1.1 Scale structure

Exclusives can impose different orderings on the alternatives they exclude. (3) can be interpreted exhaustively, as conveying that the student possesses absolutely no relevant properties other than intelligent (3a). Following Coppock & Beaver (2014), we’ll call this the complement-exclusion reading. (3) can also be interpreted as only excluding alternatives ordered higher than the prejacent along some pragmatically determined dimension (3b). We’ll call this the rank-order reading.

These readings can be given a uniform semantic analysis (Bonomi & Casalegno 1993; van Rooij 2002; Klinedinst 2005; Beaver & Clark 2008; Coppock & Beaver 2014). For example, Coppock & Beaver (2014) propose a unified typology of exclusives using two operators min and max. The presuppositional content of exclusives is specified in terms of min, and the assertive content is specified in terms of max. min and max apply to the prejacent and an ordered set of alternatives, which are modeled as answers to the current Question Under Discussion (CQ). Following Beaver & Clark’s (2008) implementation of QUDs as ordered sets of propositions, or “scales”, the ordering relation ≥ is retrievable from the CQ. min contributes existential quantification over the alternatives: some alternative ranked at least as high as the prejacent is true (4a). max contributes universal quantification: the prejacent is ranked at least as high as all true alternatives. The inference that the prejacent itself is true results from the combined effect of min and max.

Different readings (e.g., (3a) vs. (3b)) result from variation in the ordering relation and the structure of the alternative set (Coppock & Beaver 2014). Complement-exclusion scales can be represented as a semilattice closed under conjunction (5), in which the higher-ranked alternatives entail the lower ones. In (5), the prejacent is The student is intelligent (abbreviated as intelligent). Application of max excludes all alternatives that are not ranked lower than the prejacent, resulting in the reading that the student is intelligent and has no other relevant properties. We indicate this in (5) by bolding the prejacent and crossing out the excluded alternatives.

Rank-order scales impose an ordering on atomic alternatives (6). We consider Horn scales like <clever, intelligent, brilliant> paradigmatic examples of rank-order scales, as they involve atomic alternatives that stand in an entailment relation. However, since rank-order scales are not closed under conjunction and lack the semilattice structure of (5), the alternatives can also be logically independent or mutually exclusive (e.g., <assistant professor, associate professor, full professor>), and can in principle be ordered by a wider range of relations. In this paper we will mostly focus on Horn scales.

Different exclusives are compatible with differently structured scales, but there is debate as to how freely exclusives actually vary in this regard. Horn (2000) argues from data involving projection (7) that only sentences presuppose the prejacent itself, while just sentences presuppose a lower bound on the prejacent. Since the only sentences presuppose the prejacent, it projects under negation, which leads to oddness when the alternatives are mutually exclusive. By contrast, no oddness is perceived with the just sentences.

Translated into Coppock & Beaver’s (2014) scalar framework, Horn’s argument amounts to the claim that only selects for complement-exclusion scales and just selects for rank-order scales. Since stronger alternatives on a complement-exclusion scale entail the prejacent, negating the exclusive content preserves the inference to the prejacent. With rank-order scales, the alternatives do not need to stand in an entailment relation, so the inference to the prejacent can disappear under negation.

The generalization that only selects for complement-exclusion and just for rank-order scales might be too strong: some speakers can access the rank-order reading with only in examples like (7). Coppock & Beaver reinterpret the contrast between just and only in (7) as indicating that exclusives have weaker pragmatic preferences for different scales: “only prefers entailment scales [i.e., complement-exclusion scales] and just has a slight preference for non-entailment scales [i.e., rank-order scales]” (Coppock & Beaver 2014: p. 425), without committing to a pragmatic analysis of what these preferences are or what factors influence them. The authors analyze merely as selecting an “evaluative” rank-order scale whose alternatives are ordered according to what the speaker considers good or bad. This is motivated by examples like (8), in which the higher-ranked alternatives are considered “better” (for further discussion of evaluativity effects with merely, see Wiegand, 2018; Windhearn, 2021; as well as Orenstein & Greenberg, 2010 on the Hebrew exclusive stam).

The goal of both experiments in this paper is to provide a quantitative experimental assessment of these claimed pragmatic preferences in scale structure.

1.2 Strength of exclusion

No theory of exclusives modeled after Horn’s (1969) analysis of only, Coppock & Beaver’s min/max entry schema included, can straightforwardly account for the just examples in (9). As the paraphrases show, these examples do not obviously communicate the exclusion of alternatives in the same way as the examples in (1).

