Horn scales are a popular vehicle in the investigation of implicatures. Yet even this most user-friendly of implicature research categories is plagued by methodological and extrapolating difficulties. One of these difficulties is the possible existence of pungent semantic discrepancies that get lost in translation. To form a basis for past and future Dutch scalar implicature research, we investigated the popular quantifier 'some'. In an experiment we registered different elements that make up its numerical description (i.e. minimal, most likely and maximal value) and compared them to those of other quantifiers from its Horn scale. The experiment showed that the parameter values for some are overall higher than those for a few. A scaling effect on some, however, appears to blur some's discrepancies with a few for lower population sizes.
Communication consists of a process where: a sender
encodes his or her message into language, transmits the
message through a certain medium or channel (e.g., speech),
and a receiver decodes and interprets the meaning of that
message
(1) (2)
It is nice to meet you.
Such information is not explicitly mentioned, though vital
for proper communication. It is part of the conventions that
make language more compact and manageable. It is not
practical and opportune to repeat all this information with
every conveyed message: due to its sheer magnitude, and
because human beings tend to think faster than they can
articulate
(3)
Conversational Implicatures, on the other hand, cannot be
derived from such a secluded inspection of a sentence.
Looking back at (1), the pragmatic meaning of “Could you
crack a window” is part of linguistic convention, i.e. a
Conventional Implicature. The reason for this request could
only be detected from conversational cues (e.g., body
language indicating feeling cold), i.e. a Conversational
Implicature. While Conventional Implicatures rely on
convention, Conversational Implicatures depend on certain
rules of conversation known as Grice’s four maxims
And appropriately delivered (Maxim of Manner) to avoid for example ambiguity.
Example (2) is informative if the correct intensity is phrased (i.e., nice, not great or OK), truthful if the speaker means it, relevant if said at an introduction, and appropriately delivered if spoken with a sincere demeanor. These four conditions being met, the listener may make the presumed correct pragmatic inference that the speaker indeed finds it nice to meet them (in this case being the same as the linguistic message). If, for example, the delivery was in a sarcastic tone, a different pragmatic meaning might be assigned to the message.
Conversational Implicatures can be subdivided into Generalized Conversational Implicatures and Particularized Conversational Implicatures. The difference between the two boils down to the level in which they depend on contextual factors. Particularized Conversational Implicatures are particular to a specific conversation. In (4), Tom’s utterance may hold an implied message, a pragmatic meaning that Amy mistook Paul’s tiredness for looking unsatisfied. This implicature cannot be drawn from Tom’s utterance itself, only from the broader conversational context. If Tom had said: “He was tired.” in response to a different question, for example: “Why did the hare take a nap midrace?”, the aforementioned implicature would not have been part of the pragmatic meaning of his message. (4)
Tom: “He was tired.”
Generalized Conversational Implicatures, such as in (2), can
be derived from the message itself (including delivery and
body language). A specific type of Generalized
Conversational Implicatures is Scalar Implicatures.
Implicatures of the scalar kind are relatively clear-cut and
lenient to manipulation, with a relatively low chance at
confounding variables. Conventional Implicatures are
conceptually more difficult to discern from the linguistic
meaning of messages than Conversational Implicatures are,
and Particular Conversational Implicatures’ higher
dependence on context factors makes them a lot harder to
control compared to Generalized Conversational
Implicatures. Of this latter category, Scalar Implicatures are
the best known and most explored. Therefore this scalar
type of implicatures is a welcome and often preferred
subject of research. Previous research shows for example
that making a pragmatic inference is not the default
behavior, even though certain scalar inferences are found to
be made in high percentages of cases (e.g., cf. Table 1).
