Minimizers and EVEN

3.1 Scope out of negation

In contrast with lexical NPI renhe in (7), which is required to occur in the scope of negation, Chinese minimizers may occur in either positive or negative sentences. As discussed in Section 2, when minimizers occur in positive sentences, they function as a cardinal numeral or canonical degree modifier as (8a) and (9a). When they occur in negative sentences, they are three-way ambiguous: simply negating the quantity/degree (other than one, other than a little) as in (8b-i), expressing the litotes reading (not one, not little meaning a lot) (8b-ii), or total negation (8b-iii). In order to avoid ambiguity and be more informative, the lian... dou construction is preferred to emphasize either the scalar superlative use of the minimizers in positive sentences, and total negation in negative ones. In either case, the object minimizer is obligatorily displaced to precede dou in the preverbal position required by the lian... dou construction. Negative sentences (11a) and (12a) are repeated below in (11ʹ) and (12ʹ) to show that dou is obligatory. ^[7]

In general the syntactic order of dou and negation determines their relative scope. For example, the plural subject they and the object these books in (18) and (19) respectively are universally negated when dou precedes the negation as in (a) sentences; by contrast, they render existential meaning when negation precedes dou, as shown in (b) examples.

As mentioned above, the ungrammaticality of (6c) and (7c) is because the subject lexical NPIs (any, renhe) are not in the scope of the predicate negation. It does follows that the subject lian-minimizer in (20) is not in the scope of the negation as well, syntactically representing the semantics of lian+one-N+all+NEG, ‘even one not, all not, not even one’. Its comparison with FC renhe will be further discussed in Section 3.5.

We thus see that it is the lian... dou structure that makes the lian-minimizer to scope over negation giving rise to the intended “negative polarity”.

3.2 Licensing conditions

Like English any, Chinese NPI renhe is licensed by negation as well as in non-veridical contexts, such as in a conditional protasis as in (21), or in a Yes/No question as in (22) (Wang and Hsieh 1996; Kuo 2003, etc.).

By contrast, the in-situ object minimizers in (23) and (24) do not express the strengthening effect as NPI renhe does in (21) and (22). Rather they are interpreted as their canonical existential reading.

Total negation, however, is derived when they occur in negative lian... dou sentences as illustrated in (25) and (26) respectively, in which the object minimizer is preposed to precede dou.

This thus indicates that total negation is syntactically derived in lian... dou construction, independent of the non-veridical contexts that otherwise license regular NPI-renhe.

3.3 Clausemate relation between dou and negation

It has been noted that lexical NPI-renhe can be licensed by a negation in a higher clause as shown in (27) and (28) from Wang and Hsieh (1996) and Kuo (2003), on a par with the NPI’s occurring in the scope of the so-called NEG raising predicate (dated back to Klima 1964; Horn 1978; and see the review in Collins and Postal 2014).

However, the above condition says nothing about the intended total negation in the embedded clause shown in (29) and (30). In addition, when the negation occurs in the higher clause as in (31) and (32), the embedded minimizers (yiju hua ‘one.CL word’ and yikou fan ‘one-mouthful of rice’) express their cardinal existential reading: ‘that the kids utter even a word is not expected by Zhangsan’, and ‘that Lisi ate even a mouthful of rice surprised Zhangsan’, respectively, rather than the intended negative polarity as marked as a “#” sign.

This contrast indicates that a clausemate relation should be respected between dou and negation; thus when it is not, the intended total negation is not obtained. In other words, while NPI-renhe is licensed in-situ by a c-commanding Neg or licensor, lian-DP is required to have a Spec-head agreement relation within DouP. The total negation is possible when dou scopes higher than Neg in the same clause. ^[8]

This clausemate relation between dou and negation holds not only in lian... dou but also in sentences involving FC renhe. As shown in (33), dou and its associated FC renhe have to precede negation. When the negation appears in the matrix NEG raising predicate in (34), it doesn’t trigger NPI-renhe; rather the universal FC-renhe remains due to the occurrence of dou, cf. (27). However, the NPI-renhe reading becomes possible when dou is absent as shown in (35), on a par with (27) and (28).