One way that prior literature has accounted for such uses of just is by positing that it differs from other exclusives in (what we refer to as) its strength of exclusion. For example, Warstadt (2020) proposes an entry for just that differs from only and other exclusive modifiers in two places. First, just excludes answers to “potential” questions, or “intuitively possible future QUDs” (p. 373, see also Onea 2016), rather than the current QUD. Second and crucially for our purposes, Warstadt argues that a unified account of just’s various readings requires relaxing the truth-conditional status of the exclusive operation. He proposes a distinction between “strong” exclusives which declare alternative propositions false, and “weak” exclusives which declare them unassertable.¹

On Warstadt’s analysis, the semantic contribution of just in, e.g., (9b) is as follows. A speaker who asserts that the lights turn off and on might anticipate the addressee asking why this is. Just marks the answers to this potential question as unassertable, before the addressee can ask why, “thus preventing the addressee from asking a useless question” (Warstadt 2020: p. 373). However, just can also target the current QUD. In this case, the claim that other alternative answers are unassertable, together with the presupposed truth of the prejacent, leads to a meaning very similar to what a canonical exclusive entry would have delivered, the primary difference being one of strength: a speaker who uses just is refusing to commit to either the truth or falsity of alternatives, unlike a speaker who uses only to mark alternatives as false. Warstadt analyzes the full range of just’s readings as involving this weaker exclusive operation—in contrast with only, which Warstadt analyzes as a strong exclusive.

Other accounts of non-canonical readings with just have posited other sources of variation in the set of alternatives just can operate on, suggesting that it can target: covert modifiers with trivial semantic content (Wiegand 2018; Windhearn 2021), alternative scale granularities (Thomas & Deo 2020), or metalinguistic alternatives at the speech act level (Beltrama 2021).

Altogether, whether an exclusive is weak or strong arises as a subtle pragmatic effect. Experiment 1 therefore tests just’s claimed “weakness”, or more generally, the possibility that it allows for non-canonically exclusive readings.

1.3 Scalar diversity

Our testing ground in this paper is pairs of lexical items that form a scale. More specifically, we turn to the scalar diversity phenomenon: the observation that scalar expressions vary in how likely they are to lead to scalar implicature (SI) (i.a. van Tiel et al. 2016; Gotzner et al. 2018; Sun et al. 2018). A classic example of SI is (10): upon encountering an utterance containing some, hearers compute the negation of its stronger scalar alternative all (Grice 1967; Horn 1972).

Similarly to <some, all>, e.g. <intelligent, brilliant> also forms a scale: an utterance containing intelligent can lead to the SI not brilliant (11). But variation exists across different scales: the SI in (10) arises much more robustly than the one in (11).

Scalar diversity persists even in the presence of exclusives. Ronai & Xiang (2024) found that even when sentences such as (10)–(11) contain only, variation still remains in the likelihood of deriving a not all or not brilliant inference. This is puzzling, since while SI is a cancellable pragmatic inference, only encodes alternative exclusion in the semantics—which would predict uniformly ceiling-level inference rates. Ronai & Xiang hypothesized that interpretations of only were split between rank-order and complement-exclusion readings, leading to variation in whether the stronger scalar term was included in the alternative set. Given The student is only intelligent, the not brilliant inference would arise with rank-order only, but not necessarily with complement-exclusion only, which could be understood as excluding other unrelated properties (not curious, not charming, etc). By experimentally comparing only to other exclusives, potentially less flexible in scale structure preference, we will also be able to test Ronai & Xiang’s hypothesis.

As mentioned, although Horn scales like <some, all> and <intelligent, brilliant> stand in an entailment relation, we class these as rank-order scales because the structure of the alternative set does not bottom out in logically independent “atomic” propositions; that is, the scale structure is as in (6), not (5). Throughout this paper we use the terms “complement-exclusion” and “rank-order” to characterize scale structure rather than the precise relations used to order alternatives.

2.1 Participants

120 monolingual native speakers of American English participated in the experiment (40 in each of the between-participants conditions), which was administered on the web-based PCIbex platform (Zehr & Schwarz 2018). Participants were recruited on Prolific and compensated $2. Native speaker status was established via a language background questionnaire, where payment was not conditioned on the participant’s response. Participants were excluded for making more than 3 mistakes on the 7 attention check items. After exclusions, data from 111 participants was analyzed (37 for only, 39 for just, and 35 for merely.)