Children tend to interpret messages more as their linguistic
meaning than as their pragmatic meaning
These findings are not only valuable in exploring the
inner workings of implicature processing, they also have
repercussions for the paradigms used in research on scalar
inferences. Several methodological features influence the
frequency of implicature generation. Next to
aforementioned effect of task structure (e.g., dual task
paradigm with adults), and salience of the goal of the task
(seven-year-olds), in younger children (five- but not
sevenyear-olds) the type of task is paramount. Action-Based
Tasks, for example, stimulate far more production of scalar
inferences in five-year-olds than Truth-Value Judgement
Tasks do
The scales used in scalar implicatures are called Horn
scales, named after Laurence R. Horn who first introduced
them
It is even ill-advised to casually compare results of
different studies if they did not implement the same Horn
scale. Let us consider for example: Noveck (2001, Exp. 1)
who registered implicatures for 65% of participants on the
might/must scale,
The or/and scale, with aforementioned result of 54%
In order to gain some uniformity between studies, despite experimental differences between their paradigms, critical quantifiers in studies should be identified on a uniform measure. For existential quantifiers, we suggest using worldly categories with fixed population counts. Some/all could for example be expressed as there being 83 cars (i.e. all = 83) at a certain location, and participants could be asked to define ‘some’ as an amount of those cars. The current study looks into such a numerical definition for the quantification pair some/all.
This study aims to be a starting point for that semantical
comparison between sommige (to improve readability, from
here on identified as ‘some’) and enkele (henceforth ‘a
few’). We will look into their numerical description, i.e. a
numerical expression of their position on the none/some/all
Horn scale used in implicature studies. In a renowned Dutch
dictionary
We will enquire about the preferred value, i.c. the most
likely amount the quantifiers indicate given a certain
population size. As elaboration on this numerical estimate,
the minimal and maximal value the quantifier could
represent are requested as well, for several population sizes
and categories. As a control for our method, the quantifier
‘most’ will be added to the inquiry: most is likely to be
considered a more informative quantifier (i.e. representing a
higher amount) than a few and some. The partitive attribute
of most is also clearer than that of a few or some: most is
named after indicating over half of the population. This
partitive feature is not the core of the current study, but
given its proclaimed central role in the semantic difference
between the French analogues quelques and certains
216 first-year bachelor students in psychology participated in partial fulfilment of course requirements (17-28 years of age, M = 18.5; female: 168, male: 48). All participants were native Dutch speakers.
Each participant was presented a pen-and-paper questionnaire in Dutch. It consisted of three items. They were constructed in the same general fashion.
The instructions for each item started off with: 'Imagine that at a certain location there are <amount> <category>.' The first item spoke of 1019 flowers, the second item regarded 10 chairs and the third item 83 cars. The amounts and categories were matched so that they would make sense, so that participants might be able to envision in a lifelike situation for them. In Belgium it is a tradition in certain folk festivals to display a huge flower tapestry on the floor of a big square. Such a scene, or for example a vast meadow, might feature a flower count of 1019. 10 chairs is an amount that one might imagine around a large living room table. And 83 cars might summon the mental picture of a large parking lot. The amounts were presented in a non-linear sequence, to make it harder for participants to extrapolate their previous answer to the next item.
The instructions continued with: <Name> says: "<Quantifier> <category> are <color>." The quantifier was 'A few', 'Some' or 'Most'. In the first item, it read: Jan says: "<Quantifier> flowers are red.", in the second item: 'Mieke says: "<Quantifier> chairs are brown.", and in the third: Ingrid says: "<Quantifier> cars are green." Following the statement, the items featured the same three questions: a. If this utterance of <Name> is appropriate, how many <color> <category> are there minimally at that location? b. If this utterance of <Name> is appropriate, how many <color> <category> are there maximally at that location? c. If this utterance of <Name> is appropriate, what is the most likely amount of <color> <category> at that location?' The participants filled in the questionnaire with the three items, covering the three amounts and categories (i.e. resp. 1019 flowers, 10 chairs and 83 cars). Each item of a questionnaire regarded the same quantifier, resulting in three between-subjects conditions: A Few, Some and Most. The conditions only differed in which quantifier was presented in the statements. For Condition Some, for example, the statements read: (1) Jan says: "Some flowers are red." (2) Mieke says: "Some chairs are brown." (3) Ingrid says: "Some cars are green."
Four participants did not answer every question (with a numeric amount), one participant answered every question with the population size and 22 participants reported a most likely value outside their reported [min;max] zone. Therefore they were excluded from further analyses. Two participants responded on certain questions with two adjacent amounts (e.g., '7 or 8'), for those answers we used the average of the two amounts (i.c., 7.5). All of the remaining 189 participants (i.e. 62 in Condition A Few, 66 in Some and 61 in Most) reported minimal values lower than the reported maximal values.
