Elsevier

Journal of Pragmatics

Volume 189, February 2022, Pages 55-65
Journal of Pragmatics

The scalar interpretation of double negation

https://doi.org/10.1016/j.pragma.2021.12.013Get rights and content

Highlights

  • Double negation has logical and enriched interpretations.

  • A novel range-marking task allowed testing for the range of potential meanings.

  • 1st Empirical evidence for multifunctionality of double negation.

  • Different mitigation effects for double negation and hedges.

  • Context may affect the range of interpretation for double negation.

Abstract

The meaning of expressions modified by double negation (e.g., not unhappy or not not interesting) has long been discussed, with views advocating that the two negations must be logically interpreted (i.e., not unhappy means happy), and others arguing that the modified expression always yields a weaker version than the unmodified expression. The current study aimed to understand the possible interpretations of double negation experimentally. We used a novel range-marking task, allowing (Hebrew-speaking) participants to mark not only the location of a certain expression on the scale, but also the size it occupies. We collected measures of the range sizes, their location, as well as the inclusion of the edge of the scale. Doubly-negated adjectives were compared to unmodified adjectives and singly-negated adjectives, and adjectives modified by hedges, considering their mitigation effect. We were able to provide the first empirical evidence that double negation can be interpreted both logically and pragmatically. Additionally, we showed dissimilarities between double negations and hedges, suggesting that doubly-negated expressions present a stronger mitigation effect than hedges.

Introduction

Linguistic communication is a complex process, which requires varying levels of interpretation. Consider the sentence: “I am not unhappy”, and try to understand what the speaker meant to convey. Logically, this expression should be simply interpreted as happy. This idea is expressed in Frege's words (1919): “Clothing a thought in double negation does not alter its truth value.”. If, as Frege suggests, the meaning of adjectives modified by double negation is identical to their affirmative counterparts, a question is raised of why speakers expend an effort in using the more complex construction of two negatives to arrive at the result of the equivalent affirmative.

The continuous usage of double negation1 in both speech and written works (Horn, 2017), as well as intuitions of speakers, seems to suggest an enriched interpretation for doubly-negated adjectives, rather than a simple logical one. Jespersen (1924) follows this intuition by saying that “The two negatives…do not exactly cancel one another … the longer expression is always weaker …”. In other words, Jespersen argues that double negation is used for mitigation.

Indeed, several scholars have adopted this view, and now propose varied interpretations for double negation (e.g., logical interpretation, mitigation, and understatement; see Neuhaus, 2016 for a summary). Most scholars agree that both the logical and the enriched interpretations are possible, but propose different circumstances for each interpretation. The logical interpretation is more likely in cases of denial, where a speaker negates an already mentioned negated expression. For example, if the word unhappy is uttered, it may be denied using the expression not unhappy, to convey the logical meaning of happy (Van der Wouden, 1996; Krifka, 2007). This interpretation does not involve an inferential process, and is considered less effortful. As such, it is defined by Horn (1991) and Van der Wouden (1996) as the “unmarked” interpretation. In other cases, where the preceding context does not contain the negated adjective, the enriched interpretation of mitigation is more readily available. This interpretation is considered as the “standard” interpretation (Horn, 1989) or the most distinct meaning of double negation (Krifka, 2007).

How does the enriched interpretation come about? Horn (1989) reasons that the bare expression and its doubly-negated form cannot truly be identical. He, therefore, suggests that the use of the longer, marked expression with the two negatives (in lieu of the less effortful, unmarked, un-negated expression) leads to a q-based implicature, causing an enrichment effect intended by the speaker. He further assumes that double negation generates a middle area between two scalar terms of the same scale which defines a “neither-nor” area. Take for example the terms pretty and ugly. We can easily outline such an area for these terms, because an object can be neither pretty nor ugly. For contradictory terms, where the polar items are exclusive, double negation compels contrariety, creating an unexcluded middle. For example, animates can be either alive or dead with no clear “neither-nor” area (also termed “zone of indifference” by Sapir (1944)). The expression not not alive could force such an area, in attempt to describe a scenario where the animate is not completely alive (and not completely dead).

The matter of interpretation of doubly-negated adjectives by speakers has seen very little experimental work (Ruytenbeek et al., 2017; Schiller et al., 2017; Tessler and Franke, 2018). In these studies, participants were presented with several statements including character descriptions using an adjective (e.g., “Paul is tall”, in Ruytenbeek et al., 2017 or “William is not unhappy” in Tessler and Franke, 2018). The participants were asked to rate the degree to which the expression containing the adjective applied to the character on a scale between the adjective and its antonym (e.g., “tall” and “short” in Ruytenbeek et al., 2017, or “the most happy person” and “the most sad person” in Tessler and Franke, 2018). The participants ranked several types of phrase constructions, such as unmodified adjectives (e.g., happy), adverbially-negated adjectives (e.g., not happy), prefixal-negated adjectives (e.g., unhappy), and doubly-negated adjectives combining adverbial and prefixal negations (e.g., not unhappy). Ruytenbeek et al. (2017) showed that the mitigation effect of doubly-negated adjectives is stronger than that of singly-negated adjectives. Tessler and Franke (2018) further showed that the ordering of these expressions followed predictions made by Krifka (2007), according to whom doubly-negated adjectives would reside closer to unmodified adjectives compared to singly-negated adjectives.