2.2 Materials and procedure

The experiment used a two-alternative forced choice inference task, identical to Ronai & Xiang’s experiments (see also i.a. van Tiel et al. 2016). On each trial, participants saw a target sentence uttered by Mary, which contained an exclusive (e.g., The student is {just/only/merely} intelligent), and they were asked whether Mary thinks that the rank-order alternative is not true (e.g., the student is not brilliant). Figure 1 shows an example with just. Here, a “Yes” response indexes that the participant has calculated the exclusionary (not brilliant) inference, while selecting “No” suggests that the inference was not calculated. The experiment tested three different exclusives—only, just, and merely—as a between-participants manipulation.

Figure 1

Example experimental trial from Experiment 1 (just condition).

We tested 51 lexical scales as critical items, a subset of those used by Ronai & Xiang (2024). Of their 60 items, we removed those incompatible with just or merely. This amounted to removing a subset of the adverbial scales, e.g., <mostly, entirely> (#Peter’s answers were merely [mostly]_F wrong.); <primarily, exclusively> (#The residents are merely [primarily]_F Greek.); or <probably, necessarily> (#A delay will merely [probably]_F occur.). An additional modification was made to the verbal scales in the just condition: wherever a temporal interpretation of just would have been possible, we modified the tense of the carrier sentence to rule this out. For example, for <survive, thrive>, The plant only/merely survived was changed to The plant is just surviving. Similarly, for <reduce, eliminate>, The city only/merely reduced waste was modified to The city will just reduce waste.²

In addition to the critical items, the experiment tested 7 fillers that served as attention checks. The fillers, adapted from Ronai & Xiang (2024) and van Tiel et al. (2016), contained two antonyms (wide → not narrow) and therefore had an unambiguous “Yes” answer. The experiment began with 2 practice items.

2.3 Results

Figure 2 shows the results of Experiment 1. For the statistical analysis, we fit a logistic mixed effects regression model using the lme4 package in R (Bates et al. 2015). The model predicted Response (“Yes” vs. “No”) as a function of Exclusive (just vs. only vs. merely). Random intercepts for participants and random slopes and intercepts for items were included. Since predictions were made for just vs. only (strength of exclusion) and merely vs. only (scale structure bias), the predictor Exclusive was treatment coded, with only coded as the reference level. The model revealed significantly lower rates of inference calculation with just compared to only (Estimate = –0.63, SE = 0.27, z = –2.33, p < 0.05), as well as significantly higher rates with merely than with only (Estimate = 1, SE = 0.3, z = 3.4, p < 0.001). Averaged over the 51 different scales, the target exclusionary inference was calculated at the rate of 52.9% with just, 63.2% with only, and 80.2% with merely.

Figure 2

Results of Experiment 1: just, only, merely. The y axis shows the percent of calculating the target exclusionary inference, i.e., the mean percent of “Yes” responses in the inference task. Error bars represent standard error.

Since inference rates were lowest with just, the question may arise whether it can be maintained that just excludes alternatives semantically. To test this, we also conducted a replication of Ronai & Xiang’s (2024) SI experiment.³ We found an average rate of 34.3% SI calculation; Figure 3 shows the SI results together with the three exclusives, also visualizing the by-item variation. An additional statistical model compared the findings of this experiment to just. The fixed effects predictor was sum-coded (SI: –0.5 and just: 0.5). Inference rates were found to be significantly higher with just than in the case of SI (Estimate = 1.29, SE = 0.27, z = 4.8, p < 0.001). This confirms that alternative exclusion with all three exclusive modifiers is stronger than alternative exclusion via SI.

Figure 3

Results of Experiment 1: SI, just, only, merely. The percent of exclusionary inference calculation corresponds to the percent of “Yes” responses in the inference task.

One may wonder whether different lexical scales interact differently with the two tested parameters of variation, scale structure bias and strength of exclusion. In order to check whether the relative order of the 51 items remained consistent across manipulations, we calculated rank-order correlations using Kendall’s τ_B, and found significant by-item correlations between conditions. As SI rates increase, so do inference rates with just (τ _B = 0.67, p < 0.001); as rates with just increase, so do rates with only (τ_B = 0.64, p < 0.001); and rates with merely are also correlated with only (τ_B = 0.39, p < 0.001).⁴ In other words, we found that items that lead to low SI rates also lead to relatively low rates of inference calculation with exclusives, even as the overall rate of inference calculation goes up with an exclusive as compared to SI. To give an example, <small, tiny> led to SIs at a rate of 7.9%, and with exclusives, it also continued to trigger inference calculation at a rate lower than the average for that exclusive: 23.1% with just, 43.2% with only and 61.1% with merely.

