3.1 THE BASIC IDEA

We suggest that on both of its readings be-sax ha-kol is a focus sensitive particle which conveys the positive and negative components conveyed by scalar exclusive particles cross linguistically, i.e. the truth of its prejacent, p, and the falsehood of all stronger alternatives in C (the contextually supplied set of focus alternatives to p). This is seen in (13).⁵

(13) (see e.g. Beaver & Clark 2008 and Roberts 2011) is based on the assumption that exclusive particles are focus sensitive, namely that they operate on alternatives triggered by focus. This is captured in the literature by letting the focus sensitive operator associate with a focused element (which is usually also stressed and accented) and to create a set of alternatives C, which is a contextually supplied subset of the focus semantic value of this element. These alternatives are constructed by substituting this element with another element of the same semantic type (cf. Rooth 1985; 1992).

Our main claim is that although be-sax ha-kol shares these interpretative components with e.g. Hebrew rak and English only, it differs from them in that it is more flexible regarding the overtness or covertness of its associate, and as a result, with respect to the kind of alternatives it operates over. In particular, we suggest that be-sax ha-kol, but not rak, can associate with the covert degree modifier pos (cf. e.g. von Stechow 1984a and Kennedy & McNally 2005a). In this case too, alternatives are constructed by substituting this focused element with other (covert or overt) elements of the same semantic type, i.e. with other degree modifiers. We suggest that the approximative reading of be-sax ha-kol results from its association with the covert pos.

Preliminary support for the idea that the apparent ambiguity of be-sax ha-kol is due to its ability to operate over two different sorts of alternatives can be seen in (14). In particular, we observe that changing the salience of alternatives in the context affects the prominence of the two readings. Above we saw that a sentence like (2) ((14b here) has an approximative reading. But (2) can also have an exclusive reading, indicating that the room is clean, but does not have other properties. This reading is made more prominent when properties which can replace the one denoted by the overt adjective clean are made salient in the context. In contrast (14a) with rak is not ambiguous and can only have the exclusive reading, i.e. mean that the room is clean but does not have the other relevant properties, i.e. is not large and does not have a view to the sea.

3.2 THEORETICAL BACKGROUND: THE “TYPE OF ALTERNATIVE” PARAMETER, AND ASSOCIATION WITH OVERT VS. COVERT FOCUS

Before showing in more detail how the exclusive and approximative readings of be-sax ha-kol can be derived from the difference in the type of alternatives this particle operates over, we would like to point out that our suggestion is similar in its general reasoning to a suggestion made in Liu (2017) regarding apparent ambiguities between Mandarin jiu, and dou. Let us quote Liu here (2017: 62):

“I take it to be our basic assumption that an FP [a focus particle] operates on a set of alternatives (Rooth 1985). Then, the meaning of an expression containing an FP is a function of (a) the meaning of the FP, (b) the meaning of FP’s prejacent, π and (c) π’s alternatives. With this background, what we propose about Mandarin FPs is that (c), instead of (a), is the locus of ‘ambiguity’: with varieties of alternatives, apparent distinct meanings can be derived without altering the semantics of the FP.”

Liu takes this behavior of Mandarin focus particles to be part of a more general pattern, where different sorts of alternative sets are posited for a single alternative operator to create different interpretations (cf. Chierchia 2013 for different alternatives for only-like and for even-like operators). To the extent that our suggestion is on the right track, the behavior of be-sax ha-kol in Hebrew can further support this pattern.

More specifically, the variation in the type of alternatives we propose concerns overt-based vs. covert-based alternatives, which we take to derive from the association of be-sax ha-kol with overt vs. covert focused material.

This claim is not trivial, though, since focused elements are usually taken to be overt and prosodically marked. Moreover, some authors explicitly claim that focus must be realized phonologically, as in the discussion of Second Occurrence Focus⁷ (SOF henceforth). For example, Partee 1999 argues that the second occurrence of vegetables in (15) is not prosodically marked, although it is bound by only, and concludes that it is not focused. Rooth 1992 makes a similar claim regarding the second occurrence of rice in (16).

In contrast, some theories argue that SOF is prosodically marked after all, although not in the same form as the first occurring focus (see e.g. Beaver et al. 2007). What is more important to us are suggestions that prosodic prominence is actually not a necessary condition for the status of an expression as focused. For example, Féri & Ishihara (2009: 8) argue that in many cases “phonetic marking of focus can be masked by independent phonetic/phonological effects”, such as de-accentuation due to competition with stronger phonetic realization on another element in the sentence, or having an element in post-nuclear position. In such cases, Féri & Ishihara propose, an element can be focused even if it has no prosodic prominence.

