PI-licensing and PI-unlicensing: A Grammatical View of Exhaustification with Focus Movement1 Yimei Xiang — Harvard University [email protected] Abstract This paper investigates two main issues on the interaction of polarity items and exhaustifications. The first main issue is about the NPI-licensing effect of the exclusive focus particle only (e.g., Only JOHN read any papers.). I propose to incorporate focus movement (Wagner 2006) into the grammatical view of exhaustification (Krifka 1995; Lahiri 1998; Chierchia 2006, 2013), with a simple assumption that focus movement is motivated to avoid contradictions. This grammatical account also addresses side-issues such as the NPI-unlicensing effect of negation (e.g., *Not only JOHN read any papers.) The other main issue is on the contrasts between the overt focus particle only and the covert exhaustification O-operator with respect to the licensing and unlicensing effects on polarity items. First, the overt particle only licenses NPIs, but the covert operator O does not. I show that this contrast can be immediately predicted by the basic assumptions of the grammatical view. Second, in certain cases, applying only over an NPI/FCI-licenser makes the corresponding NPI/FCI unlicensed, while applying a covert O does not lead to such an unlicensing effect (e.g., *John only didn’t read ANY papers. vs. John didn’t read ANY papers.) I re-evaluate the semantics and the usage of only and attribute the second contrast to the assumption that only has an additive presupposition and no pre-exhaustification use.

1. Introduction This paper investigates the interaction of polarity items (PIs henceforth) and exhaustifications. A prominent example for PIs is the emphatic expression any, which exhibits both negative polarity item (NPI henceforth) and free choice item (FCI henceforth) usages. In particular, any is licensed as a (weak) NPI2 under the following contexts, which are uniformly described as downwardentailing (henceforth DE) contexts, based on the tradition initiated by Fauconnier (1975, 1979) and Ladusaw (1979). (1) Under negation a. John didn’t read any papers. b. * John read any papers. (2) Under negative quantifiers a. Few/no/at most 3 students read any papers. b. *Many/most students read any papers. 1 [Acknowledgement to

be added.] NPIs (e.g., any, ever) can appear in any DE environments, while strong NPIs (e.g., in weeks, until, either) can only appear in a limited subset of DE environments such as under clause-mate negation or under negative quantifiers. I will not discuss strong NPIs in this paper. But the licensing condition of strong NPIs can be easily captured by the present exhaustification-based proposal. See more in footnote 10. 2 Weak

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(3) Left argument of universal quantifiers a. Every student who has read any papers passed the exam. b. *Every student who has read some papers passed any exams. c. *Some student who has read any papers passed the exam. (4) Antecedent of conditionals a. If John knows any big names, he will be invited. b. *If John is invited, he will know any big names. A context is DE if it supports a downward inference. For instance, observe in (5) and (6) that a downward inference holds from a set to its subset in the left argument of the universal quantifier every, but not in the left argument of the existential quantifier some. (5)

a. Every student passed the exam. b. →Every smart student passed the exam.

(6)

a. Some student passed the exam. b. 6→ Some smart student passed the exam.

The DE-based account of NPI-licensing is schematized in (7), adopted from von Fintel (1999) and Gajewski (2007). (7)

a. An NPI is grammatical iff it appears in a constituent that is DE w.r.t. to this NPI. b. A constituent A is DE w.r.t. α of type δ iff the function λ x.JA[α /vδ ]Kg[vδ →x] is DE. [A[α /v] is the result of replacing α with v in A.] c. A function f of type < σ , τ > is DE iff for all x, y of type σ s.t. x ⊆ y: f (y) ⊆ f (x). [“⊆” stands for cross-categorical entailment]

Klima (1964) firstly observed that the exclusive focus particle only can also license NPIs. The prototypical NPI ever, for instance, can be licensed under in the following sentence. (8) Only young writers ever accept suggestions with any sincerity.

(Klima 1964: 311)

The emphatic expression any, likewise, can be licensed as an NPI in the right argument of NP-only or in the immediate scope of VP-only, as shown in (9) and (10), respectively. Here and throughout the paper, I use CAPITAL letters to mark stressed items, and the F subscript to mark the semantic focus. (9) Right argument of NP-only a. Only JOHNF read any papers. b. *JOHNF read any papers. c. *Only any students saw John. (10) Under VP-only a. Mary only gave any funding to JOHNF . b. *Mary gave any funding to JOHNF . 2

One empirical constraint having been observed for the NPI-licensing effect of only is that NPIs cannot appear within the semantic focus or any focus-contained island (Wagner (2006), among the others). In particular, NP-only does not license NPIs in its left argument, as we have seen in (9c); and VP-only, for instance, cannot associate with or into an anyP, as shown in (11): when only directly associates with the determiner any, the entire DP any paper, or the NP complement paper, the NPI any is not licensed. Here (11c) is to illustrate the inviability of associating only into an NPI-contained island: according to Abels 2003, the complement of a phasal head (e.g., the D head any) cannot move by itself, stranding its embedding phrase head, but must always pied-pipe that phrase head; therefore the anyP in (11c) exhibits an island-effect, to the extent that the NP complement cannot be moved out of the anyP. (11)

a. *John only read ANYF papers. b. *John only read [any PAPERS]F , (he didn’t read every book). c. *John only read any PAPERSF , (he didn’t read any books).

Another constraint with respect to NPI-licensing that I want to draw your attention to is that the licenser only has to be used overtly. This constraint may seem obvious, but it is theoretically important for understanding covert exhaustifications. Consider the corresponding some-sentence to (9b) in (12). It yields an exhaustivity inference regardless of whether the exclusive focus particle only is pronounced. (12) Everyone slept the day away, (only) JOHNF read some paper. Hence it is plausible to say that in (9b) and (12) the semantic focus is associated with a covert exhaustivity operator (notation: O). Accordingly, the requirement of spelling-out only can be reduced to a contrast with respect to NPI-licensing between the overt focus particle only and the covert operator O, namely that overt only is an NPI-licenser while covert O is not.3 Thus, the contrasts in (9a-b) and (10a-b) can be represented as in (13a) and (13b), respectively. (13)

a. Only/*O JOHNF read any papers. b. Mary only/*O gave any funding to JOHNF .

More interestingly, despite the NPI-licensing effect of only, there are cases where spelling-out only makes a licensed PI unlicensed, which I call a “PI-unlicensing effect”. For instance, in (14a) the NPI any is licensed under negation, but in (14b) adding an occurrence of only over negation and associating this only with the NPI any make this any unlicensed. Likewise, in (15a) the FCI any is licensed by a weak modal, but an unlicensing effect arises in (15b) where an overt only associates with the FCI any across over the weak modal. These unlicensing effects, however, are not observed in the corresponding O-sentences in (14c) and (15c). (14)

a. John didn’t read any papers.

3 This contrast is also observed with the other exclusive focus particle exactly: to license the NPI any in the unassociated part, the focus particle exactly must be spelled-out.

(1)

a. Exactly two students read any readings at all. b. *Two students read any readings at all are.

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b. *John only didn’t read ANYF papers. c. John O didn’t read ANYF papers. (15)

a. You are allowed to read any paper. b. *You are only allowed to read ANYF paper. c. You are O allowed to read ANYF paper.

The contrasts on PI-unlicensing between only and O are more prominent for the analyses of NPI-licensing from the G(rammatical)-view of exhaustification (Chierchia 2006, 2013; Fox 2007; among the others). According to this line, PI-licensing effects are results of interacting PIs with covert O-operators: a PI is licensed only if exercising an O-operator does not yield a G-triviality. In particular, under the formalizations by Chierchia (2006, 2013), (14a) and (15a) would take the LFs in (16a) and (16b), respectively, each of which contains a covert OD -operator at the left edge associating with any. (See section 2.2.2 and section 4.3 for more details.) The contrasts between only and O shown in (14b-c) and (15b-c) suggest that the OD -operators in (16) cannot be spelledout as the exclusive focus particle only; in other words, overt only exhibits a PI-unlicensing effect, but covert O does not. (16)

a. OD not [John read any papers] b. OD-E XH ✸ [John read any paper]

To sum up, this article will investigate two questions, namely the NPI-licensing effect of only and the contrastive licensing or unlicensing behaviors between only and O with respect to PIs. The remainder of this paper is organized as follows. Section 2 and section 3 will be centered on the NPI-licensing effect of only. In particular, section 2 will show that neither the F(ocus)-movement theory (Wagner (2006)) nor the G-view of exhaustification (Krifka 1995; Lahiri 1998; Chierchia 2006, 2013) can properly address the NPI-licensing effect of only by its own. Thus in section 3, I will propose an approach that incorporates features of both theories, built up from an assumption that F-movement is motivated by the requirement of avoiding contradictions. Section 4 will turn to the puzzling distinctions between only and O with respect to PI-licensing and PI-unlicensing. In section 4.1 and 4.2, I will argue that the distinctions with respect to the NPI-licensing effect in (13) and the NPI-unlicensing effect in (14) can be attributed to the nature of the prejacent inference and the status of the additive presupposition, respectively. In section 4.3, I will show that overt only has no pre-exhaustification use and argue that its FCI-unlicensing effect is due to the failure of satisfying its additive presupposition.

