Breheny, Katsos, & sarcastic tone, a different pragmatic meaning might be Williams, 2006; Noveck & Posada, 2003), working memory assigned to the message. (De Neys & Schaeken, 2007; Dieussaert et al., 2011) and Conversational Implicatures can be subdivided into other cognitive resources (Dieussaert et al., 2011) to process Generalized Conversational Implicatures and Particularized the pragmatic meaning of messages. If more of these mental Conversational Implicatures. The difference between the resources are otherwise engaged, fewer inferences will be two boils down to the level in which they depend on made. contextual factors. Particularized Conversational These findings are not only valuable in exploring the Implicatures are particular to a specific conversation. In (4), inner workings of implicature processing, they also have Tom’s utterance may hold an implied message, a pragmatic repercussions for the paradigms used in research on scalar meaning that Amy mistook Paul’s tiredness for looking inferences. Several methodological features influence the unsatisfied. This implicature cannot be drawn from Tom’s frequency of implicature generation. Next to utterance itself, only from the broader conversational aforementioned effect of task structure (e.g., dual task context. If Tom had said: “He was tired.” in response to a paradigm with adults), and salience of the goal of the task different question, for example: “Why did the hare take a (seven-year-olds), in younger children (five- but not seven- nap midrace?”, the aforementioned implicature would not year-olds) the type of task is paramount. Action-Based have been part of the pragmatic meaning of his message. Tasks, for example, stimulate far more production of scalar inferences in five-year-olds than Truth-Value Judgement (4) Amy: ”Did Paul seem unsatisfied to you?” Tasks do (Janssens & Schaeken, 2012). The content of the Tom: “He was tired.” message that is to be interpreted, is vital as well. More semantically complex quantifiers (cf. supra) or more Generalized Conversational Implicatures, such as in (2), can abstract statements (Janssens & Schaeken, 2012) result in be derived from the message itself (including delivery and fewer pragmatic interpretations in respectively nine- and body language). A specific type of Generalized seven-year-olds, and the specific syntax of the statement Conversational Implicatures is Scalar Implicatures. influences implicature production in adults (Breheny, et al., Implicatures of the scalar kind are relatively clear-cut and 2006). Even though scales of quantifiers are a very popular lenient to manipulation, with a relatively low chance at representation of implicatures, their interpretation appears to confounding variables. Conventional Implicatures are be prone to task- and procedure-related influences (e.g., conceptually more difficult to discern from the linguistic training: Papafragou & Musolino, 2003). Therefore one has meaning of messages than Conversational Implicatures are, to take great care in considering such paradigm and Particular Conversational Implicatures’ higher discrepancies when comparing experiments and dependence on context factors makes them a lot harder to generalizing results. Moreover, these extrapolation issues control compared to Generalized Conversational emphasize the importance of a strong basis, a solid central Implicatures. Of this latter category, Scalar Implicatures are concept for paradigms in implicature research. Yet, as we the best known and most explored. Therefore this scalar will explore next, even a vehicle as straight-forward as type of implicatures is a welcome and often preferred 206 scales of quantifiers could do with a more uniform illustrated this concern by investigated aforementioned understanding. influence of working memory strain, both with a some/all The scales used in scalar implicatures are called Horn scale as with numerals. In their experiment using numerals, scales, named after Laurence R. Horn who first introduced a higher workload was contradictorily accompanied with a them (Horn, 1972). Geurts defines Horn scales as: ”(…) higher preference of the pragmatic meaning. simply a sequence of increasingly informative expressions.” In order to gain some uniformity between studies, despite (Geurts, 2010). These expressions are all part of the same experimental differences between their paradigms, critical variable or dimension. Take, for example, a grouping of quantifiers in studies should be identified on a uniform quantifiers that all indicate a certain degree of temperature: measure. For existential quantifiers, we suggest using cold/cool/warm/hot. Such quantifiers do not represent fixed worldly categories with fixed population counts. Some/all measures of temperature, yet they can easily be ranked on a could for example be expressed as there being 83 cars (i.e. temperature-related dimension line (i.e. hotness, or all = 83) at a certain location, and participants could be coldness). In research on scalar implicatures, a weaker, asked to define ‘some’ as an amount of those cars. The logically less informative term is compared to a stronger, current study looks into such a numerical definition for the logically more informative term (e.g., warm and hot). In quantification pair some/all. their logical semantic meaning, the stronger term includes Pouscoulous et al. (2007) raised an