One question raised by one of the anonymous reviewers concerns a complication of the possible long-distance displacement of lian-DPs. Following Shyu’s (1995, 2014) long-distance movement of the lian-DP (evidenced by the embedded dou and Binding reconstruction effects in her discussion), I suggest that the lian-minimizer in (36a) is construed with the embedded dou and negation, rendering total negation. By contrast, the intended polarity reading is hard to receive in (36b) when dou is not interpreted with the negation in the same clause, on a par with the contrast between (29) and (31). ^[9]

To recapitulate, the position of dou that is construed with FC-renhe and lian-DP syntactically determines its relative scope with negation within a minimal clause domain regardless of the position of the lian-DP (S-initial or S-medial), thus irrelevant to the NEG raising context that otherwise licenses NPI-renhe.

The contrast between NPI-renhe and lian-minimizers is further attested when they occur in islands. While the matrix negation can license NPI-renhe in complex DP and adjunct clause islands as in (37a) and (37b) respectively (as noted by Yang (2008: Ch. 5)), the matrix negation cannot do so to lian-minimizer in islands to render the intended readings of (38a-ii), (38b-ii); rather, the negative polarity reading (38a-i), (38b-i) obtains when the negation stays in a clausemate relationship with dou.

3.4 Lack of intervention effects

In English strong quantifiers (every, most, all) block NPI-any licensing as in (39); for example, Linebarger’s (1987) Immediate Scope Constraint requires NPIs and negation be in the immediate scope, not be separated by “logical” elements. Similarly, NPI-renhe licensing is blocked by strong quantifiers (meige-N ‘every’ and dabufen-N ‘most’) at syntax as noted by Kuo (2003), and Yang (2008), repeated in (40).

By contrast, the strong quantifiers meige-/dabufende-N do not affect the interpretation of the in-situ object minimizer. On a par with the readings of the in-situ object in (8b) and (9b), the direct object minimizer in (41) is ambiguous among existential, litotes, and total negation readings. ^[10]

Likewise, the embedded (in-situ) object minimizer in (42a) is interpreted existentially or with litotes reading, (42a-i). Note that the negative polarity reading of (42a-ii) as well as (42b-ii) is hard to obtain due to the violation of clausemate relation (between dou and negation) as mentioned above, rather than the intervention of the embedded strong quantifier subject in discussion here.

The lack of intervention effect is further attested when the lian-minimizer co-occurs with a wh-phrase. In Chinese wh-phrase can be interpreted as free choice indefinite when quantified by dou. Cheng (1995: 220) has observed an adjacency requirement of dou’s binding the wh-indefinite. As repeated in (43), the object shenme ‘what’ being adjacent to dou is interpreted as everything, whereas the non-adjacent shei ‘who’ as the interrogative who as in (43i). ^[11] Other interpretations, as in (43ii, iii), are not possible.

By contrast, dou’s quantifying over the lian-minimizer preempts its associating with the wh-indefinite. No matter whether the lian-minimizer is adjacent to dou as in (44a), or topicalized to the sentence-initial position as in (44b), it is construed with dou rendering (44b-i). Thus, unlike (43), the subject wh-phrase in (44b), though adjacent to dou, is not interpreted as an wh-indefinite reading in (44b-ii).

This indicates that the wh-indefinite does not intervene dou’s quantificational construal with the lian-minimizer.

3.5 Free choice?

Having seen the above asymmetric properties between lexical NPI-renhe and lian-minimizer, one may wonder if the minimizers may pattern with free choice (FC-) renhe in (45), since both of them require dou, and scope out of negation. In addition, FC-renhe subject is well-formed. ^[12]

FC-renhe further differs from NPI-renhe with respect to the clausemate relationship with dou, and the lack of an intervention effect. Firstly, unlike NPI-renhe, dou-related FC-renhe cannot be interpreted existentially even in the scope of a higher negation, as illustrated in (47) from Kuo (2003). Thus, (47a) is interpreted as negating the proposition that everyone can talk, rather than no one can talk. Total negation becomes possible when the FC-renhe is construed with an embedded negation in (47b): rendering it is not the case that all the (any) people cannot talk.