Similar cases were pointed out in e.g. the free-focused construction in (17), where an element is de-accented due to givenness, although it is focused (cf. Kadmon 2001 and Wagner 2012).

Even more relevant to our proposal is (18) from Kadmon & Sevi (2011), where the exclusive particle only is argued to associate with the focused element Larry, even though it is not accented (see also Umbach 2009 on accented noch and Egg & Zimmermann 2011 on accented doch):

In general, then, focused material is argued to optionally carry no prosodic prominence, and focus sensitive particles were argued to be able to associate with prosodically unmarked focus.

Our proposal takes such suggestions one step further, in that it takes be-sax ha-kol to be able to associate with elements which, by virtue of being covert, have no phonological realization, and hence cannot be accented. We can take this to be a special (and, in fact extreme) case of Féri & Ishihara’s (2009) idea that a focused element can have no phonological marking if this marking is blocked due to some other phonological conditions (in our case, due to being covert).

Importantly, in this sense too, be-sax ha-kol is not isolated, since the ability to associate with covert material has been reported for other focus sensitive operators as well, for example for the covert O and E (as in the interpretation of any and give a damn) and the overt Hindi bhii (Chierchia 2013), the only-like particle just in English (Wiegand 2017), yielding an unexplanatory reading, the even-like BIXLAL in Hebrew (Greenberg 2020), and voobsce in Russian (Miashkur 2017; 2018), yielding intensification effects similar to very, as well as readings similar to at all. The ability to associate with covert material was claimed in these theories to explain special readings of these operators, which are not found with the unmarked correlates of these particles, e.g. the exclusive only, or the unmarked even-like particles in Hebrew (afilu) and Russian (daze).

Given this background, we turn now to show in detail how the proposed ability of be-sax ha-kol to associate with both overt and covert material can derive its exclusive and approximative readings, respectively.

3.3 DERIVING THE EXCLUSIVE READING OF BE-SAX HA-KOL

Henceforth, we will refer to the exclusive reading of be-sax ha-kol as in (3), repeated here, as be-sax ha-kol_excl. We propose that this reading results from the fact that be-sax ha-kol associates with overt focused elements, just like rak (and only) do, leading to standard, Roothian alternatives.

Given these focused elements, the sets of alternatives in (3a, b) look as in (19a, b), respectively, where the prejacent is in boldface.

Given the two semantic components conveyed by exclusives in (13) and these sets of alternatives, (3a) and (3b) convey (a) the truth of the prejacent, i.e. that Danny invited Rina/that my grandfather was a clerk, and (b) the negation of all stronger alternatives in C, e.g. that it is false that Danny invited Rina and Yosi, Rina and Yosi and Moshe/that it is false that my grandfather was a manager or the president of this company.

Notice that be-sax ha-kol_excl, like rak, is compatible both with entailment scales, as in (19a), where stronger alternatives asymmetrically entail weaker ones, and with evaluative, or rank order scales, as in (19b) (cf. Orenstein 2016). However, there is a slight difference between rak and be-sax ha-kol_excl in terms of the scales. For example, in (3b) with rak we can also get the complement exclusion reading (using Coppock & Beaver’s 2014 terminology), where my grandfather had no other profession besides being a clerk, derived by an operation over entailment scales. Though this reading is less prominent than the evaluative reading (probably due to the real-world knowledge according to which people have one profession at a time), it is still possible. In contrast, with be-sax ha-kol_excl this reading is harder to get, and the evaluative reading, where my grandfather never had any profession more prestigious than being a clerk, is much more prominent. On this reading, even if my grandfather worked for some time in a less prestigious job, e.g. as a cleaning person, the sentence is still true and felicitous. When an evaluative ordering is salient, then, it seems that be-sax ha-kol_excl prefers it, whereas rak is more neutral, or less specified.⁸

3.4 DERIVING THE APPROXIMATIVE READING OF BE-SAX HA-KOL

5.1 THE DIFFERENCE IN THE STATUS OF THE PREJACENT AND THE EXCLUSION OF STRONGER ALTERNATIVES

In the previous sections we argued that be-sax ha-kol, on both its exclusive and approximative readings, conveys the same two components as scalar exclusive particles cross linguistically, namely the truth of the prejacent (the positive component) and the exclusion of stronger alternatives (the negative component).