The current study aims to expand on the matter of the interpretation of double negation using empirical tools. Previous experiments testing the meaning of scalar expressions, as described above, have used tasks that included location marking with discrete locations (or numbers) (e.g., Colston, 1999; Giora et al., 2005a; Paradis and Willners, 2006; Fraenkel and Schul, 2008; Ruytenbeek et al., 2017; Tessler and Franke, 2018; Mazzarella and Gotzner, 2021). Critically, this method is not able to fully capture the interpretation of scalar items. Specifically, discrete location marking ignores the possibility that an expression could allow for a wide-range interpretation. As such, this type of marking restricts the participants, and forces them to settle on a single interpretation (i.e., the doubly-negated expression must either be logical or mitigating to some degree).

To tackle this issue, we designed a novel range-marking task that allowed our participants to mark a range on the scale, rather than a single discrete point. This allowed us not only to examine the location of different expressions in relation to each other, as was done before, but also to measure the size of the range that each expression occupies on the scale. By marking a wide range on a scale, participants could specify the full range of interpretations that they allowed, rather than commit to a single interpretation of double negation. Therefore, our task allowed our participants to indicate some vagueness in their interpretations and possibly to reveal that they accept both the logical interpretation and the enriched one. In this fashion, range marking is better-suited for examining the scalar interpretation of double negation than a discrete location marking which forces the selection of a particular meaning.

Importantly, our range marking task also allowed our participants to include the edges of the scale in their marking (see Fig. 1). Including the relevant edge of the scale (e.g., including the edge happy for the expression not not happy) can clearly indicate that the logical interpretation of double negation is accepted. Thus, testing for edge inclusion could help us determine whether speakers accept both the logical interpretation and the enriched interpretation of double negation. In other words, the inclusion of edges for doubly-negated adjectives would indicate that speakers allow for the logical interpretation, and a wide range for these expressions (especially in comparison with the range size assigned to the affirmative expressions) would indicate that speakers allow for the enriched interpretation of mitigation.

Another important aspect in previous studies is the reference point for the doubly-negated expressions. Doubly-negated adjectives were compared with affirmative adjectives and/or negated adjectives. In this study, we propose hedges as another group of modifiers as reference to double negation (based on Krifka, 2007 among others). Hedges, such as sort of or pretty, are modifying phrases which adapt expressions to non-prototypical situations (Prince et al., 1982). They are considered to mitigate the meaning of the expressions they modified, by reducing the illocutionary force of the utterance (Caffi, 2007). For example, “A penguin is a sort of bird” is a weaker statement than “A penguin is a bird” (taken from Lakoff, 1975). Thus, hedges, similarly to double negation, are assumed to have an effect of mitigation. Additionally, hedges can provide a good comparison for double negation, because they too are considered to be scalar (Caffi, 2007). For these reasons, we included hedges in our experiment.

Importantly, Krifka (2007) notes the similarities between the interpretation of doubly-negated adjectives and that of adjectives modified by hedges. He suggests that in his examples doubly-negated expressions (such as not unhappy) could be replaced by hedges (such as rather happy, or quite happy) with no change in meaning. Based on this assumption, one should expect robust similarities between expressions modified by hedges and those modified by double negation. Notably, our range-marking task will enable a sensitive comparison of these two mitigators, because we collect several measures, including size, location and the inclusion of the logically-relevant edge (see more detail below). It is possible that certain hedges will overlap with double negation on some, but not all, of our intended measures.

We examined double negation in Hebrew speakers. Double negation in Hebrew can be simple, with two identical consecutive negatives, similar to the adverbial double negation in English (e.g., lo lo sameax in Hebrew, literally not not happy in English). A second structure in Hebrew is possible where two different negators are combined (e.g., lo bilti sameax; colloquially ‘not un-happy’). English too has two structures of double negation, adverbial and the combination of adverbial and prefixal negation. The combined form seems to be the most tested and discussed form of double negation. The usage of the two forms is distinguished by Horn (2017), who states that adverbial double negation appears in more predictable environments, usually primed by the affirmative or its negation (i.e., not not happy is likely to appear after hearing happy or not happy). Krifka (2007), on the other hand, includes only the combined form (e.g., not unhappy), and not the adverbial form (e.g., not not happy) in his analysis. Note that Hebrew does not have the combined adverbial and prefixal form (the equivalent of not unhappy). Moreover, the adverbial form, with the two consecutive identical negations, is natural for Hebrew speakers.