Secondly, FC-renhe does not display intervention effects as shown in (48), in contrast with that attested in NPI-renhe (40a)/(49) (Kuo 2003).

Despite the above symmetries between FC-renhe and lian-minimizers, grouping the latter as the former type runs into problems (vs. Lahiri 1998). It has been known that FC-renhe occurs in modals and generic sentences, as shown in (50). By contrast, lian-minimizers in these sentences do not yield to the intended readings of the FC renhe, as illustrated in (51).

Sentences in (51) are not acceptable without considering the conventional implicautre contributed by lian. In other words, renhe (NPI or FC) introduces alternatives that are contextually specified set of properties, e. g., people in the world relevant in the context of (50). By contrast, the alternatives evoked by the minimizers in (51) include not only the asserted individual or entity but also contextually determined propositions that are ranked against some domains; see Section 4.3 for details. In short, minimizers as yi-CL-N and yidian-N do not parallel canonical FC-renhe with respect to the scalar implicature contributed by lian. In the following section, it is shown that previous analyses that maneuver means of fulfilling c-command licensing condition fails to account for Chinese minimizers. Consequently, I propose a syntactic composition approach.

4.1 LF movement of negation for negative polarity licensing?

One might postulate the LF movement of negation in order to maintain the general consensus of the c-command licensing requirement, such as Mahajan’s (1990) analysis for Hindi NPI koii bhii ‘lit. someone+emphatic marker, anyone’; but see Kumar’s (2006: 132–133) objection to Mahajan’s claim, and Benmamoun’s (1997) objection to NPI licensing at LF in Moroccan Arabic. If the negation mei were able to raise to c-command the lian-minimizer at LF, it would have predicted that (8b) and (11a) would have been interpreted the same, namely neg > one-N rendering negative polarity. Contrary to the fact, (8b) is three-way ambiguous, as mentioned in Section 1, whereas (11a) is unambiguously total negation.

Another more serious problem concerns the generality of the LF movement of the negation. As mentioned in Section 3.1, when plural (quantifying) objects are preposed and quantified by dou, they are syntactically outside the scope of negation, isomorphic to their semantic interpretation, e. g., many/every > Neg in (52), not vice versa.

If LF movement of the negation were equally possible in both (11a) and (52), it would have wrongly allowed the scope of Neg > many/every. In short, postulating the LF movement of negation solely for licensing minimizers would be ad hoc and results in over-generalization.

4.2 Reconstruction of the S-medial minimizers?

It has been suggested by Barss (1986) and Chomsky (1995) that scrambled NPIs are to be LF reconstructed to a position where they can be c-commanded by their licensors. This approach, however, is threatened by the lack of reconstruction effects in Hindi’s scrambled DPs as discussed in Kumar (2006). Similarly, it has also been shown by Shyu (1995; 2001: 96) that medial lian-phrases are in the surface construal with their antecedents in terms of Binding Principle; e. g., the reflexive taziji in (53b) and the proper noun Zhangsan in (54b) are interpreted as in their surface medial preverbal position as in (53a) and (53a), respectively. ^[14] It is thus evident that the medial lian-DP is interpreted in their surface position.

4.3 Syntactic decomposability

Regardless of various approaches of the licensing conditions (syntactic, semantic and pragmatic), the general consensus is that polarity sensitivity pertains to the inherently lexical properties of NPIs (Giannakidou 2011; Israel 2011, among many others). However, some polarity items are lexically indeterminants, e. g., the taboo expressions the hell/devil discussed in Hoeksema and Napoli (2008), who have noted that (their G-type) the hell/devil...”sometimes produces negative polarity items [55] and sometimes positive polarity item [56], which is ‘not uncommon’” (p. 556) in languages. Moreover, another use of the hell (their B-type) occurs either in positive (57a) or regular negative (57b) sentences.