However, a close look at these readings reveals that they differ in the status of these components. For be-sax ha-kol_excl this status is the same as the one reported for typical exclusive particles: the prejacent is presupposed/not-at-issue, and the exclusion of stronger alternatives is asserted/at-issue.²⁰ In contrast, for be-sax ha-kol_approx the status seems to be the opposite, and in fact more similar to what we find with true approximators like more or less.²¹

This conclusion is supported by several diagnostics. For space reasons we present here two of them. The first is embeddability under antecedents of counterfactuals, which is supposed to target at-issue/asserted content. With be-sax ha-kol_excl what is being targeted by the counterfactual is the negative component that no stronger alternative is true: for example, from (46a) we infer that Danny has more than two dogs (and that this is why I am complaining). As seen in (46b) the same holds for English only/just.²² In contrast, for be-sax ha-kol_approx what is being targeted seems to be the positive component: from (47a) we do not infer that the room is maximally clean but that the room is not considered clean (and that if it was clean my aunt would agree to sleep in it). The same holds for the English translation with more or less seen in (47b):

Another diagnostic involves because-clauses. Coppock & Beaver (2014) show that such clauses target asserted/at-issue content, and that in the case of scalar exclusives like only or just they target the negative component, namely the exclusion of stronger alternatives, which they indeed assume to be asserted/at-issue. This seems to be the case for the negative component of be-sax-ha-kol_excl as well: from (48a) we infer that the reason that Danny is sad is because he didn’t publish more than two papers (and not because he published two papers). This is what makes the minimally contrasting version with happy a bit odd, given that people typically want to publish as many papers as they can. As seen in (48b) the same holds for English only, as expected.

In contrast, for be-sax ha-kol_approx the situation is reversed, and the because-clause seems to target the positive component: From (49a) we infer that Danny is happy because the room is clean (and not because it isn’t completely clean). This is what makes the minimally contrasting version with sad a bit odd, given that people typically prefer cleaner to less clean rooms. As seen in (47b) the same seems to hold for English more or less:

In sum, while be-sax ha-kol_excl behaves like typical exclusive particles in terms of the status of its components, be-sax ha-kol_approx behaves like typical approximators.

One can attempt to take this observation as an indication that be-sax ha-kol is ambiguous between an exclusive and an approximative operator after all. However, given the differences we pointed out in the previous section between be-sax ha-kol_approx and clear approximators (in terms of compatibility with pointal adjectives, with relative multidimensional adjectives, with precise measure expressions and with adjectives which are themselves modified by degree modifiers), we believe that this direction is not the right one to take. Instead, in the next section we explore two ways to handle this data within the present proposal.

5.2 LEXICAL OR PRAGMATIC VARIABILITY IN THE STATUS OF THE COMPONENTS WITH BE-SAX HA-KOL

One way to handle the data above is to simply take be-sax ha-kol to have two entries as in (50a) and (50b), for the exclusive and the approximative readings, respectively.²³

The entry in (50a) is the typical entry for scalar exclusives, and (50b) differs minimally from it just in the reversed at issue vs. not at issue status of the positive and negative components. While on this proposal be-sax ha-kol is strictly speaking ambiguous, we think that taking this particle to have developed two closely related entries is still a more economical and plausible suggestion than taking it to be associated with two entirely distinct semantic operations (as an exclusive particle and as an approximator).

A relevant point to make here is that although on this hypothesis be-sax ha-kol_approx differs from be-sax ha-kol_excl and from typical exclusive operators (like English only and just, Hebrew rak, etc.), there is at least one other exclusive operator which seems similar to it in this respect. As already mentioned in the introduction, Bassi et al. (2019) argue that in order to account for a number of puzzles with scalar implicatures it is necessary to assume that unlike only, which presupposes its prejacent and asserts the exclusion of stronger (or non-weaker) alternatives, the status of these components with the covert exclusive operator involved with deriving scalar implicatures, which Bassi et al. (2019) call p-exh, is reversed. According to them, then, the prejacent of p-exh is asserted and the exclusion of non-weaker alternatives is presupposed (similarly to what has been sometimes claimed for clefts).²⁴ This is in contrast to previous analyses of exh, the covert operator assumed to be involved with scalar implicatures, which took it to assert both components (see e.g. Chierchia et al. 2011 and much subsequent work). To the extent that this suggestion is on the right direction, the status of the positive and negative components can be seen as one of the parameters of variation along which exclusives differ. Thus, the fact that be-sax ha-kol can be associated with the two lexical entries in (50) is less surprising, and still allows us to consider it as part of the typology of exclusive operators. be-sax ha-kol may then be taken to be unspecified along this parameter.²⁵