2. Previous studies This section will review two popular theories on the NPI-licensing effect of only. One is the Fmovement theory by Wagner (2006), and the other is the G-view of exhaustification, along the lines of Krifika (1995), Lahiri (1998), and Chierchia (2006, 2013).

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2.1. The theory of F-movement 2.1.1. The SDE-condition The invalidity of downward inferences under only, firstly indicated by Atlas (1993, 1996), casts a doubt to Fauconnier-Ladusaw’s strict DE-account of NPI-licensing. or instance, while a weak NPI can be licensed when appearing in the right argument of NP-only and within the unassociated part of VP-only, those contexts do not support downward inferences, as shown in the following. (17) Right argument of NP-only4 a. Only JOHNF ate vegetables for breakfast . b. 6→ Only JOHNF ate kale for breakfast. (18) Under VP-only a. John only ate VEGETABLESF for breakfast. b. 6→ John only ate KALEF for breakfast. Considering this problem, von Fintel (1999) proposes an S(trawson)DE-condition, as schematized in (19). The SDE condition, to the extent that it grants all presuppositions of the consequence when the validity of a downward inference is assessed, is weaker than the canonical DE condition. (19)

a. An NPI is only grammatical if it is in the scope of a function f such that f is SDE. b. A function f of type < σ , τ > is SDE iff for all x and y of type σ such that x ⊆ y and f (x) is defined: f (y) ⊆ f (x).

Further, von Fintel (1999) argues that only is an SDE function, given that the the complement of only is DE once if the prejacent presupposition is satisfied, as illustrated by the reasoning in (20). (20) Kale is a vegetable. John ate kale for breakfast. Only John ate vegetables for breakfast. ∴ Only John ate kale for breakfast

x⇒y f (x) is defined f (y) ∴ f (x)

2.1.2. Wagner (2006) The SDE condition alone still cannot explain why the exclusive focus particle only cannot license an NPI any when F-associated with or into the anyP. In response to this question, Wagner (2006) adopts the SDE condition and proposes a theory of F(ocus)-movement. He firstly assumes that the exclusive focus particle only has two syntactic arguments, including a syntactic restrictor and a scope. In the case of NP-only, the restrictor and the scope correspond to the left argument and right argument, respectively. 4 Horn

(2009, to appear) points out that the downward inference still holds if the left argument of NP-only is not a proper name but a count noun. (1)

a. Only GRADUATES ate kale for breakfast. b. → Only STUDENTS ate kale for breakfast.

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(21)

onlyP

only restrictor

scope

In particular, the scope of only is SDE but the restrictor is not. For instance, when the prejacent presupposition of only is granted, a downward inference is supported in (22) but not in (23). (22) Kale is a vegetable. John ate kale. Only JOHNF ate vegs. ∴ Only JOHNF ate kale

x⇒y f(x) is defined f (y) ∴ f (x)

(23) Smart students are students. Smart students ate kale. Only STUDENTSF ate kale. 6→ Only [smart students]F ate kale.

x⇒y f(x) is defined f (y) 6→ f (x)

Further, Wagner assumes that VP-only association always invokes a covert phrasal movement of the focused expression to the syntactic restrictor of only. For cases where only associates into an island, he assumes that F-movement is sensitive to islands (cf. Anderson 1972, Jackendoff 1972, Rooth 1985) and that it is the minimal F-contained island that undertakes F-movement (as in Drubig 1994). For instance, what gets F-moved in the following examples would be the complex DP and the when-clause. (24)

a. Dr. Smith only rejected [the proposal that JOHNF submitted]. b. Dr. Smith only complains [when BILLF leaves the lights on].

This analysis immediately predicts that an NPI is not licensed in the immediate scope of VPonly once if this NPI appears within the F-moved constituent. This prediction is fully compatible with the observations in (10) and (11), repeated below in (25). (25)

a. b. c. d.

Mary only give any funding to JOHNF . *John only read ANYF papers. *John only read [any PAPERS]F , (he didn’t read every book). *John only read any PAPERSF , (he didn’t read any books).

In (25a), the focused NP moves alone to the syntactic restrictor of only, while the NPI any stays and gets licensed within the scope part, as illustrated in (26a). In (25b-d), in contrast, the NPI any is part of the F-moved constituent, therefore is not licensed, as illustrated in (26b). (26)

a. NPI is licensed

b. NPI is not licensed

VP only

VP

JOHNF,i

only

Mary gave any funding to ti

DPi

John read ti

ANYF papers/[any PAPERS]F /any PAPERSF

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It is important to note that in (25b-d) the F-moved expression has to be the entire anyP, regardless of whether only associates with the entire anyP or with just a sub-constituent of the anyP (namely, the determiner any or the complement NP). On the one hand, the D head any cannot be F-moved alone, because F-movement is a phrasal movement. On the other hand, according to Abels 2003, the complement of a D head always pied-pipes that D head; therefore, once the NP complement of the NPI any is forced to take F-movement, the entire anyP would be F-moved. 2.1.3. Problems with the F-movement theory Despite of many advantages, Wagner’s (2006) analysis faces several empirical or conceptual problems. NPI-licensing condition Like its predecessors, Wagner (2006) does not provide an explanation as to why NPIs are not licensed in non-(S)DE contexts; saying that NPIs must appear in SDE contexts or DE contexts is still a description. What’s more, although Hsieh (2012) develops an explanation to the NPI-licensing effect of only based on Wagner (2006), recent works on NPIs point out some empirical problems with the SDE condition, arguing that this condition is neither necessary nor sufficient. On the one hand, as Crniˇc (2011) indicates, another prototypical focus-sensitive expression exactly two licenses NPIs in its left argument, but exactly two is non-presuppositional and hence by no means SDE; therefore the SDE condition is unnecessary for NPI-licensing. (27) Exactly two students did any reading at all. On the other hand, the SDE condition appears to be insufficient. For instance, DPs like the student and both students are SDE in their left arguments. If being SDE condition were sufficient for NPIlicensing, then the following sentences would be grammatical (Gajewski 2011, Chierchia (2013)). (28)

a. * The student who had any linguistics did well. i. Presupposition: | studentsw | = 1 ii. Assertion: studentsw ⊆ did wellw b. * Both students who had any linguistics did well. i. Presupposition: | studentsw | = 2 ii. Assertion: studentsw ⊆ did wellw

To sum up the main problem with a single sentence: Wagner’s (2006) analysis lacks of an explanation to the NPI-licensing condition independent from the SDE-condition.5 Motivation of movement & semantics of only Wagner (2006) argues that the exclusive focus particle only presupposes an existential premise rather than the truth of its prejacent (Horn 1996, cf. Horn 1969). He schematizes the lexical entry of only as in (29), where the arguments f and P correspond to the syntactic restrictor/complement and the scope, respectively. (29)

a. JonlyK( f )(P) = ∀a ∈ C[P(a) → P( f ) ⊆ P(a)]

5 See

Gajewksi (2011) and Crniˇc (2014a) for details as to how the G-view overcomes the problems with the SDE condition.

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b. Presupposition: ∃x.P(x) Note that the existential presupposition schematized in (29b) is unconventional; it is generated by abstracting directly over the complement of only, rather than over the semantic focus (cf. Horn 1996). For instance, (30) and (31) have the same semantic focus (i.e. basketball) but different existential presuppositions: the existential import abstracts over the NP “basketball” in (30) but over the entire VP “played basketball” in (31). Here Wagner uses underlining to mark the syntactic complement or the syntactic restrictor of only, pcorner symbolsq to mark the scope of only, and italics to mark the semantic focus. (30) With F-movement: a. John only pplayed basketballq. b. Presupposition: ∃x. John played x.

(31) Without F-movement: a. John only pplayed basketballq b. Presupposition: ∃x. John x-ed.

