Borderline Contradictions with Polar Antonyms: An Experimental Study ´ e & J´er´emy Zehr Paul Egr´ (IJN, CNRS; UPenn) Summary. [1] found that speakers can describe borderline-tall men as neither tall nor not tall and tall and not tall (see also [5] who refers to such sentences as borderline contradictions). We conducted an experiment showing that such neither-descriptions are accepted more often than such and-descriptions. The contrast is maximal when not tall is replaced by the polar antonym short. Prima facie these results argue against [4]’s view of antonyms as contradictories, and in favor of a more traditional Gricean representation of antonyms as contraries [3]. However, a Krifkaian approach to antonyms remains compatible with our findings provided that the strengthening mechanisms that he posits can be applied locally. 1. Background. In a truth-value judgment task, [1] found that (1-a) and (1-b) were strongly rejected as descriptions of men of extreme heights, but were accepted respectively 53.9% and 44.7% of the time as descriptions of a man of average height. They did not report, however, whether this difference was significant nor included true controls for comparison. (1)

a. b.

This man is neither tall nor not tall. This man is tall and not tall.

Both the Horn-Gricean and the Krifkaian views of antonyms are compatible with the acceptance of (1-a), but they are at first sight incompatible with the acceptance of (1-b). Our study aims to assess the contrast between (1-a) and (1-b) and compare it with the contrast between (2-a) and (2-b): (2)

a. b.

This man is neither tall nor short. This man is tall and short.

2. Experimental Design. Drawing on one of [6]’s studies, we presented our participants with explicit descriptions of borderline cases for various pairs of antonyms and asked them to judge whether they could describe them with and-, neither- and true and false control descriptions, as illustrated in Fig. 1. Consider the scale of age. You have people whose age is very high, and people whose age is very low. Then there are people who lie in the middle between these two areas. Imagine that Sam is one of those people. Can you say the following? Sam is neither old nor not old Yes No

Yes No Sam is old and not old

Yes No Sam is not extremely old Figure 1: An item with syntactic antonyms and a control true description (bottom line). 80 participants were recruited via the Amazon Mechanical Turk platform and were divided into two groups: one group judged a first block of 8 successive descriptions with syntactic antonyms as illustrated in Fig. 1, and a second block with the polar versions of these antonyms, as shown in (2). Another group was presented with the same blocks in the opposite order. Each screen contained a true or a false control description, depending on the presence/absence of the negation. 3. Predictions. [3] and [4] posit distinct literal and strengthened meanings for antonyms, as illustrated in Fig. 2. They both predict the neither-descriptions to be accepted with the syntactic and the polar antonyms under a strengthened meaning. Neither predicts the acceptance of anddescriptions, but advocates of a Horn-Gricean approach might still expect a greater rejection with the polar antonyms than with the syntactic ones given that the literal extensions of the former define a gap but those of the latter do not. In contrast, Krifka’s literal extensions define no gap and therefore predict a similar rejection for all the and-descriptions.

Gap TallStrengthened Not Tall Gap Short Literal =⇒ Not Tall Gap Short Tall  Krifka’s approach Not Tall Figure 2: Horn-Gricean and Krifkaian accounts of antonyms. Short

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4. Results. 47 participants were excluded because of their participation in a previous experiment and because of low accuracy on the control items. We leave aside the discussion of a possible flaw in their design (all the subjects were consistent on the test items). Fig. (2) shows the answers of the 33 remaining participants (16+17). We observe a significant contrast between the and- and the neither-descriptions in every condition (Wilcoxon Signed Rank). The and-descriptions for the polar antonyms were accepted significantly more often when presented in the second block (Wilcoxon Rank Sum). When the polar antonyms were presented first, the subjects rejected the neither-descriptions significantly more often in the second block (Wilcoxon Signed Rank). 1.00

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Figure 3: Mean acceptance rates of each type of description. 5. Discussion. Focusing on the results for the first blocks, we note in particular that the rate of acceptance of the and-descriptions is at floor for the polar antonyms but increases with the syntactic antonyms (p < .5, Wilcoxon Rank Sum). This seems to argue in favor of a HornGricean view where polar (but not syntactic) antonyms define a gap at the literal level. However, both accounts require a mechanism to explain the acceptance of the and-descriptions with the syntactic antonyms. One possibility would be the existence of a covert operator mapping the literal extensions of the adjectives to their strengthened extensions as represented in Fig. 2 (see [2]). Embedding this operator under syntactic negation – as in the paraphrase “literally tall but not strictly tall” – would account for the acceptance of the and-descriptions with the syntactic antonyms in both views. But the fact that the and-descriptions were accepted even with the polar antonyms in the second block remains problematic. That in most conditions the antonyms in the second blocks tended to be interpreted as those in the first blocks regardless of the group might actually be seen as an argument in favor of Krifka’s view, where syntactic and polar antonyms are literal synonyms. References. [1] Alxatib S., Pelletier F. The Psychology of Vagueness. Mind & Language 26(3), 2011. [2] Cobreros P., Egr´e P., Ripley D., van Rooij R. Pragmatic Interpretations of Vague Expressions. JoPL, to appear. [3] Horn L. Toward a new taxonomy for pragmatic inference. Meaning, Form, and Use in Context, 1984. [4] Krifka M. Negated Antonyms: Creating and Filling the Gap. Presupposition and Implicature in Compositional Semantics, 2007. [5] Ripley D., Contradictions at the Borders, Vagueness in Communication, 2011. [6] Serchuk P., Hargreaves I., Zach R. Vagueness, Logic and Use: Four Experimental Studies on Vagueness, Mind & Language, 2011.