A second, more unified hypothesis we would like to examine is that be-sax ha-kol has only the entry in (50a), typical for exclusives. Unlike the previous proposal, where be-sax ha-kol differs from classical exclusive particles in two distinct properties (the ability to associate with covert focus and the status of its interpretative components), on this proposal it differs from them only in the former, and the different status of the interpretative components, observed in the approximative reading, will be pragmatically derived.

This kind of hypothesis is inspired by recent research on the flexibility of the asserted vs. presupposed status of interpretive content. While traditionally this status was assumed, implicitly or explicitly, to be totally fixed and lexically determined for each lexical item (cf. Heim 1992; van der Sandt 1992), there are now various theories which question one of these assumptions, or even both. We now briefly review some relevant claims made in such theories (although for space reasons we cannot do justice to their richness nor to the differences between them).

5.3 EXISTING CLAIMS REGARDING GRADIENCER AND VARIABILITY IN PROJECTIVITY AND (NOT)-AT-ISSUENESS

As is well known, presupposed/not at issue material is traditionally assumed to project over entailment cancelling operators like negation, questions, possibility modals, etc. even when embedded under such operators. However, various authors observed cases where such material does not project. In general, such authors observed that projectivity is gradient – some presuppositions are judged to be more projective than others. Moreover, projectivity of presupposed material has been argued to be affected by information structural factors, which in turn affect the degree to which such material ends up being at-issue, or up for debate/up for discussion.

To illustrate, consider the sentential complement of factive verbs like find out or discover, which is assumed to be presupposed, and does indeed usually project. As Simons et al. (2017) show, such commitments are weakened or disappear when relevant parts of such sentential complements are accented (which they take to indicate that they are focused), as in (51), or are answers to explicit or implicit questions in the context, (e.g. the question of where Sally is in (52)).

Given this and similar observations, Tonhauser et al. (2018) hypothesize that a content C projects to the degree to which it is not-at-issue (what they call the gradient projection principle). This hypothesis was given experimental support in e.g. Amaral et al. (2011); Cummins et al. (2012); Smith and Hall (2011) and Xue and Onea (2011). For example, based on examining the projectivity of content in 19 constructions in English (e.g. non-restrictive relative clauses, possessive NPS, the prejacent of only and complements of stop, discovered and annoyed), as well as the at-issueness of such contents (using assent/dissent reactions), Tonhauser et al. (2018) found that the more not-at-issue a content is judged, the more projective it is.

A result which is of particular interest to us is that of all these 19 constructions, the prejacent of only was found to have the lowest degree of not-at-issueness, and also the lowest degree of projectivity. A similar result regarding only was also reported in Amaral et al. (2011).

As to the sensitivity of projective content to information structure factors, we follow Abrusán’s (2011) approach, who assumes that while not-at-issueness/presuppositional status can be originally conventionalized/lexicalized in the semantics of presupposition triggers,²⁶ it can be overridden when we pay attention to the not-at-issue material, so it becomes at-issue (in which case it is not presupposed to begin with).²⁷ Here is a relevant quotation:

Abrusán (2011: 501)

“Some aspects of the information conveyed are such that we pay attention to them by default, even in the absence of contextual information. On the other hand, contextual cues or conversational goals can divert attention to types of information that we would not pay attention to by default. Either way, whatever we do not pay attention to, be it by default, or in context, is what ends up presupposed.”

5.4 BACK TO BE-SAX HA-KOL

Given the claims in the above reviewed theories, let us now go back to the status of the components of be-sax ha-kol. Following Abrusán’s (2011) view, let us assume that the lexical entry for this particle starts out as (50a) above, where the prejacent is presupposed/not-at-issue and the exclusive component is asserted/at-issue.