The Most condition was included as a test of the protocol we used. The semantic meaning of most is captured in its name, and in this protocol indicates ‘more than half’. 154 out of 183 (84%) minimal values for most were indeed higher than half of the population size. The minimal values that were lower than expected might be explained by the comment of a few participants that the number of subgroups in the population is unknown. They seem to have interpreted most as indicating ‘the largest of all subgroups’ (e.g., “Most flowers are red.” interpreted as: “There are more red than any other color flowers.”), which might have a size lower than half of the total population if there are more than two subgroups. This alternative interpretation does not interfere with our current basic investigation of the numerical description of some and a few, yet it could be subject to future, more in-depth research.
Table 1 summarizes the different conditions. All numbers are scaled to 100, in order to make comparisons between the different population values easier. In this view on the mean numbers, some seems to be described with higher values than a few and most features higher mean values than the other two quantifiers.
We tested the differences between the three conditions with the non-parametric Mann-Whitney U on the data scaled to 100. In looking at all population categories together, some is indeed seen as significantly higher than a few: in its minimal value (U = 16169.50, p = .02), in its most likely value (U = 15791.50, p = .008) and its maximum (U = 15430.00, p = .003). The values of most are significantly higher than those of a few (resp. U = 776.50, 758.00 and 6638.00, all with p < .001) and of some (resp. U = 1199.00, 685.5 and 7944.50, all with p < .001). The range (i.e. maximum minus minimum) of some is also broader than that of a few (16426,00, p = .03), and the range of most is broader than that of both a few (U = 14588.50, p < .001) and some (U = 12738.50, p < .001).
At the population level the results tell a more nuanced story (see Table 2). In each case some still produces higher values than a few, yet only in three cases these differences remain significant: the most likely value in the population category of 83 cars, and the most likely value and maximum in 1019 flowers. The difference in maximal value borders significance in the population category of 83 cars, as well as the minimal value and the range in 1019 flowers. The differences in numerical interpretation between some and a few appear to be bound by certain contextual factors such as population size. Not only do discrepancies in minimum, most likely value, maximum and range diminish when looking at a specific conceptual (e.g., ‘cars’) and/or numerical population size (e.g., 83). The number of these aspects that are found to be significantly different, grows with the population size. At the population level the results tell a more nuanced story (cf. Table 2). In each case some still produces higher values than a few, yet only in three cases these differences remain significant: the most likely value in the population category of 83 cars, and the most likely value and maximum in 1019 flowers. The difference in maximal value borders significance in the population category of 83 cars, as well as the minimal value and the range in 1019 flowers. The differences in numerical interpretation between some and a few appear to be bound by certain contextual factors such as population size. Not only do discrepancies in minimum, most likely value, maximum and range diminish when looking at a specific conceptual (e.g., ‘cars’) and/or numerical population size (e.g., 83). The number of these aspects that are found to be significantly different, grows with the population size.
We hypothesized that some is more partitive, more scaled to the population size than a few. In this case, some should exhibit lower differences between population sizes (i.e. in the data scaled to 100). Within subjects, per description category (e.g., the minimum) we computed a variable D; e.g., Dmin = (carsmin – chairsmin)² + (flowersmin – carsmin)² + (flowersmin – chairsmin)². A lower value for D means that the data is more scaled, i.e. that the numerical description of the quantifier in question is more influenced by population size. The results show that some is significantly more scaled than a few in its minimum (U = 1668.00, p = .04) and its most likely value (U = 1545.50, p = .009). Its maximum is also more scaled, yet to a degree that only borders significance (U = 1743.00, p = .07). Overall we can conclude that the numerical description of some is more dependent on population size than that of a few.
The current study looks into a numerical description for
several quantifiers on the none/some/all Horn scale, to form
a basis for Dutch research on scalar implicatures. We
enquired about the minimal, most likely and maximal value
of quantifiers (most,) some and a few, given a certain
population size (i.e. all). A more fine-grained methodology
(e.g., not only focusing on one population size) is important
given the diversity of findings in the literature. This
approach paid off. Although the general picture is more or
less straightforward, i.e. the parameter values for some are
indeed higher than those for a few, our approach also
showed some important nuances. This general trend was not
significant for all population sizes. It seems that especially
with lower population sizes, differences between a few and
some are less pronounced. Analogous to the partitive
attribute of the French certains
This research was carried out with the financial support of the National Council for Scientific Research – Flanders, Belgium (FWO grant G.0634.09).