important point in that the weaker term. This less informative, weaker term refers research on scalar implicatures is done by different research to a section of the measurement the stronger term groups in different countries, i.e. in different languages, and represents: if someone has five apples they also have three therefore may exhibit small lexical differences. The apples, if it is hot outside it is also warm outside. Yet comparison of some versus all, for example, has been pragmatically, these might seem like incorrect claims, due researched in a number of languages, using the translation to Grice’s Maxim of Quantity. The interpretation that, given of these quantifiers from English to the language in a stronger term, the weaker term is incorrect, is called a question. A non-exhaustive list of languages, in which scalar implicature or scalar inference. some/all implicatures were investigated, could be: Dutch It is even ill-advised to casually compare results of (Belgium e.g., De Neys & Schaeken, 2007; the Netherlands different studies if they did not implement the same Horn e.g., Geurts & Pouscoulous, 2009, Exp. 2), English (e.g., scale. Let us consider for example: Noveck (2001, Exp. 1) Katsos & Bishop, 2011), French (e.g., Bott & Noveck, who registered implicatures for 65% of participants on the 2004), German (e.g., Röhrig, 2010), Greek (e.g., Breheny, might/must scale, Pijnacker et al. (2009) with 54% for the Katsos, & Williams, 2006), Italian (e.g., Guasti et al., 2005). scale or/and, Papafragou and Musolino (2003, Exp. 1) who Previous studies have shown distinct differences in semantic found 93% for start/finish and 100% for the numeral scale nuances dependent on the language(s) one is brought up two/three (where three counted all members of the group). with (e.g., Dutch versus French versus bilingually Dutch Studies can have very different results in using the same and French: Ameel et al., 2004). Concerning implicature Horn scale, due to intended manipulations or research, Pouscoulous et al. (2007) specified the issue in methodological influences. For some/all, the most popular French experiments to the quantifiers ‘quelques’ and scale, Papafragou and Musolino (2003, Exp. 1) and ‘certains’ both being valid translations of ‘some’. The use of Zevakhina (2012) found 93% of implicature generation. Yet certains produced fewer scalar inferences in 9-year-old other results were found for this scale reading for example children than quelques did, plausibly due to the former 59% (Bott & Noveck, 2004, Exp. 3; Noveck, 2001, Exp. 3), being of a higher lexical complexity (by adding a partitive or even down to 34% (Geurts & Pouscoulous, 2009, Exp. attribute). In Dutch, analogue to French, ‘some’ can be 2). translated as ‘sommige’ or as ‘enkele’ (Van Dale, 2014). The or/and scale, with aforementioned result of 54% Therefore a similar investigation should be held on the (Pijnacker et al., 2009), brought results of 25% in a different semantic differences between sommige and enkele, to study (Chevallier et al., 2008, Exp.1). For other scales, improve the interlingual extrapolation of research using similar fluctuations in results can be presented. Undoubtedly these translations in its paradigm. these differences in results are mostly due to the This study aims to be a starting point for that semantical experimental manipulations of the specific studies. But it comparison between sommige (to improve readability, from does pose questions on how to validly extrapolate from here on identified as ‘some’) and enkele (henceforth ‘a individual studies and formulate funded, meaningful few’). We will look into their numerical description, i.e. a statements regarding the workings of scalar implicatures in numerical expression of their position on the none/some/all general, i.e. regardless of which Horn scales were used. Horn scale used in implicature studies. In a renowned Dutch Most research implements the some/all scale to test a claim dictionary (Van Dale, 2014), both some and a few are regarding scalar implicatures without taking into account the described as being a low amount. Yet, in comparison, a few existence of many other Horn scales and other quantifiers is more often described as referring to one single unit. within a Horn scale that could produce significantly Therefore, and intuitively, we hypothesize that in general a different results. Marty, Chemla and Spector (2013) few indicates a lower amount than some. 207 We will enquire about the preferred value, i.c. the most 'A few', 'Some' or 'Most'. In the first item, it read: Jan says: likely amount the quantifiers indicate given a certain " flowers are red.", in the second item: 'Mieke population size. As elaboration on this numerical estimate, says: " chairs are brown.", and in the third: the minimal and maximal value the quantifier could Ingrid says: " cars are green." Following the represent are requested as well, for several population sizes statement, the items featured the same three questions: and categories. As a control for our method, the quantifier ‘most’ will be added to the inquiry: most is likely to be a. If this utterance of is appropriate, how many considered a more informative quantifier (i.e. representing a are there minimally at that location? higher amount) than a few and some. The partitive attribute b. If this utterance of is appropriate, how many of