With be-sax ha-kol_excl nothing interesting happens, so the components keep their status. But something does happen with be-sax ha-kol_approx. We hypothesize that this might have to do with the way the interpretation of the prejacent in this reading is calculated: as already pointed out in Section 3.4.2, when calculating the meaning of the prejacent and the exclusive component with be-sax ha-kol_approx, there is a possible clash between them. To illustrate again, the interpretation of the positive component of The room is be-sax ha-kol clean, namely the prejacent The room is pos clean, is that the degree to which the room is clean is at least as high as the standard, where crucially the context can, and often does, set this standard at the scale maxima. The negative component, on the other hand, requires that the room is not maximally clean. In a context where the standard in the prejacent is maximal, then, the two components clash.

Hence, as argued in Section 3.4.2 above, the presence of be-sax ha-kol forces us to go back to the prejacent and re-interpret it in such a way that the value of the standard variable is set to being non-maximal (no matter what the original value of this standard is set to by the context).

We thus hypothesize that although the prejacent of be-sax ha-kol_approx is originally backgrounded, this process of re-interpreting the prejacent may be the reason for why it cannot stay backgrounded anymore. In particular, this re-interpretation moves the prejacent to the foreground, so it becomes at-issue. In Abrusán’s (2011: 501) terms, this can be considered a case where a “conversational goal… can divert attention to types of information that we would not pay attention to by default”, and hence makes this type of information at-issue.

Given that there is independent experimental evidence that the not-at-issueness of the prejacent of exclusives seems rather weak to start with (cf. again Amaral 2011; Tonhauser et al. 2018), we end up with the prejacent of be-sax ha-kol_approx getting an at-issue status.

This is not the whole story, though, because remember that given the data in Section 5.1 the change in the status of the prejacent of be-sax ha-kol_approx – from being not-at-issue to being at-issue – is accompanied by a change in the status of the exclusive component – from being at-issue to being not-at-issue. Why don’t both interpretive components with be-sax ha-kol_approx end up being at-issue?

A suggestion made in Bassi et al. (2019) can perhaps help shed some light on the reason for this issue. As pointed out above, Bassi et al. argue that unlike what is traditionally assumed for covert exh, p-exh presupposes exclusion of non-weaker alternatives and asserts the prejacent, in a way which mirror-images overt only: “Only presupposes its prejacent and asserts exhaustivity; p-exh asserts the prejacent and presupposes exhaustivity; and exh presupposes nothing and asserts both the prejacent and the exhaustivity component” (Bassi et al. 2019: 23). Importantly, they further suggest that this proposal for p-exh fares better than the proposal for exh, since p-exh is compatible with the general requirement (which they take to be inspired by Schlenker 2007) that “a contribution must not lead to multiple novel inferences or answer different questions” (Bassi et al. 2019: 23).

Given such a general requirement, then, it can perhaps be also used to explain why, as far as the status of the components is concerned, be-sax ha-kol_excl is the mirror image of be-sax ha-kol_approx., similarly to the way only is the mirror image of p-exh in Bassi et al. (2019).

This suggestion needs to be further clarified and motivated, as well as empirically validated.²⁸ At this point, however, we can at least point out one more construction where such a status mirror image is found, involving evaluative adjective sentences (EASs), described in Tonhauser et al. (2019). Tonhauser et al. discuss two meaning components conveyed by EASs, as in (53a), namely the truth of the prejacent (e.g. Feynman danced on the table) and the generalization (that for Feynman to dance on the table was stupid). The prejacent in such constructions is taken to be presupposed, while the generalization is asserted. This is evidenced in (53b), where the former, but not the latter projects.

Tonhauser et al. attribute to Karttunen et al. (2014) the observation that there is variability in the status of the prejacent in this construction. This is seen in attested examples like (54), where the prejacent does not project, i.e. there is no commitment of the speaker that he went stumbling through the junkyard.

What is relevant for us is that Tonhauser et al. observe that in such cases there is variability in the status of the generalization as well. Thus, unlike the prejacent in (54), which indeed does not project, the generalization does project (there is commitment that stumbling through the junkyard is stupid). Tonhauser et al. conclude that in this construction “when the prejacent projects, the generalization does not, and when the prejacent does not project, the generalization does” (Tonhauser et al. 2019: 3).

It seems, then, that the swapped status of the positive and negative components of be-sax ha-kol_excl and be-sax ha-kol_approx is part of a more general pattern found in other constructions, where a change in the not-at-issueness status of one interpretive component leads to a change of the at-issueness status of another component. Whether this pattern is indeed due to the general requirement suggested in Bassi et al. (2019), and whether it applies to all constructions are questions which require further research and are beyond the scope of this paper.