It has also been documented that NPI formation does not solely pertain to lexical property. Specifically Postma (2001) has proposed a syntactic construal for Dutch taboo words like e:ne+zak/flikker/duvel... ‘any.DRAGTONE’+scrotum/faggot/devil... ’ and English comparative individual-level small clause like I have never seena manmore proud/smart. ^[15]

Our previous discussion of the asymmetric properties between lian-minimizers and lexical NPI-renhe in Section 3 strongly argues for the syntactic formation of negative “polarity”. While the NPI-renhe is licensed in the scope of negation (i. e., ¬∃), total negation involving the minimizer is compositionally derived via lian... dou construction, which requires the lian-minimizer to scope out of the negation, thus syntactically and semantically isomorphic to the logical representation of ∀¬. Assuming dou heads a functional projection DouP, and internally merges with the lian-DP, as shown in (58), cf. Shyu (1995). It is suggested that lian is syntactically represented as a preposition (e. g., Lü 1984), assuming that it has been grammaticalized from a lexical verb meaning connect, include into a functional category; see references cited in Pai (2013).

An immediate question arises as to why dou can quantify over the singular weak QP, seeing that dou has been widely known as quantifying over strong QPs (or Liu’s 1990 G-specific QPs) and plural DPs (e. g., Cheng 1995; Lin 1998). How does the “universal” reading obtain? I claim that it is actually facilitated by lian, which plays two major functions. Like regular focus particles or adverbs, it functions as a focus particle (Paris 1998; Shyu 1995, 2004) that evokes a set of propositional alternatives (Rooth 1985, 1996, etc.) that are salient in the context. In addition, it is a scalar operator that places the asserted proposition containing the focus at an (near) endpoint of a scale of likelihood/expectedness in the set (cf. Xiang 2008). This facilitates dou to quantify over the focus and the members in the alternative set (Shyu 2004) without violating the general constraint of dou quantification.

Following the widely acknowledged conventional implicature of EVEN introduced by Karttunen and Peters (1979) and adapting Rooth’s (1985) formulation, I show that lian... dou syntactically manifests the decomposability of quantificational and scalar properties. Consider the semantics of lian... dou stated in (59). (59i) is the asserted proposition Q containing the focus DP (a) attributed with the property P, e. g., Lisi atea in (60). Lian, as a focus operator, introduces a set of alternatives C with the property P other than the asserted proposition P(a) in a pragmatically relevant context under consideration (Rooth 1985), as shown in (59ii). Moreover, the scalar function of lian is stated in (59iii): the asserted proposition containing the focus is placed at the (near) endpoint of the likelihood/expectedness scale (Fauconnier 1975a, 1975b; Karttunen and Peters 1979; Rooth 1985; or Kay’s 1990 the most informative in normal situations) that includes the alternative set C and Q. Then (59iv) adds the function of dou in the nucleus part: it universally quantifies over the variables (z) in a union set containing the variable x in the alternative set C and the focused DP ˇa having the characteristic function of P. ^[16] It then follows that in (60) and (61iv) among all the contextually relevant things that Lisi may possibly eat, his eating a mouthful of rice is considered as the (near) least expected.

As for the negative lian... dou clause as in (62), the negation reverses the scale of the scalar implicature of EVEN (e. g., Fauconnier 1975a, 1975b; Karttunen and Peters 1979, Kay 1990; Lahiri 1998; Lee 2004, etc.). The implicature in (63iii) is interpreted as not eatingais the least likely thing, inferring that eating a as the most likely proposition compared with other “x’s” that Lisi may eat in C.

This naturally accounts for why minimizers are preferred in negative contexts, e. g., (60) vs. (62). ^[17] Entities with a minimal quantity/quality are usually the lowest bound at a contextually relevant scale. Totally negating the minimal value via lian... dou thus achieves an emphatic informative function as in (62). On the contrary, the plain affirmative counterpart as in (60) is not informative unless the focus expresses the superlative or at the extreme of a contextual scale, in the sense of Fauconnier’s (1975a, b) scalar principle. This point is further illustrated by the contrast between (51ʹ) and (51b): in the former the superlative use of the minimizer in the affirmative sentence is perfect. By contrast, when the minimizer a story is employed without a scalar context in the affirmative (51b), it becomes infelicitous.