Next, adopting the Maximize Presupposition Principle from Heim (1991), Wagner assumes that F-movement is motivated to strengthen the existential presupposition of only: “F-movement minimizes the size the of the syntactic restrictor, which may have an effect on the strength of the statement that is grammatically encoded by the sentence.” (Wagner 2006: 314) For instance, For instance, the existential presupposition of only in (30) is stronger than the one in (31), motivating an F-movement.the semantic focus basketball. Aside from the debate as to whether only has an existential presupposition (Horn 2002, 2009, to appear; Ippolito 2006; van Rooij and Schulz 2007), a more serious and immediate problem with Wagner’s manipulation is that the existential presupposition he assumes predicts overly strong readings for cases where only associates into an island. Recall Wagner’s stipulation that the existential presupposition of only is generated by abstracting over the syntactic complement of only, rather than over the semantic focus. Then to keep the consistency with the lexicon of only, we have to conjecture that the quantificational domain of only, namely the contextual variable C in (29a), would be generated by abstracting over the complement of only as well; in other words, if the F-moved constituent is of type α , then the variable C would be the set of all the contextually relevant items of type α (cf. Rooth 1985, 1992). Consider (32) for instance to see why these unconventional definitions of the domain variable C and the existential presupposition are problematic. (32) Sue only p invited JOHNF ’s advisors q. a. → Sue didn’t invite anyone’s advisors except John’s advisors. b. 6→ Sue didn’t invite anyone except John’s advisors. Under the F-movement theory and the Left-Branch Extraction Constraint (Ross 1967, 1986), the entire possessive NP, JOHN’s advisors, as the minimal F-contained island, would be F-moved to the syntactic restrictor of only. Then following the lexical entry in (29), we would predict that the only-sentence (32) presupposes Sue invited someone rather than Sue invited someone’s advisors. Likewise, we would predict that the quantificational domain C includes all individuals, not just individuals that are someone’s advisors. If those predictions were correct, however, (32) would take the overly strong reading in (32b).

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Island-(in)sensitivity Wagner (2006) assumes that F-movement is sensitive to island-effects (cf. Anderson 1972, Jackendoff 1972, Rooth 1985); when only associates into an island, it is the minimal F-contained island that undertakes F-movement. The main merit of this assumption is that it captures the Island Restriction: “Association with a constituent within an island cannot license an NPI in the same island.” (Wagner 2006: 312) In other words, only cannot associate into an NPIcontained island. This restriction follows the contrast that the NPI any is licensed in (33b) but not in (33a): in (33a), only associates into the because-clause, therefore it is the whole because-clause, including the NPI any, that moves to the syntactic restrictor of only; while in (33b), the NPI any stays outside the because-clause, and hence it does not participate in the F-movement. (33)

a. *Mary only gave a book to John [because BILLF gave any book to him]. b. She only gave anything to anyone [because YOUF did].

Nevertheless, this analysis has difficulties with predicting the island-insensitivity of multi-foci constructions. For instance in (34), the complex NP island contains two focis (MARILYN and BOBBY) associated with different operators (only and also, respectively). If here the F-associations were both realized by F-movement, then the complex NP island (accompanied by the D head the) would have to be moved to the restrictor of only as well as to the restrictor of also. Such an operation is clearly untenable. (34) We only1 recovered the diary entries that MARILYNF1 made about John. We also2 only1 recovered [the diary entries that MARILYNF1 made about BOBBYF2 ]. To fix this problem, Wagner claims that the complex NP island in (34) is moved to the restrictor of only but not to the restrictor of also, based on the impossibility of extracting from beneath only (Beaver and Clark 2003).6 Nevertheless, if F-association with also can be realized at a distance, then we would expect F-association with only to be allowed at a distance as well, contrary to Wagner’s claim that VP-only association always invokes a covert F-movement. Association with licensed NPIs Recall Wagner’s (2006) prediction that an NPI is not licensed under only if it is part of the F-moved constituent. Conjoining this prediction with his claim that F-movement is mandatory for VP-only association, we get a stricter constraint stated as follows: VP-only cannot associate with an NPI or an NPI-contained island within which the NPI is not licensed. This constraint, however, is too strong for cases like (35), where only associates with the anyP across another NPI-licenser (i.e. clause-mate negation); 6 The following two

examples illustrate Beaver and Clark’s (2013) main observation. In (1), only can associate with the c-commanding item chocolate, but not with the extracted item the guy. While in (2), the focus-sensitive operator always can associate with both items. (1) Kim is the guy who Sandy says she only gives chocolate. a. × ‘Kim is the guy such that Sandy says she gives him and nobody else chocolate.’ √ b. ‘Kim is the guy such that Sandy says she gives him chocolate and nothing else.’ (2) Kim is the guy who Sandy says she always gives chocolate. √ a. ‘Kim is the guy such that Sandy says she gives him and nobody else chocolate.’ √ b. ‘Kim is the guy such that Sandy says she gives him chocolate and nothing else.’

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(35) Mary only didn’t give [any FUNDing]F to John. (She did her best to help him.) The stricter constraint drawn above predicts (35) to take the following LF, under which the NPI any would not be licensed: the anyP, as the minimal F-contained island, would be moved to the syntactic restrictor of only, a context that is non-SDE and cannot license NPIs.7 (36) VP only

DPi Mary didn’t gave ti to John

any funding

Not only Although the exclusive focus particle only and the clause-mate negation are both NPIlicensers, they two together do not necessarily license NPIs. As illustrated in (37), when embedded under a clause-mate negation or appearing inside the complement clause of a negated neg-raising predicate (i.e. believe, think), only does not license the NPI any. This phenomenon can also be described as “an NPI-unlicensing effect of negation”, to the extent that applying negation over only makes the NPI, which should have been licensed by only, unlicensed. This phenomenon can also be described as “negation bleeding the NPI-licensing effect of only”. (37)

a. Mary didn’t only give some/*any funding to JOHNF . b. Sue doesn’t think that Mary only gave some/*any funding to JOHNF .

Wagner (2006) cannot address this phenomenon: in (37), the use of NPI any satisfies all the constraints that Wagner has made, namely, it appears within the immediate scope of VP-only and outside the F-moved constituent. More generally speaking, the NPI-unlicensing effect of negation suggests that the licensing of an NPI is determined not only by the local environment between the licenser and the NPI (for instance, the monotonicity pattern of onlyP with respect to the NPI) but also by the environment beyond the projection of the licenser (for instance, the clause-mate negation that embeds the onlyP). This observation poses a doubt to all the currently available syntactic and semantic lines on NPI-licensing that I am aware of, except the G-view of exhaustification. I will address this problem in section 3.5 following the basic assumptions of the G-view. Head restriction In addition to the Island Restriction shown above, Wagner (2006) claims that his analysis is also followed by the so-called “Head Restriction”, which says that “if only associates with the head of a constituent, it does not license NPIs in the complement of the head.” (Wagner (2006): 310) This restriction is a schematic description for the failure of NPI-licensing in sentences like (38), where only directly associates with a verb that takes an anyP complement. (38) *John only CUTF any vegetables. 7

Note that the NPI any is not licensed if only merely associates with any. See section 4.2 for explanations.

(1) How much funding is such that Mary didn’t give to John? *Mary only didn’t give ANYF funding to John.

