Abstract
This study investigates the difference between more than n and at least n + 1. It is observed that these two quantifiers can generate different implicatures in intensional contexts due to their exhaustivity properties. Building on theoretical notions of argumentation in discourse, it is proposed that more than n, but not at least n + 1, is associated with positive argumenatative orientation (an attempt to convince the addressee of something). In a large-scale corpus investigation, more than n is shown to be associated with much larger numerical values than at least n (as well as other comparative quantifiers). Based on a qualitative investigation of the data, I propose that more than n is used more commonly to convey subjective positions that are being made more convincing by larger values of n, while at least n + 1 is used more commonly to convey objectively informative content. The quantifiers’ behavior in intensional contexts is explained as a combined effect of their respective argumentative orientation and the exhaustivity implicatures they generate.
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Notes
From the technical perspective, when a sample standard deviation renders most observations negligibly small, no statistical generalizations are usually possible. p values grow monotonically alongside variance, and therefore gargantuan variance leads to high \( p \) values even when sample means are truly different. Arguably, the abnormally high variance does not reflect the true variance of numerical expressions but rather the diversity of discourse domains. From the conceptual perspective, the argumentative impact of numerical values does not grow to scale with their numerical magnitude. Mentioning 5 million billion is not a million billion times more impressing than mentioning 5—it simply means you are probably talking about some scientific domain, like biology or physics. This problem is ameliorated by reducing numerical values to log space, since it bins all numbers into their respective orders of magnitude without losing the linear ordering. This makes comparison possible between numbers without creating unrealistic variance.
A shortcoming of the above model is that it treats all numerical expressions as being on the same scale. But arguably, comparison is usually made between numbers no more than one order of magnitude (oom) above or below each other. For example, in (35), in my judgment, the set of salient alternatives to the expression 35,000 is probably somewhere in the broad range of 1000–1,000,000, but probably not below or above this range. Therefore, an interesting question is whether comparatives differ in the magnitude of their arguments even after oom is taken into account. Presumably, the numbers within each 3-oom window correspond to the approximate range of alternatives perceived by speakers in discourse. So after accounting for the oom of a numerical expression, do comparative quantifiers still contain any information about its magnitude?
To answer this question, the model was rebuilt, but now the oom of each numerical value was subtracted from it. So for example, 3.16 was replaced with .16, and .16 remained .16. This new target variable represents the variation within each oom—the higher this variable is, the larger the number is within its respective oom. This setup thus controls for the variation in oom described above. The Aikaike Information Criterion (AIC) was then applied to the resulting model. The AIC uses the statistical equivalent of Occam’s Razor to test whether some variable in a model accounts for more variation than it inherently introduces by strengthening the model. The null hypothesis is that there is no interaction between comparatives and numerical values within an oom window. That is, all variation is explained by the oom of the number and none is due to the comparative following it (or lack thereof). The alternative hypothesis is that a comparative does correlate with higher/lower numerical values within the same oom. If the alternative hypothesis is true, then the coefficient for that comparative is very unlikely to be removed by the AIC.
In the new model, all coefficients remained significant and none was removed by the AIC, with the exception of the coefficient for AM.
Defined as: \( p \cdot \surd p\left( {1 - p} \right) \), where \( p \) is the proportion of numbers satisfying a rounding expression. The observed proportion \( p \) is multiplied by its binomial standard deviation \( \surd p\left( {1 - p} \right) \) to account for sampling variance, as when computing \( t \) -values.
For the same reason, for \( (m/2) \cdot 10^{n} \), 9 was replaced by 18, and for \( 10^{n} \), 9 was replaced by 1.
However, recall that the coefficient for AM did not survive the AIC in the model described in footnote 2, and the difference of the means for AM and LT was not significant. This is likely due to the relatively small number of observations for AM, and so these results warrant further research. The fact that AM is so infrequent in COCA relative to its alternative LT suggests that AM is dispreferred due to markedness considerations. Therefore, some of the semantic effects observed involving AM might be a result of its markedness rather than AO or lack thereof.
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The code and data for this paper are available in the following repository: https://github.com/Omerkorat/comparatives.
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Korat, O. Comparing Comparatives: The Argumentative Force of Comparative Quantifiers. Corpus Pragmatics 2, 399–423 (2018). https://doi.org/10.1007/s41701-018-0042-2
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DOI: https://doi.org/10.1007/s41701-018-0042-2