Although the weak DPs (yi-CL-N/yidian-N) pertain to semantic endpoints, polarity strengthening is facilitated by the scalar operator lian and universal operator dou. Without such a syntactic mechanism, they do not necessarily give rise to the intended scalar strengthening effect. This amounts to saying that lian and dou compositionally manifest the strengthening effect; lian widens the quantification domain including not only the asserted proposition containing the focused DP, but also its contextually relevant propositions that contain members alternative to the focused DP. In addition, the asserted proposition containing the focused minimizer in a negative sentence is ranked as the highest of the scale of likelihood in context. When the quantification domain being evoked, dou universally quantifies over the members in the domain. We thus exemplify a syntactic representation of decomposing the existential and scalar implicatures. Traditionally it is this strengthening effect that correlates the minimizers in discussion with regular NPI’s. Nevertheless, this paper stresses that the strengthening effect is lexically encoded in the latter, but syntactically derived in the former on account of the availability of lian... dou construction in Chinese.

5.1 Implicit EVEN

Having seen that minimizers in dou sentences are actually construed with overt lian, in this section I further show that this point is syntactically, semantically, and pragmatically motivated. As mentioned in Section 2, a lian-focused object has to precede the obligatory dou in the preverbal position, as shown in (64); see Shyu (1995) and Shyu’s (2014) review.

Due to the overt lian in (64b), the plural DP zhexie shu ‘these books’ is scalar implicated, whereas the bare plural object in (65) lacks this interpretation.

However, the informative scalar implicature obtains when the focused phrase is a minimizer no matter whether lian is overt or phonetically null, as shown in (66), which is rendered as reading a book being considered as the mostly expected thing for him to do but he failed to do so. ^[18]

The scalar reading expressed in (4), (5) and (66) even without the overt lian echoes the implicit even construed with English NPI-minimizers like say a word, do a thing, give a dime, etc. Schmerling (1971) considers (67a) as semantically equivalent to (68), and even is interpreted in (69) even though it is optional.

She further notes that do a thing or a thing are distinguished from NPIs, because they can occur in positive sentences as in (70). Another reason is that they are productive as they can be selected by verbs freely as show in (71) despite that only few VPs are idiomatic, like lift a finger or move a muscle.

Following Schmerling’s view, Heim (1984) notes that quantificational superlatives (e. g., so much as x) and these indefinite minimizers (e. g., say a word, bat an eyelash) are NPI’s with inherent even, “semantically equivalent to expressions containing the word even” (p. 105). A piece of Heim’s evidence comes from the contrast between the lexical NPIs (any, ever) in (72) and the minimizers in (73) in the similar contexts. The downward entailing (Ladusaw 1979) condition every can successfully license the typical NPIs in the former, but not necessarily for the latter type in (73b). Heim assumes that there is an invisible even in so much as a dime that contributes the conventional implicature, although even does not affect the truth condition of the sentences. ^[19]

Thus, (73a) is acceptable because its implicature is not controversial. Among the values other than a dime that “every restaurant that charges for x for iceberg lettuce ought to be closed down”, one dime is less expected than those other values. It is natural that restaurants charging such low prices tend to be closed down. However, the implicature expressed in (73b) is unnatural. The presupposition that every restaurant charging some x ≠ 10¢ for lettuce and being four stars is not conventionally held. Despite that 10¢ is ranked at the bottom of the scale of the price, this implicature is quite undesirable in natural contexts. The above discussion indicates that the NPI rendition of English minimizers is contributed by an implicit even, lending further support to Chinese lian’s interplaying with minimizers. However, unlike English implicit even, Chinese utilizes this lian... dou construction to syntactically represent total negation and EVEN implicature.