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In response to the ungrammaticality of (38), Wagner argues that what gets F-moved in (38) is the entire VP, including the anyP, because the focused verb (as a head) alone cannot take Fmovement (as a phrasal movement). This explanation, however, as Jon Gajewski points out to Wagner (2006: fn. 14), is still insufficient: the anyP should be allowed to vacate the VP, and the remnant VP subsequently associate with only. Moreover, the Head Restriction does not apply to the conditional sentence (39), which takes the only-clause (38) as its antecedent. Therefore, an alternative analysis is needed to capture the ungrammaticality of (38) as well as the contrast between (38) and (39). (39) If John only CUT any vegs (and didn’t STEAM any vegs), Mary would be unhappy. Summary Wagner’s (2006) F-movement theory faces the following problems: (i) it does not explain the NPI-licensing condition; (ii) F-movement is not well-motivated; (iii) the unconventional lexical entry of only predicts overly strong readings in the cases of associating only into an island; (iv) it cannot capture the island-insensitivity of multi-foci constructions; (v) it overly excludes the possibility of associating only with a licensed NPI; (vi) it cannot address the failure of licensing NPIs under not only (namely the NPI-unlicensing effect of negation); (vii) the Head Restriction is theoretically and empirically problematic. 2.2. The G-view of exhaustification 2.2.1. The G-view of scalar implicatures The G-view of exhaustification (Chierchia 2006, Fox 2007, Chierchia et al. 2012, among the others) is firstly introduced to analyze scalar implicatures. This view argues that the phenomenon of scalar implicature is not purely pragmatic (cf. Grice 1989), given the fact that scalar implicatures can be generated in embedding contexts. The main idea of the G-view is as follows. First, propositions containing scalar items are associated with sets of alternative, which are computed in the same way as the answer sets of questions (Hamblin 1973) and the alternative sets of focus (Rooth 1985, 1992). A recursive definition of alternative sets is schematized as below, adopted from Chierchia (2013). (40) Basic Clause: For any lexical entry α , ALT(α ) = a. {Jα K} if α is lexical and does not belong to a scale; b. {Jα1 K, ..., Jαn K} if α is lexical and part of a scale hJα1 K, ..., Jαn Ki. Where ALT is a function from expressions to a set of interpretations. (41) Recursive Clause: ALT(β (α )) = {b(a) : b ∈ ALT(β ), a ∈ ALT(α )} Next, alternatives keep growing until factored into meaning via a covert exhaustivity operator O (also notated as “EXH” in some works). The O-operator affirms the prejacent and negates all

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the alternatives that are not entailed by the prejacent, as schematized in (42).89 The non-entailed alternatives are also called excludable alternatives. (42) O(p) = p ∧ ∀q ∈ ALT(p)[p 6⊆ q → ¬q] Accordingly, a scalar implicature is derived as a logic consequence of applying an O-operator over a sentence containing a scalar item. For instance in (43), applying an O-operator over the some-sentence (notation: φSOME ) affirms the prejacent φSOME and negates the stronger alternative φALL , yielding the scalar implicature ¬φALL . (43)

a. Some of the students came. Not all of the students came. b. ALT(φSOME ) = {φSOME , φALL } c. O(φSOME ) = φSOME ∧ ¬φALL

2.2.2. The G-view of NPIs Chierchia (2006, 2013) extends the G-view of scalar implicatures to the issue of NPI-licensing with assumptions compatible with the Alternative Semantics (Rooth 1985, 1992, 1996) and the standard DE condition (Fauconnier 1975, 1979; Ladusaw 1979). He proposes that the NPI any is an indefinite existential item like some but encoded with a grammatical feature [D]. This feature obligatorily activates a set of domain (D)-alternatives and must be checked off by a c-commanding OD -operator. Exercising an OD -operator over a sentence containing an occurrence of any has consequences in both syntax and semantics: in syntax, it checks off the [D] feature in the lexicon of any, just like a regular feature-checking operation; in semantics, it affirms the assertion and negates D-alternatives that are not entailed by the assertion. A schematic example for the total domain D and its corresponding D-alternative sets is as follows. The D-alternative set includes the prejacent, while the proper D-alternative set does not. (44)

a. Total-D: {a, b} b. Sub-D: {a, b}, {a}, {b} c. Proper sub-D: {a}, {b}

Assertion = ∃x ∈ {a, b} f (x) D-ALT = {∃x ∈ {a, b} f (x), ∃x ∈ {a} f (x), ∃x ∈ {b} f (x)} Proper D-ALT = {∃x ∈ {a} f (x), ∃x ∈ {b} f (x)}

Consider the basic positive sentence in (45) to see how the G-view captures the DE condition of NPI-licensing. With an indefinite existential expression any, the sentence (45) asserts the existential inference in (46b). Moreover, the [D] feature of any activates a set of D-alternatives, generated by substituting the total domain D with a subdomain D′ , as schematized in (46c). Crucially, the monotonicity pattern of the entire clause with respect to the NPI any is upward-entailing (UE), and hence the proper D-alternatives are not entailed by the assertion. Next, applying OD negates all 8 Here

and throughout the paper, the symbols O and p are sloppily used for both syntactic phrases and truth conditions. A stricter semantic representation of O is as follows, where S is the immediate c-commanded phrase of O. (1) JO

w,g ′ ′ ′ SK = JSK(w) ∧ ∀S ∈ ALT(S)[JSK 6⊆ JS K → ¬JS K(w)]

9 Note

that the O-operator used in this article negates all non-entailed alternatives, different from the one proposed by Fox (2007), which negates only alternatives that can be negated consistently (viz. the so-called “innocently excludable alternatives”).

12

the proper D-alternatives, yielding the exhaustivity inference in (46d), which however contradicts the asserted existential inference (46b), as shown in (46e). This contradiction makes the sentence ungrammatical and the NPI any unlicensed. (45) *John read any papers. (46)

a. OD [John read anyD papers] b. Assertion: ∃x ∈ D[P(x) ∧ R( j, x)] (John read some papers in the total domain D) c. D-ALT = {∃x ∈ D′ [P(x) ∧ R( j, x)] | D′ ⊆ D} d. ∀D′ [D′ ⊂ D → ¬∃x ∈ D′ [P(x) ∧ R( j, x)]] (for any proper subdomain D′ , John read no paper in D′ ) e. J(46a)K = J(46b)K ∧ J(46d)K = ⊥ (# John read some papers in D, but he read no paper in any proper sub-domain D′ )

Consider the mini model in (47) for a simpler illustration of this idea. Assume that the total domain D contains exactly two items, paper p1 and paper p2. The D-alternative set is thus schematized as in (47b), containing exactly three elements: the asserted proposition John read a paper in {p1 , p2 } and two proper D-alternatives including John read a paper in {p1} and John read a paper in {p2}. The proper D-alternatives are not entailed by the assertion. Therefore, applying an OD -operator affirms the assertion and negates both proper D-alternatives, yielding the contradictory inference John read p1 or p2 , and he did not read p1 , and he did not read p2 , as schematized in (47c). (47)

a. D = {p1 , p2 } b. D-ALT = {R( j, p1 ) ∨ R( j, p2 ), R( j, p1), R( j, p2 )} c. R( j, p1 ) ∨ R( j, p2 ) ∧ ¬R( j, p1 ) ∧ ¬R( j, p2 ) = ⊥

The contradiction in (46e) is essentially different from the one in (48). The former one makes the utterance ungrammatical, while the latter one makes the utterance infelicitous but not ungrammatical. (48) # It is raining and it isn’t raining. To tell them apart, Chierchia (2013) adopts the notions from Gajewski (2002) and describes the contradiction in (46e) as “G(rammatical)-triviality”, a special case of L(ogical)-triviality. Ltrivialities are tautologies or contradictions in the traditional sense. While G-triviality means that a sentence receives the same value (1 or 0) regardless of how the lexical terminals are replaced in the structure. Compare the following sentences for instance. Expressions like John, smokes, and student are lexical terminals, and the rest are functional terminals. The contradiction in (49a) can be avoided if the two occurrences of smoke are substituted with distinct lexical items (e.g. John smokes and doesn’t dance). In contrast, the meaning of (49b) is always contradictory no matter which lexical items are used. Therefore, we identify (49a) as L-trivial, while (49b) as both L-trivial and G-trivial. (49)

a. # John smokes and doesn’t smoke. b. * Some student but John smokes.

[ x P and not P ] [ some P but x Q ] 13

It might be counter-intuitive to consider the truth value of (49b), as in a traditional sense we do not judge the truth value of an ungrammatical sentence. For the purposes of this paper, it is enough to vaguely understand “G-triviality” as a type of L-triviality assessed at the grammatical level. Under the G-view, the contradiction in (46e) can be avoided only if the OD -operator is applied immediately over a constituent that is DE with respect to the NPI any. Consider the basic negative sentence in (50) for instance. By virtue of the DE-operator negation, all the D-alternatives are entailed by the assertion and therefore not excludable. The OD -operator, although has to be present to check off the grammatical feature [D], is vacuous in semantics. (50) John didn’t read any papers. (51)

a. O [John didn’t read anyD papers] b. Assertion: ¬∃x ∈ D[P(x) ∧ R( j, x)] (John read no paper in the total domain D.) c. D-ALT = {¬∃x ∈ D′ [P(x) ∧ R( j, x)] | D′ ⊆ D} d. J(50a)K = J(50b)K = ¬∃x ∈ D[P(x) ∧ R( j, x)] (John read no paper in the total domain D.)