In Hebrew, both forms of double negation are adverbial, and the second structure mentioned above is not similar to the combination of adverbial and prefixal negation in English. Therefore, it is possible that they convey the same meaning (i.e., both allow for the logical and enriched interpretations). However, differences in the usage of the structures do exist: the double negation structure of lo bilti is restricted, it is not possible with all adjectives and can modify adjectives only. On the other hand, the double negation structure of lo lo is more productive, it can appear with any adjective, and can be used to modify nouns and verbs as well. In this vein, it seems prudent to determine if these potential differences in use and distribution also entail differences in interpretation.

All in all, this study addresses these three questions: (1) does double negation allow for both logical and enriched interpretations?; (2) does double negation function as a hedge?; and (3) do the two structures of double negations in Hebrew show differences in their interpretation?. As explained above, these questions were tested using a range marking task that allows for a sensitive measure of scalar interpretations. In addition to doubly-negated adjectives and adjectives modified by hedges, we included in our task also unmodified adjectives and singly-negated adjectives. These were included to address predictions made by Krifka (2007), according to which doubly-negated adjectives would reside below affirmatives on a scale, but above adverbially negated adjectives (such as not happy). It is important to note two aspects of Krifka's predictions that do not apply in our study. First, Krifka made his prediction regarding combined adverbial and prefixal negations (such as not unhappy), which do not occur in Hebrew, and did not include double adverbial negation (such as not not happy). Furthermore, these predictions concern unipolar scales, ranging from an adjective to its prefixal negation (i.e., from “happy” to “unhappy”). In the current experiment, because prefixal negation is impossible in Hebrew, we use bipolar scales, ranging from the adjective to its antonym. Single negations and unmodified adjectives were further used to determine the level of vagueness of doubly-negated expressions.

Section snippets

Participants

One hundred and thirty-one adults participated in the experiment (82 females, mean age = 25.7, range 18–47, SD = 5.1). Seven additional participants were excluded from the analysis due to illegible writing or failure to complete the questionnaire according to instructions. Sample size was determined based on Experiment 1 in Tessler and Franke (2018). Participants were recruited via Facebook, and on-campus ads. All of the participants provided written informed consent for taking part in the

Results

The average results of the three measures we collected in the range-marking task, per experimental form is given in Table 1 and visualized in Fig. 2. Statistical analysis was further conducted to determine the differences between the seven forms. Linear regression analyses were conducted for the measurements of size and location, and a logistic regression analysis was conducted for the measure of edge inclusion. We used the lmerTest package (Kuznetsova et al., 2017) in the R software

Discussion

This experiment focused on the possible interpretations of double negation. We conducted an experiment using a novel task, where participants used marked range on a scale rather than a discrete point to indicate their interpretations. We compared doubly-negated adjectives to affirmatives, singly-negated adjectives and adjectives modified by hedges, examining differences on 3 measures: size, location and inclusion of the logically-relevant edge. We selected these measures to be able to inform

Conclusion

In conclusion, our results show that double negations have a prominent mitigation effect, but that they allow for a logical interpretation as well. Further, we show that both double negations and hedges have a mitigating effect, but their interpretation differs. Specifically, we found that double negations are vaguer, possibly due to being well-suited for more states of affairs. Finally, it is worth noting that our study examined adjectival expressions sans context. Thus, the conclusions that

Declaration of competing interest

None.

Acknowledgement

This research was supported by the Israel Science Foundation grant (1824/17 to E.S.) and the Alon Fellowship (to E.S.). We are grateful to Nitzan Trainin, Hila Davidovich, Alon Fishman and Nicole Katzir for helpful discussions on this manuscript.

Yechezkel Shabanov is a PhD Student at the School of Philosophy, Linguistics and Science Studies at Tel Aviv University, Tel Aviv, Israel. His research concerns speaker and listener interaction, and multiple negation.

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    Yechezkel Shabanov is a PhD Student at the School of Philosophy, Linguistics and Science Studies at Tel Aviv University, Tel Aviv, Israel. His research concerns speaker and listener interaction, and multiple negation.

    Einat Shetreet is an assistant professor at the Linguistics Department and the Sagol School of Neuroscience at Tel Aviv University, Tel Aviv, Israel. She studies language comprehension, focusing on sentence and discourse level, using behavioral and neurocognitive methods. She heads the Cognition and Language Learning Lab which explores semantic and pragmatic processing in children and adults, both typically-developing and language-impaired.

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