5.2 A comparison with Hindi and Japanese

The above discussion indicates that even is implicitly interpreted with English minimizers like a thing. By contrast, some languages explicitly encode scalar EVEN morphemes suffixed to minimizers, such as Hindi ekbhii and Japanese one-CL-mo. In Hindi, some NPI minimizers are made up of an indefinite or a weak predicate indicating small amounts and the emphatic particle bhii ‘even, also’ such as ekbhii ‘one+even, any’ and zaraa bhii ‘a little+even, even a little,’ as studied by Lahiri (1998) and Kumar (2006). ^[20] In Japanese, Nakanishi (2006) has proposed a compositional analysis of Japanese NPI’s containing -mo/-demo/-dake demo in contrast to the traditional lexical approach, and argues that Japanese hito-ri-mo ‘one-CL-also/all’ is decomposed to one+even (cf. -mo as the universal particle in Hagstrom (1998)).

This section presents some parallels of these minimizers in comparison with those in Chinese, thus lending further support for the presence of the scalar EVEN with minimizers. Firstly, these minimizers scope out of the negation, as they may occur in the subject position in (74) and (75). ^[21]

Secondly, there is a clause mate relation between the negation and the minimizers in Hindi and Japanese: a negative element in the matrix clause is not able to license the minimizers in the lower clause, as noted by Kumar (2006) in Hindi and Aoyagi (p.c.) in Japanese. ^[22]

Thirdly, these minimizers are not freely licensed by adversative predicates in Hindi (Kumar 2006) and Japanese (Nakanish 2006).

In addition, as noted by Aoyagi (p.c.), hito-ri-mo may not be licensed in a conditional clause.

Fourthly, minimizers do not render generic free choice reading in the context of modals in Japanese (Aoyagi, p.c.) and Hindi (Kumar (2006), vs. Lahiri (1998)). Hence sentences below denote regular even one, rather than the intended free choice reading; see Section 3.5.

In addition, like English minimizer even and Chinese lian... dou (Section 4.3), these EVEN morphemes (Hindi -bhii and Japanese -mo) induce a set of alternatives and the conventional implicature as studied in Lahiri (1998) and Nakanishi (2006) respectively. Specifically Nakanishi states that Japanese -mo attached to the cardinal predicate one evokes a ScalarP. When -mo is in the scope of a DE operator, just like in positive contexts, no total negation is rendered. When it is out of the scope of negation, it gives rise to total negation.

To recapitulate, it has been shown that the minimizers containing a cardinal weak predicate and EVEN morpheme are distinguished from lexical NPI’s with respect to their scoping over negation, the clausemate relation between minimizers (or Chinese dou) with the negation, and the inert long-distance and (some) non-veridical licensing conditions. Moreover, this type of minimizers cannot be felicitously interpreted without taking the scalar implicature into consideration.

One more thing that should be noted is that polarity sensitivity of the scalar minimizers is not solely lexically encoded across languages. Rather they can be morphologically encoded or syntactically derived. One implication of this study is to call for a continuum of these minimizers in reference to the synthetic versus analytical ends. At the (implicit) lexical (synthetic) extreme include Greek strong NPI-minimizers (e. g., dhino, oute from Giannakidou 2007, 2011), or English ones (e. g., a bit, Bolinger 1972). Miminizers like a thing and so much as discussed in (Schmerling 1971; Heim 1984) can be considered as lexical NPI minimizers in the sense that they have inherently incorporated the implicit even. Then it comes to the explicit lexical NPI-minimizer with an EVEN morpheme, such as Hindi ek-bhii. It is lexical because ek and -bhii have become a chunk that cannot be separated as shown in (74). As noted by Lahiri (1998), the particle -bhii in (83) cannot be attached to other numerals like do ‘two’ to form an idiom chunk. ^[24]

Japanese hito-ri-mo is morpho-syntactically formed by attaching -mo to the weak cardinal numeral, as -mo can be freely attached to focused NPs. Chinese minimizers in lian+yi-CL-N+dou construction fall at the analytic end. As mentioned above, polarity sensitivity is not lexically encoded in yi-CL-N and yidian-N; rather it is compositionally derived. Consequently a continuum can be represented as in (84).

Presumably, the above discussion suggests a new direction of examining polarity sensitivity in terms of the lexical (synthetic) - analytic (syntactic) continuum cross linguistically. ^[25]