most is also clearer than that of a few or some: most is are there maximally at that location? named after indicating over half of the population. This c. If this utterance of is appropriate, what is the partitive feature is not the core of the current study, but most likely amount of at that location?' given its proclaimed central role in the semantic difference between the French analogues quelques and certains The participants filled in the questionnaire with the three (Pouscoulous et al., 2007), we included it in our items, covering the three amounts and categories (i.e. resp. investigation. This partitive quality might translate into the 1019 flowers, 10 chairs and 83 cars). Each item of a parameter values for some being more scaled to the questionnaire regarded the same quantifier, resulting in population size than those for a few. Our quantifiers will be three between-subjects conditions: A Few, Some and Most. manipulated between subjects, in order to avoid that The conditions only differed in which quantifier was participants’ responses would be influenced by the presented in the statements. For Condition Some, for presentation of other quantifiers than the one at hand. We example, the statements read: used a number of non-linear population sizes in order to avoid that every quantifier would be assessed proportionate- (1) Jan says: "Some flowers are red." by-default to the previous population size (cf. Borges & (2) Mieke says: "Some chairs are brown." Sawyers, 1974). (3) Ingrid says: "Some cars are green." Method Results and Discussion Four participants did not answer every question (with a Participants numeric amount), one participant answered every question 216 first-year bachelor students in psychology participated with the population size and 22 participants reported a most in partial fulfilment of course requirements (17-28 years of likely value outside their reported [min;max] zone. age, M = 18.5; female: 168, male: 48). All participants were Therefore they were excluded from further analyses. Two native Dutch speakers. participants responded on certain questions with two adjacent amounts (e.g., '7 or 8'), for those answers we used Design, Material and Procedure the average of the two amounts (i.c., 7.5). All of the Each participant was presented a pen-and-paper remaining 189 participants (i.e. 62 in Condition A Few, 66 questionnaire in Dutch. It consisted of three items. They in Some and 61 in Most) reported minimal values lower were constructed in the same general fashion. than the reported maximal values. The instructions for each item started off with: 'Imagine The Most condition was included as a test of the protocol that at a certain location there are .' we used. The semantic meaning of most is captured in its The first item spoke of 1019 flowers, the second item name, and in this protocol indicates ‘more than half’. 154 regarded 10 chairs and the third item 83 cars. The amounts out of 183 (84%) minimal values for most were indeed and categories were matched so that they would make sense, higher than half of the population size. The minimal values so that participants might be able to envision in a lifelike that were lower than expected might be explained by the situation for them. In Belgium it is a tradition in certain folk comment of a few participants that the number of subgroups festivals to display a huge flower tapestry on the floor of a in the population is unknown. They seem to have interpreted big square. Such a scene, or for example a vast meadow, most as indicating ‘the largest of all subgroups’ (e.g., “Most might feature a flower count of 1019. 10 chairs is an amount flowers are red.” interpreted as: “There are more red than that one might imagine around a large living room table. any other color flowers.”), which might have a size lower And 83 cars might summon the mental picture of a large than half of the total population if there are more than two parking lot. The amounts were presented in a non-linear subgroups. This alternative interpretation does not interfere sequence, to make it harder for participants to extrapolate with our current basic investigation of the numerical their previous answer to the next item. description of some and a few, yet it could be subject to The instructions continued with: says: future, more in-depth research. " are ." The quantifier was 208 Table 1: The mean minimum (Min), most likely (ML) and Table 2: Mann-Whitney U comparison per population size maximum (Max) value for the three quantifiers for each of between Some and A Few (from the data scaled to 100). the three population categories (scaled to 100). Value Min ML Max Range Value A Few Some Most U 1933,50 1872,50 1806,50 1824,00 10 Min 22 22 59 chairs P .30 .21 .13 .14 10 chairs ML 40 41 72 U 1910,00 1602,00 1736,00 1882,00 83 cars Max 64 68 89 P .26 .02 .07 .26 Min 6 10 55 1019 U 1731,00 1588,00 1572,50 1731,00 83 cars ML 27 32 75 flowers P .07 .01 .01 .07 Max 58 66 96 Min 4 10 56 At the population level the results tell a more nuanced story 1019 (cf. Table 2). In each case some still produces higher values ML 29 36 78 flowers than a few, yet only in three cases these differences remain Max 59 72 98 significant: the most likely value in the population category of 83 cars, and the most likely value and maximum in 1019 Table 1 summarizes the different conditions. All numbers flowers. The difference