2.2.3. Extending the G-view to only Krifka (1995), Lahiri (1998), and Chierchia (2006, 2013) extend the G-view of NPIs to the case of the exclusive focus particle only. They adopt the lexical entry of only from Horn 1969, which assumes that only asserts an exhaustivity inference and presupposes the truth of its prejacent. The unfocal part of the asserted exhaustivity inference, crucially, is DE and hence is capable of being an NPI- licensing environment. For instance, under the schematic notations in Chierchia (2013), the only-sentence (52) takes the LF in (53a). This LF contains two exhaustification operators, OD and only, checking off the [D] feature of any and the [F] feature of the semantic focus, respectively. The prejacent presupposition (an existential inference) and the asserted exhaustivity inference are schematized as in (53b) and (53c), respectively. The D-alternatives are generated from the assertion by replacing the total domain D with a subdomain D′ , as schematized in (53d). (52) Only JOHNF read any papers. (53)

a. OD [only [JOHNF read anyD papers ]] b. Presupposition: ∃x ∈ D[P(x) ∧ R( j, x)] (John read a paper in the total domain D.) c. Assertion: ∀y ∈ De [∃x ∈ D[P(x) ∧ R(y, x)] → j ⊆ y] (For any individual y, if y read a paper in the total domain D, then y is John.) d. D-ALT = {only [JOHNF read anyD′ paper] : D′ ⊆ D } = {∀y ∈ De [∃x ∈ D′ [P(x) ∧ R(y, x)] → j ⊆ y] | D′ ⊆ D}

The presupposed component (52b), as argued by Gajewski (2011) and extended by Chierchia (2013), is irrelevant for assessing the [D] feature of weak NPIs like any.10 The asserted component 10 Gajewski

(2011) proposes that presuppositions and implicatures are relevant only for assessing the [D] feature of

14

(53c) is DE with respect to the focused part (underlined), where the NPI any appears. Therefore, the NPI any is licensed in (52), as it would be in any DE contexts. To sum up, the G-view provides an explanation to the DE condition of NPI-licensing: checking off the [D] feature of any with a covert OD -operator yields a contradiction/G-triviality, if and only if the OD -operator is applied immediately over a constituent that is non-DE with respect to this NPI. As for case of only, the G-view shows that the assertion of an only-clause is DE in the unfocal part, which therefore gets (weak) NPIs licensed. 2.2.4. Problems with the G-view The G-view, however, is not yet the best solution. As a successor of Roothean Alternative Semantics (Rooth 1985, 1992, 1996), the G-view assumes that focus is interpreted in-situ and that F-alternatives are propositional. For both NP-only and VP-only, this view defines their quantificational domains as proposition sets (notation: ALT (p)). (54) JonlyK(p) = ∀q ∈ ALT (p)[q → p ⊆ q ] Nevertheless, to capture the NPI-licensing effect of only, the quantificational domain of only should not be a proposition set. In (54), we can easily see that the boxed position for q is nonDE. To be more accurate, let us look at a stricter representation for the asserted component of the only-sentence (52). If the F-alternatives were propositional, then the assertion of (52) would be schematized as follows. (55) ∀q ∈ ALT (p)[ q → ∃x ∈ D[P(x) ∧ R( j, x)] ⊆ q ]

where ALT (p) = {∃x ∈ D[P(x) ∧ R(y, x) | y ∈ De }

Here the quantificational domain of only is characterized as a set of propositions in the form of “y read a paper in the total domain D”, where y is a relevant individual. This schematic representation has three positions relevant to the assessment of the [D] feature, each marked with a box. The first boxed position, as the restriction of a universal quantification, is DE; but the latter two boxed positions, as within the scope of the universal quantification, are UE. Therefore, under this representation, the entire assertion would be non-monotonic with respect to the NPI any, which however would predict the NPI any to be unlicensed in (52). Hence, to capture the NPI-licensing effect of only, the G-view has to give up its own convention and write the quantificational domain of only as a set of individuals (namely De ), as we have seen in (52c) and repeated below. In this representation, only the restriction part of the universal quantification is relevant to the assessment of the [D] feature. (56) ∀y ∈ De [ ∃x ∈ D[P(x) ∧ R(y, x)] → j ⊆ y] strong NPIs. This proposal captures the contrast between weak NPI-licensing and strong NPI-licensing under only. For instance, only does not license the strong NPI in years in the unfocal part. (1) *Only JOHN came in years. The prejacent presupposition of only is purely UE, making the entire only-clause non-monotonic with respect to the strong NPI in years. Then applying OD to assess the [D] features in the prejacent and assertion yields a contradiction. See Chierchia (2013) for extensive discussions.

15

This problem is severer in the case of VP-only. While NP-only has a chance to generate nonpropositional F-alternatives without any additional operation,11 VP-only does not. If focus were always interpreted in-situ, then built up compositionally, the F-alternatives associated with VP-only would have to be propositional.

3. My analysis: A G-view of exhaustification with F-movement Wrapping things up, I have shown that neither the F-movement theory nor the G-view can properly address the NPI-licensing effect of only on its own. On the one hand, the F-movement theory is lacking of an explanation to the NPI-licensing condition. On the other hand, the G-view does provide a plausible explanation to the licensing condition, but this explanation relies on an operation (e.g., F-movement) that can split up the c-commanding domain of only and create a DE-context. In such a situation, a natural move would be to incorporate F-movement into the G-view. To integrate the F-movement with the G-view, the only needed assumption is as follows. (57) Motivation of F-movement The requirement of avoiding G-trivialities motivates F-movement. A question arises as to why logical inferences motivate syntactic operations. I would link this question to the architecture of the universal grammar. Chierchia (2006, 2013) indicates that the structure-building apparatus (e.g., Merge, Move, Agree) and the inferential one are not radically different; “grammar only sees functional/logical material; logic sees functional/logical material and whether the lexical material is the same or different.” (Chierchia 2013: 444) The notion of Gtriviality, in particular, relates logic tightly to grammar, as a L-triviality taking effects in grammar. It is worthy of noticing that G-triviality is assessed at LF, therefore the rule (57) only applies to covert movement, not to overt movement. For instance, it is not the source of the overt F-movement in languages like Hungarian and Basque (for further instances, see Kiss 1995). The rest of this section is organized as follows. Section 3.1 to section 3.3 will discuss the three basic cases stated in (58a-c), exemplified in (59a-c), respectively. (58)

a. Case 1: F-movement is not motivated b. Case 2: F-movement is motivated and salvages G-trivialities c. Case 3: F-movement is motivated but does not salvages G-trivialities

(59)

a. Mary only didn’t give any funding to JOHNF . b. Mary only gave any funding to JOHNF . c. *Mary only gave [any funding]F to John.

Case 1 covers sentences without NPIs or with NPIs that are licensed by operators other than only. Discussions on Case 2 and Case 3 will explain the NPI-licensing effect of only, in particular, why only licenses NPIs, and why NPIs cannot appear within the semantic focus or an F-contained island. In section 3.4 and section 3.5, I will move onto two special cases, namely the so-called “Head Restriction” and the “NPI-unlicensing effects” in sentences containing two adjacent DEoperators (e.g., not only). 11 For

instance, in the case of NP-only, one can assume that the F-alternatives are defined compositionally from the left argument and factored into meaning as soon as the left argument composes with only.

16

3.1. Case 1: F-movement is not motivated Under the motivation of F-movement assumed above, focus should be interpreted in-situ as long as interpreting it in-situ does not yield a G-triviality/contradiction. For instance in (60), the NPI any can be licensed by the clause-mate negation and hence F-movement is not motivated. (60) Mary only didn’t give anyD funding to JOHNF Only OD not [Mary gave anyD funding to JOHNF ] Assuming F-movement to be a conditional operation can easily overcome Wagner’s problem with the island-insensitivity of the multi-foci construction in (34), repeated in (61), as well as eliminating his incorrect prediction with sentences like (35), repeated in (62), where only associates with an anyP across an NPI-licenser. Under the present analysis, F-movement is not motivated in these sentences, because interpreting focus in-situ does not yield a contradiction: in (61) there is no NPI; in (62), the NPI any is licensed by negation. (61) We only recovered the diary entries that Marilyn made about John. We also1 only2 recovered the diary entries that MARILYNF2 made about BOBBYF1 . (62) Mary only didn’t give [any FUNDing]F to John. She did her best to help him. When focus is interpreted in-situ, F-alternatives are propositional. The asserted meaning of VP-only can be schematized as in (63), à la Rooth (1985, 1992). The propositional letter p stands for the complement of VP-only. JpK f and JpK0 correspond to the focus value of p and the ordinary value of p, respectively: the ordinary value of p is simply the truth value of p; the focus value of p is a set of F-alternatives to p, built up compositionally from the focus value of the semantic focus, as schematized in (64). For the rest part of the denotation in (63), the letters p and q are used sloppily for both syntactic phrases and truth values. (63) JonlyK(p)(w) = ∀q ∈ JpK f [q(w) → JpK0 ⊆ q] = ∀q ∈ JpK f [q(w) → p ⊆ q] (Any true proposition within the focus value of p is entailed by the ordinary value of p.) (64)

a. JαF K f = Dtype(Jα K0 ) b. Jα K f = {Jα K0 } c. Jα (β )K f = {a(b) | a ∈ Jα K f , b ∈ Jβ K f }