2.4 Discussion

Both predictions made by the relevant theoretical accounts regarding strength of exclusion and scale structure bias were borne out by the results. First, Experiment 1 found lower rates of exclusionary inference calculation—that is, lower rates of “Yes” responses in the inference task—with just than with only. This is consistent with Warstadt’s (2020) proposal that just is a weak exclusive, while only is a strong exclusive. Or alternatively and more generally, this finding confirms that just is not always canonically exclusive; if (some) participants accessed a non-exclusive reading, that could have lowered the overall observed rate of exclusion. Second, Experiment 1 found higher inference rates with merely than with only. Since all our items tested rank-order alternatives, this strongly supports Coppock & Beaver’s (2014) claim that while only allows both complement-exclusion and rank-order readings, merely prefers rank-order ones. These results also support Ronai & Xiang’s (2024) hypothesis that when interpreting target sentences with only, participants are split between rank-order and complement-exclusion readings. When a rank-order bias is introduced by merely, the stronger scalar term in the “Would you conclude from this…?” task question is more unambiguously understood as one of the salient alternatives, which leads to an increase in calculating the target inference.

While we have found evidence that only and merely differ in scale structure, with the latter more strongly requiring rank-order alternatives, Experiment 1 does not allow us to straightforwardly infer anything about the (potential) scale structure bias of just. Coppock & Beaver (2014) argue that, like merely, just also has a(n albeit weaker) preference for rank-order readings (p. 425, see also Horn 2000). This would predict a higher rate of inference calculation with just, as compared to only. However, just’s comparatively weak strength of exclusion pushes in the other direction, which as we have seen has resulted in overall lower inference rates. Therefore, the current results leave open two possibilities: either just does not favor rank-order scales, contra the theoretical literature, or it does, but that preference in the Experiment 1 design was counteracted by its weak exclusive status. Experiment 2 was designed to adjudicate between these two possibilities.

3.1 Participants

120 monolingual native speakers of American English participated in the experiment (40 in each of the between-participants conditions), administered on PCIbex. Participant recruitment and screening was identical to Experiment 1; compensation was $2 or $2.40 depending on time. 5 participants were removed from the merely condition and 1 participant from the just condition for making 3 or more mistakes on the 5 attention check items. Data from the remaining 114 participants is reported below.

3.2 Materials and procedure

Experiment 2 ruled out a non-exclusive interpretation by employing a two-alternative forced choice task where participants had to choose between two alternatives as the target for exclusion. Specifically, they were presented with a target utterance by Mary, e.g., That student was just intelligent, which was followed by “Mary meant that the student was not BLANK”. Participants had to choose between a rank-order and a complement-exclusion alternative to fill in the blank.⁵ Figure 4 shows an example trial with just.

Figure 4

Example experimental trial from Experiment 2 (just condition).

Target inference-triggering sentences occurred in the context of Sue’s preceding utterance. The context provided by Sue always explicitly introduced alternatives, including the focus associate (here, intelligent), the rank-order alternative (brilliant), the complement-exclusion alternative (ambitious), and a fourth alternative (hardworking) that was not probed in the forced choice task. Our task was designed to make both the rank-order and complement-exclusion alternatives salient and relevant, with the expectation that with salience and relevance controlled for, participants’ responses would directly reflect the scale structure bias contributed by different exclusives.

This design choice was inspired by previous experimental studies on the processing of focus with only, which have successfully used discourse contexts to introduce relevant alternatives. (12) illustrates this with an example from Hoeks (2023)—see also Washburn et al. (2011); Kim et al. (2015); Fraundorf et al. (2010) for similar designs.