in maximal value borders are scaled to 100, in order to make comparisons between the significance in the population category of 83 cars, as well as different population values easier. In this view on the mean the minimal value and the range in 1019 flowers. The numbers, some seems to be described with higher values differences in numerical interpretation between some and a than a few and most features higher mean values than the few appear to be bound by certain contextual factors such as other two quantifiers. population size. Not only do discrepancies in minimum, We tested the differences between the three conditions most likely value, maximum and range diminish when with the non-parametric Mann-Whitney U on the data looking at a specific conceptual (e.g., ‘cars’) and/or scaled to 100. In looking at all population categories numerical population size (e.g., 83). The number of these together, some is indeed seen as significantly higher than a aspects that are found to be significantly different, grows few: in its minimal value (U = 16169.50, p = .02), in its with the population size. most likely value (U = 15791.50, p = .008) and its We hypothesized that some is more partitive, more scaled maximum (U = 15430.00, p = .003). The values of most are to the population size than a few. In this case, some should significantly higher than those of a few (resp. U = 776.50, exhibit lower differences between population sizes (i.e. in 758.00 and 6638.00, all with p < .001) and of some (resp. U the data scaled to 100). Within subjects, per description = 1199.00, 685.5 and 7944.50, all with p < .001). The range category (e.g., the minimum) we computed a variable D; (i.e. maximum minus minimum) of some is also broader e.g., Dmin = (carsmin – chairsmin)² + (flowersmin – carsmin)² + than that of a few (16426,00, p = .03), and the range of most (flowersmin – chairsmin)². A lower value for D means that the is broader than that of both a few (U = 14588.50, p < .001) data is more scaled, i.e. that the numerical description of the and some (U = 12738.50, p < .001). quantifier in question is more influenced by population size. At the population level the results tell a more nuanced The results show that some is significantly more scaled than story (see Table 2). In each case some still produces higher a few in its minimum (U = 1668.00, p = .04) and its most values than a few, yet only in three cases these differences likely value (U = 1545.50, p = .009). Its maximum is also remain significant: the most likely value in the population more scaled, yet to a degree that only borders significance category of 83 cars, and the most likely value and maximum (U = 1743.00, p = .07). Overall we can conclude that the in 1019 flowers. The difference in maximal value borders numerical description of some is more dependent on significance in the population category of 83 cars, as well as population size than that of a few. the minimal value and the range in 1019 flowers. The differences in numerical interpretation between some and a Conclusions few appear to be bound by certain contextual factors such as The current study looks into a numerical description for population size. Not only do discrepancies in minimum, several quantifiers on the none/some/all Horn scale, to form most likely value, maximum and range diminish when a basis for Dutch research on scalar implicatures. We looking at a specific conceptual (e.g., ‘cars’) and/or enquired about the minimal, most likely and maximal value numerical population size (e.g., 83). The number of these of quantifiers (most,) some and a few, given a certain aspects that are found to be significantly different, grows population size (i.e. all). A more fine-grained methodology with the population size. (e.g., not only focusing on one population size) is important given the diversity of findings in the literature. This 209 approach paid off. Although the general picture is more or Geurts, B., & Pouscoulous, N. (2009). Embedded less straightforward, i.e. the parameter values for some are implicatures. Semantics and pragmatics, 2, 1-34. indeed higher than those for a few, our approach also Grice, H. P. (1989). Studies in the way of words. showed some important nuances. This general trend was not Cambridge, MA: Harvard University Press. significant for all population sizes. It seems that especially Guasti, M. T., Chierchia, G., Crain, S., Foppolo, F., with lower population sizes, differences between a few and Gualmini, A., & Meroni, I. (2005). Why children and some are less pronounced. Analogous to the partitive adults sometimes (but not always) compute implicatures. attribute of the French certains (Pouscoulous et al., 2007), Language and cognitive processes, 20, 667-696. some appears to be more scaled than a few, its numerical Horn, L. R. (1972). On the semantic properties of logical description more influenced by population size. Yet since operators in English. Doctoral dissertation, UCLA. we focused on numerical descriptors, additional research is Distributed by Indiana University Linguistics Club. indicated to provide further evidence for the semantic Janssens, L., & Schaeken, W. (2012). The role of task implications of the current findings. For instance, there is characteristics in children’s scalar implicature production. clearly a generalizability issue. 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