Consider the example in (32) again, repeated below. (65) Sue only invited JOHNF ’s advisors. a. → Sue didn’t invite anyone’s advisors except John’s advisors. b. 6→ Sue didn’t invite anyone except John’s advisors. Under the present analysis, the semantic focus is interpreted in-situ, and the quantificational domain of only is the focus value of the prejacent VP, namely a set of propositions in the form of “Sue invited x’s advisors”, where x is a contextually relevant individual. Exhaustifying over this domain yields the desired reading (65a). A schematic composition is given in the following. 17

(66)

a. b. c. d.

JSue invited JOHNF ’s advisorK0 = I[s, A( j)] JJOHNF K f = De JSue invited JOHNF ’s advisorK f = {I[s, A(x)] | x ∈ De } J(65)K = ∀q ∈ {I[s, A(x)] | x ∈ De }[q → I[s, A( j)] ⊆ q] (For any true proposition q in the form of “Sue invited x’s advisors”, q is entailed by the prejacent that “Sue invited John’s advisors.”)

3.2. Case 2: F-movement is motivated Recall the main problem of the G-view: if F-alternatives were propositional, an only-sentence containing an NPI would be non-DE with respect to this NPI. Therefore, to predict the NPI-licensing effect of only in sentences like (67a-b), I assume that the semantic focus (or the F-contained island, if any) has to be moved out of the VP, splitting the VP into two sub-constituents, namely the moved phrase, corresponding to the restrictor of only, and the remnant VP, corresponding to the scope of only. In particular, to distinguish between VP-only and NP-only, I assume that F-movement is covert in (67a) but overt in (67b), as illustrated in (68a) and (68b), respectively. (67)

a. Mary only gave any funding to JOHNF . b. Only JOHNF read any paper.

(68)

a. Covert F-movement

b. Overt F-movement

OD

OD only

JOHNF,i

VP only

Mary gave anyD funding to ti

VP

JOHNF,i

ti read anyD paper

As for the semantics of only, I follow Roothean Alternative Semantics and assume that the quantificational domain of only is the focus value of the F-moved phrase. A cross-categorical definition of only is given in (69), where f and g correspond to the unmoved and moved part, respectively.12 (69) JonlyK( f )(gα ) = ∀g′ ∈ JgK f [ f (g′ ) → JgK0 ⊆ g′ ]

For instance in (70), F-movement is motivated to avoid contradictions. The Left-Branch Extraction Constraint requests the minimal F-contained island, JOHNF ’s advisors, to be moved as a whole. Then the quantificational domain of only would be the focus value of the moved NP, namely the set of (contextually relevant) individuals who are someone’s advisors. 12 ‘⊆’

stands for cross-categorical entailment (von Fintel 1999).

(1)

a. For p, q of type t: p ⊆ q iff p is false or q is true. b. For f , g of type < σ , τ >: f ⊆ g iff for all x of type σ : f (x) ⊆ g(x). In particular, for a, a′ of type e: a ⊆ a′ iff for all P of type < e,t >: λ P.P(a) ⊆ λ P.P(a′ ).

18

(70) Mary only gave anyD funding to JOHNF ’s advisors. (71)

a. JJOHNF ’s advisorsK f = {A(x) : x ∈ De } b. JJOHNF ’s advisorsK0 = A( j) c. J(70)K = ∀y ∈ {A(x) : x ∈ De }[I(s, y) → A( j) ⊆ y] (“For anyone’s advisors y, if Mary invited y, then y is/are John’s advisors.”

The quantificational domain of only defined in (69) (notation: JgK f ) strictly follows Roothean Alternative Semantics; it is built up compositionally from the focus value of the semantic focus. In cases where only associates into an island, the quantificational domain of only defined in (69) would be a proper subset of the variable C that Wagner (2006) assumes in (29), repeated below. (72) JonlyK( f )(P) = ∀a ∈ C[P(a) → P( f ) ⊆ P(a)]

(Wagner 2006)

Although Wagner does not have a clear definition for the variable C, we can conjecture its actual content from Wagner’s assumptions on the existential presupposition of only. Wagner assumes that this presupposition is generated by abstracting over the syntactic complement of only, and that F-movement is used to strengthen this presupposition. These two assumptions imply that the variable C should also be generated by abstracting over the moved phrase; for instance in (70), the C would include all contextually relevant individuals, not just people who are someone’s advisors. 3.3. Case 3: F-movement is unhelpful Recall the fact the focus particle only cannot license an NPI once if it directly associates with the NPI or into the NPI-contained island (without crossing another NPI-licenser). Relevant examples mentioned above are collected in (73). I will show that the reason why NPIs are not licensed in the these examples is that F-movement cannot salvage their G-trivialities/contradictions. (73)

a. b. c. d.

*John read only ANYF papers. *John read only [any PAPERS]F , (he didn’t read every book). *John read only any PAPERSF , (he didn’t read any books). *Mary only gave a book to John [because BILLF gave any book to him].

Consider the basic positive only-sentence (73b) for example, where only associates with the entire anyP. To pursue a stipulation-free analysis, I will consider all possible syntactically wellformed LFs, not only including LFs where the [D] feature of any is assessed by a covert OD , but also including LFs where the [D] feature is assessed by the overt particle only, as shown in (74) and (75), respectively. I will show that all of syntactically well-formed LFs of (73b) yield a semantic contradiction. (74) Assessing [D] with OD a. OD [only [John read [anyD PAPERS]F ]] b. OD [only (anyD PAPERS)F,i [John read ti ]]

Without F-movement With F-movement

(75) Assessing [D] with only a. only [John read [anyD PAPERS]F ]

Without F-movement 19

b. [only (anyD PAPERS)F,i [John read ti ]]

With F-movement

Let’s start with the option that only the covert indexed OD -operator is capable of assessing a [D] feature. If the anyP is interpreted in-situ, as in (76a), then the [D] feature of any will be assessed within the boxed assertion part, which is within the scope of the universal quantification and is a non-DE environment. Then applying OD over the only-clause to check off the [D] feature affirms the assertion and negates all the proper D-alternatives, yielding a semantic contradiction. (76) Without F-movement: a. OD [only [John read [anyD PAPERS]F ]] b. Assertion: ∀q ∈ ALT (p)[q → ∃x ∈ D[P(x) ∧ R( j, x)] ⊆ q] where ALT (p) = {Q(λ x.R( j, x)) | Q ∈ D }

c. D-ALT = {∀q ∈ ALT (p)[q → ∃x ∈ D′ [P(x) ∧ R( j, x)] ⊆ q] | D′ ⊆ D} where ALT (p) = {Q(λ x.R( j, x)) | Q ∈ D }