Inherent to the goals of our experiment is that the context sentence uttered by Sue would have to introduce two alternatives that are ranked relative to one another (intelligent and brilliant in Figure 4), in addition to an alternative that is not inherently related to either (i.e., the complement-exclusion one, ambitious in Figure 4). In order to mitigate against potential unnaturalness arising from this design, we took the following steps. First, as mentioned, a fourth alternative which can be classified as complement-exclusion (hardworking in Figure 4) was also included, in order to make sure that the target complement-exclusion alternative (ambitious) was not overly salient as being the exception. Second, to ensure a natural reading experience throughout the experiment and to prevent participants from noticing ordering patterns, the order of the four alternatives was randomized on every trial. Analysis of the Experiment 2 data suggests that the design did not introduce a bias towards one kind of alternative as compared to Experiment 1 (see footnote 6).

The basic frame of the inference-triggering sentences was kept similar to Experiment 1 (and Ronai & Xiang 2024). The focus associates (i.e., weaker scalar terms embedded under an exclusive) and rank-order alternatives were identical to Experiment 1. Complement-exclusion alternatives were generated for each item, using corpus searching (for strings such as only X but not Y, with X as the focus associate) and the intuitions of the authors. The fourth alternative was similarly generated by author intuition.

Experiment 2 tested 48 items. 3 items were removed from the item set of Experiment 1 because we were unable to generate a suitable complement-exclusion alternative (<some, all>, <or, and>, <once, twice>). We also included 3 practice items and 5 fillers to serve as catch trials. In filler items, one of the two forced-choice alternatives was the focus associate itself (e.g., The street is just wide—Mary meant that the street is not: wide vs. tree-lined) and hence unambiguously the incorrect choice.

3.3 Results

Figure 5 shows the results of Experiment 2. Averaged over the 48 different scales, the rank-order alternative (as opposed to the complement-exclusion alternative) was chosen 56.8% of the time with only,⁶ 65.6% with just, and 80.8% with merely. For the statistical analysis, a logistic mixed effects regression model was fit (lme4). We compared Response (rank-order vs. complement-exclusion choice) for each exclusive to chance, i.e., to 50% rank-order/complement-exclusion choice. Chance level reflects the hypothetical whereby an exclusive has no constraints on its scale structure, and freely allows either type of alternative to be excluded; in this case, we assume participants would choose one over the other with 50% likelihood. The model included random intercepts for participants and random slopes and intercepts for items. We found that just (Estimate = 0.98, SE = 0.26, z = 3.78, p < 0.001) and merely (Estimate = 2.01, SE = 0.26, z = 7.88, p < 0.001) differed significantly from chance level by producing a higher rate of rank-order choice. On the other hand, results with only did not significantly differ from chance (Estimate = 0.44, SE = 0.27, z = 1.65, p = 0.1).

Figure 5

Results of Experiment 2: Mean percent of choosing rank-order (as opposed to complement-exclusion) alternative with only vs. just vs. merely. Error bars represent standard error.

In order to directly compare the behavior of the three different exclusives to one another, we fit an additional model that predicted Response (rank-order vs. complement-exclusion choice) as a function of Exclusive (just vs. only vs. merely). Here, the Exclusive predictor was treatment-coded, with just serving as the reference level. We found that merely produced significantly higher rates of rank-order choice than just (Estimate = 1.03, SE = 0.32, z = 3.21, p < 0.01). The only vs. just difference (i.e., only producing fewer rank-order choices) was smaller and failed to reach significance (Estimate = –0.54, SE = 0.3, z = –1.81, p = 0.07). As visual inspection of Figure 6 shows, this was likely due to by-item variation.

Figure 6

Results of Experiment 2: By-scale variation in choosing rank-order alternative.

3.4 Discussion

By probing whether participants took the target sentence to exclude a rank-order or a complement-exclusion alternative, instead of probing whether they calculated the target exclusionary inference, we were able to more clearly isolate scale structure bias in Experiment 2. We found that merely and just are clearly different from chance level in showing a preference for the exclusion of rank-order alternatives. Merely strongly preferring rank-order exclusion successfully replicates Experiment 1, while the just finding goes beyond the previous experiment with the confound of a non-exclusive reading now ruled out. Unlike the other two exclusives, only was found not to be different from chance level, suggesting that it allows both types of alternatives (more) freely.

Experiment 2’s findings are in line with Coppock & Beaver’s (2014) observations about the scale structure bias of merely and just. These authors argue that merely requires rank-order alternatives, while just’s preference for them is only slight. Our finding that merely and just patterned significantly differently from each other constitutes strong support for this claim. The results of Experiment 2, on the other hand, are less compatible with Horn (2000), whose proposal leads to the expectation that just selects for rank-order scales—our data suggests that just’s preference is more subtle than that.