Alternatively, if the focused anyP is F-moved, it will be interpreted under the immediate scope of OD , which is also a non-DE environement. The main difference between (76) and (77) in semantics is just that the quantificational domain of only is a set of propositions in (76) but a set of generalized quantifiers in (77). (77) With F-movement: a. OD [only (anyD PAPERS)F,i [John read ti ] ] b. Assertion: ∀Q [Q[λ y.R( j, y)] → λ S.∃x ∈ D[P(x) ∧ S(x)] ⊆ Q]

c. D-ALT = {∀Q [Q[λ y.R( j, y)] → λ S.∃x ∈ D[P(x) ∧ S(x)] ⊆ Q] | D′ ⊆ D}

Now move onto the option that the overt focus particle only can check off any alternativerelated features, including the [D] feature. In such a case, the covert OD -operator should be absent from the LF, because there is no unchecked [D] left for it. This option has not been considered by the canonical version of the G-view. But in theory, we have no reason to rule it out. Consider the possibility of interpreting the focused anyP in-situ first. The only-sentence presupposes the truth of its prejacent and asserts the exhaustivity inference, as schematized in (78d) and (78e), respectively. The quantificational domain of only consists of F-alternatives and Dalternatives: F-alternatives are propositions in the form of “John read X ”, where X is a generalized quantifier; D-alternatives are propositions in the form of “John read a book in D′ ”, where D′ is a subset of the total domain D. The asserted exhaustivity inference entails the negation of each proper D-alternative, yielding the inference John didn’t read any paper in any proper subdomain D′ , as schematized in (78f). This inference, however, contradicts the prejacent presupposition John read a paper in the total domain D. (78) Without F-movement: a. only [John read [anyD PAPERS]F ] b. ALTF = {Q[λ x.R( j, x)] | Q ∈ D } c. ALTD = {∃x ∈ D′ [P(x) ∧ R( j, x)] | D′ ⊆ D} 20

d. ∃x ∈ D[P(x) ∧ R( j, x)] (John read a paper in the total domain D) e. ∀q ∈ ALTF,D [∃x ∈ D[P(x) ∧ R( j, x)] 6⊆ q → ¬q] ⇓ f. ∀D′ [D′ ⊂ D → ¬∃x ∈ D′ [P(x) ∧ R( j, x)]] (John didn’t read any paper in any proper subdomain D′ )

Presupposition Assertion

Consider the mini-model below for a simpler illustration of the reasoning in (78). Assume that the total domain D contains exactly two papers, p1 and p2 . The D-alternative set thus contains exactly three propositions, namely John read p1 or p2 , John read p1 , and John read p2 , as schematized in (79b). The exhaustivity assertion of the only-sentence negates both proper D-alternatives, yielding the inference John didn’t read p1 or p2 in (79c), which contradicts the prejacent presupposition John read p1 or p2 in (79d). (79)

a. b. c. d.

D = {p1 , p2 } D-ALT = {R( j, p1 ) ∨ R( j, p2 ), R( j, p1), R( j, p2 )} Assertion entails: ¬R( j, p1 ) ∧ ¬R( j, p2 ) Prejacent Presupposition: R( j, p1 ) ∨ R( j, p2)

This reasoning also applies to the LF in (80), where the anyP is F-moved: the exhaustivity assertion in (80e) entails the inference in (80f), which contradicts the prejacent presupposition in (80d). The major difference between the schematic derivations in (78) and (80) is on the semantic type of their alternatives: in (78), all the alternatives are propositions (of type t); but in (80), all the alternatives are generalized quantifiers (of type ). In particular, the D-alternatives in (80c) are existential quantifiers quantifying over papers in a sub-domain D′ . (80) With F-movement: a. [only (anyD PAPERS)F,i [John read ti ]] b. ALTF = D c. ALTD = {λ S.∃x ∈ D′ [P(x) ∧ S(x)] | D′ ⊆ D} d. ∃x ∈ D[P(x) ∧ R( j, x)] (John read a paper in the total domain D) e. ∀Q ∈ ALTF,D [Q 6⊆ λ S.∃x ∈ D[P(x) ∧ S(x)] → ¬Q[λ y.R( j, y)]] ⇓ ′ ′ f. ∀D [D ⊂ D → ¬∃x ∈ D′ [P(x) ∧ R( j, x)]] (John didn’t read any paper in any proper subdomain D′ )

Presupposition Assertion

To sum up, if only directly associates with an anyP, all the syntactically well-formed LFs of this only-sentence yields a G-trivial/contradictory meaning, making the NPI any not licensed. First, if the [D] feature of any is assessed by the covert OD -operator, the G-triviality would be a logical consequence of the affirmed exhaustivity assertion and the negated proper D-alternatives. Second, if the [D] feature is assessed by overt only, the G-triviality would come from the contradiction between the prejacent presupposition of only and the negated proper D-alternatives. This analysis can easily extend to cases where only associates into a single NPI or an NPI-contained island. 21

3.4. The “Head Restriction” We have seen that the Head Restriction is theoretically and empirically problematic. First, it does not follow Wagner’s basic assumptions; in (81a), the anyP should be able to vacate the VP and be free from F-movement (Jon Gajewski p.c. to Wagner 2006). Second, this restriction does not hold in (81b), a conditional which utters (81a) as its antecedent. (81)

a. *John only CUTF any vegetables. b. If John only CUT any vegs (and didn’t STEAM any vegs), Mary would be unhappy.

The facts in (81) can be predicted by the present analysis. In (81a), vacating from the VP, the anyP can and can only be raised to the place sandwiched between OD and only, as in (82a). Under this structure, the [D] feature of any is assessed under the immediate scope of OD , which is still non-DE; therefore the NPI any cannot be licensed in (81a). In contrast, the conditional (81b) is DE in its antecedent; once the anyP undertakes QR over only, the whole conditional would be DE with respect to the NPI, as illustrated in (82b). Therefore, applying OD over the conditional (81b) does not yield a contradiction, making the NPI any licensed. (82)

a. NPI is not licensed

b. NPI is licensed

OD

OD DPi

anyD vegsi

only

if

VP

IP

IP

... DPi

John CUTF ti

anyD vegsi

only

VP

John CUTF ti

Note that the NPI any is not licensed once if the anyP cannot take quantifier raising (QR) over only, even if the only-sentence is uttered as the antecedent of a conditional or in some other DE context. For instance, the NPI any is not licensed in (83), a conditional where only associates into an anyP. First, the determiner any cannot take F-movement alone, ruling out the possibility in (83a). Second, since an only-associated focus cannot be moved from beneath only (Tancredi 1990), the F-contained anyP cannot raise over only, ruling out the possibility in (83b). (83) *If John only invited [anyone’s ADVISORSF ], the students would be unhappy. a. If John only invited anyone’s ADVISORSF , ...

(×)

b. If John only invited anyone’s ADVISORSF , ...

(×)

22

3.5. Not only: the NPI-unlicensing effect of negation As seen in section 2.1.3, when embedded immediately under a clause-mate negation or a negated neg-raising predicate (e.g., think, want, believe), only cannot license NPIs. This phenomenon can be described as “negation unlicenses licensed NPIs” or “negation bleeds the NPI-licensing effect of only”. (84)

a. Mary didn’t only give some/*any funding to JOHNF . b. Not only JOHNF read some/*any papers.

(85)

a. Sue doesn’t think that Mary only gave some/*any funding to JOHNF . b. Sue doesn’t think that only JOHNF read some/*any papers.

The unlicensing-NPI effect of negation is also observed in the case of the universal quantifier every. Compare the examples in (86), despite the NPI-licensing effect in the left argument of every, some (but not all) native speakers report that the use of any in the left argument of every is deviant in (86b), where the quantifier every is embedded immediately under not. (86)

a. Every student who read any/some papers passed the exam. b. Not every student who read ?any/some papers passed the exam.

In addition to negation, this NPI-unlicensing effect is also observed with negative quantifiers (e.g., no, few, at most three). For instance in (87), the NPI any is not licensed if the only-clause appears in the right argument of a negative quantifier. (87)

a. *No one only gave any funding to JOHNF . b. *Few people only gave any funding to JOHNF . c. *At most three officers only gave any funding to JOHNF .

In sum, examples above suggest that the licensing relation between an NPI and a licenser can be affected by an item outside the projection of the NPI-licenser. Now take one step further and try to figure out the underlying restrictions for the distribution of NPI-unlicensing effects.13 The NPI-unlicensing effect appears to be sensitive to locality: this effect is observed with internal negation (including clause-mate negation, negative quantifiers, and negation over negraising predicates) but not with external negation. Consider the sentences in (88) for instance. The NPI any is licensed by only when the only-clause is embedded under a sentential negation it is not the case that, a negated non-neg-raising predicate (e.g., know), or a predicate encoded with a negative meaning (e.g., doubt, suspect). 13 Note

that the contrast between (84-85) and (88) should not be attributed to whether an only-clause appears immediately below an NPI-licenser, because negative predicates like doubt are prototypical NPI-licensers. In addition, the unlicensing effect is not observed in (1a-b), where the only-clause is uttered as the antecedent clause of a conditional and a relative clause within the restriction of every, respectively. (1)

a. If only JOHNF read any papers, the professor would be mad. b. Every investor who only gave any funding to JOHNF was punished.

The lack of NPI-unlicensing effect in (1) is also predicted by locality: the monotonic operators if and every are outside the only-clause.

23

(88)

a. b. c. d.

It is not the case that only JOHNF read any papers. Sue doesn’t know that only JOHNF read any papers. Sue doubts that only JOHNF said anything. Sue suspects that only JOHNF said anything.

Therefore, the NPI-unlicensing effect of DE-operators over only can be sloppily described as follows: a DE-operator OpDE bleeds the NPI-licensing effect of only only if OpDE is a clause-mate of only. More generally, we can say: (89) NPI-unlicensing effect For any DE-operators Op1 and Op2 , Op1 bleeds the NPI-licensing effect of Op2 iff Op1 is a c-commanding clause-mate of Op2 . Among the currently available theories on NPIs, the G-view of exhaustification seems to be the only candidate with a chance of capturing this unlicensing-NPI effect. The traditional DE-account (Fauconnier 1975, 1979; Ladusaw 1979) predicts an NPI to be licensed as long as it appears within a DE environment, as defined in the following, which says that a constituent is DE with respect to one of its subconstituents once if replacing that subconstituent with a variable of the same type and abstracting over it result in a DE function. (90) DE environment: (Gajewski 2007) A constituent A is DE w.r.t. α of type δ iff the function λ x.JA[α /vδ ]Kg[vδ →x] is DE. [A[α /v] is the result of replacing α with v in A.] This definition excludes constituents that contain a DE expression but do not support downward inferences. For instance, while negation is a prototypical DE operator, if it negates a universal quantifier every which also interferes with downward inferences, the function not every is not DE with respect to the left argument of every. (91) A semanticist is a linguist. Not every linguist loves formulas. 6→ Not every semanticist loves formulas.

x⇒y f (y) 6→ f (x)

However, this definition does not say anything as to at which scopal level the downward inference is assessed. For instance, if an NPI occurs in the left argument of every, the definition above does not restrict on whether the downward inference for NPI-licensing is assessed right above every, which is DE with respect to the left argument of every, or above not, which is UE with respect to the left argument of every. The NPI-licensing condition predicted by the G-view is stricter than the traditional DE-condition. According to the assumptions in Chierchia (2006, 2013), an NPI any is licensed if and only if exercising a covert OD -operator to check off its [D] feature does not yield a contradiction/G-triviality. Under this view, to make an NPI any properly licensed, the operator OD must immediately ccommand a constituent that is DE with respect to the NPI, as defined in the following. (92) A G-view of NPI-licensing condition: An NPI anyD is licensed in a sentence S iff 24

a. there is constituent A of S s.t. A is DE w.r.t. the NPI anyD ; b. the [D] feature of anyD is checked off by a c-commanding exhaustivity operator OD s.t. OD is exercised immediately over the constituent A. (93) A constituent A is DE w.r.t. anyD iff the function λ x.JA[anyD/D′ ]Kg[anyD′ →x] is DE. [A[anyD/D′ ] is the result of replacing the domain D with D′ .] The traditional DE-account of NPI-licensing only requests an NPI to appear in a DE environment, as in (92a), while the G-view adds the condition (92b), which ensures the OD -operator and the DE environment of the NPI are not interfered by any expression that potentially disturbs or salvages downward inferences. This move predicts that any scopal elements in between OD and the NPI, including elements in between OD and the NPI-licenser, potentially affect the licensing of this NPI; therefore, it provides a chance to capture the unlicensing-NPI effect of internal negation. Consider the structure in (94). Arrows indicate the monotonicity pattern (‘⇑’ and ‘⇓’ stand for UE and DE, respectively) of each propositional constituent with respect to the NPI any. Among the three propositional constituents, only the one at Node 2 is DE with respect to the NPI any. (94) *Not only JOHNF read any papers. 3 (⇑) : ¬∀y[∃x ∈ D[P(x) ∧ R(y, x)] → y ⊆ j] not

2 (⇓) : ∀y[∃x ∈ D[P(x) ∧ R(y, x)] → y ⊆ j]

only JOHNF,i

1 (⇑) : ∃x ∈ D[P(x) ∧ R(i, x)] ti read anyD papers

The unlicensing-NPI effect of negation is expected as long as we insist on the locality of internal negation and assume that OD -operators cannot be applied immediately over Node 2. As schematized in the following, exercising an OD -operator immediately over Node 1 or Node 3 yields a contradiction, as it would over any DE environments. (95) JOD (1)K = ∃x ∈ D[P(x) ∧ R(i, x)] ∧ ∀D′[D′ ⊂ D → ¬∃x ∈ D′ [P(x) ∧ R(i, x)] = ⊥ (# i read a paper in the total domain D, but i didn’t read a paper in any proper subdomain D′ ) (96) JOD (3)K = ¬∀y[∃x ∈ D[P(x) ∧ R(y, x)] → y ⊆ j]∧ ∀D′ [D′ ⊂ D → ∀y[∃x ∈ D′ [P(x) ∧ R(y, x)] → y ⊆ j]] =⊥ (# It is not the case that only John read a paper in the total domain D, but for any proper sub-domain D′ , only John read a paper in D′ .) The NPI-unlicensing effect in (86b), repeated below, can be predicted along the same line: on the one hand, applying an O-operator immediately over Node 1 or Node 3 yields a contradiction; on the other hand, the O-operator can not be applied immediately over Node 2 because of the locality of internal negation. 25

(97) *Not every student who read any papers passed the exam. [3 not [2 [every student whoi [1 ti read any papers]] j [ t j passed the exam]] The only remaining step is to exclude the following structures, where the anyP undertakes QR over the local NPI-licenser only/every and takes scope immediately below internal negation. If these structures were tenable, then we would expect the NPI any to be licensed. (98)

a. not only

b. not every

2: ⇓

OD not

2: ⇓

OD 1: ⇑

not DPi

DP j any papers only

1: ⇑

JOHNF,i

VP

any papers DP j

VP

ti read t j every student who read ti

t j passed the exam

The structure in (98b) can be eliminated easily by the island effect of the who-clause: the anyP cannot be moved out of the relative who-clause. As for the structure in (71a), it can be ruled out by the Generalized Scope Economy (GSE) Condition (Mayr and Spector 2010). (99) Generalized Scope Economy Condition (Mayr and Spector 2010) A covert scope-shifting operation (CSSO) is licensed in a sentence S only if there exists a constituent C of S such that the CSSO does not make the semantic value of C entail what it would be without the CSSO. The GSE condition is stricter than the traditional Scope Economy Condition by Fox (1995, 2000). The traditional condition only says that a CSSO is not allowed if the interpretation of its output structure is equivalent to the interpretation of its input structure. For instance in (100), every girl cannot cannot shift over every boy, because this scope-shifting operation is semantically vacuous. (100) Every boy loves every girl. a. [ every boy1 ... [ every girl2 [ t1 loves t2 ]]] b. *[ every girl2 [ every boy1 ... [t2 [t1 loves t2 ]]]]

(Fox 2000: 3)

This GSE condition not only incorporates cases subsumed by Fox’s Scope Economy Condition, but also predicts the inviability of CSSOs in (101), where each output structure from exercising a CSSO yields an interpretation stronger than the interpretation of the input structure. (101)

a. John didn’t meet every student of mine on time b. A/One student of mine didn’t show up on time

26

(¬ > ∀) *(∀ > ¬) (∃ > ¬) *(¬ > ∃)

Now let’s see how the GSE condition rules out the structure in (98a). Given the common view that the plain meaning of the NPI any is just an ordinary indefinite like some (Chierchia 2006; among the others), we can sue the corresponding positive some-sentence in (102) to predict whether the CSSO in (98a) is tenable. According to the GSE condition, CSSO is licensed in (102), because the inverse reading in (102b) is asymmetrically entailed by the surface scope reading in (102a). In contrast, CSSO is not licensed in (98a), because the entailment relation from (102a) to (102b) is reversed by the DE-operator not, as shown in (103). (102) Only JOHNF read some papers. a. John read some papers, no one else read any papers. ⇓ 6⇑ b. There are some papers such that only John read them. (103) *Not only JOHNF read any papers. a. Not [John read some papers, no one else read any papers] 6⇓ ⇑ b. Not [There are some papers such that only John read them]

(only > ∃) (∃ > only) (not > only > ∃) *(not > ∃ > only)

In sum, for any DE-operators Op1 and Op2 such that Op1 is an adjacent c-commanding clausemate of Op2 , as illustrated in (104), Op1 exhibits an NPI-unlicensing effect because any scopal level at which the OD -operator can be applied (i.e., above Op1 and below Op2 ) is UE with respect to the NPI. First, due to the locality of Op1 , the OD -operator cannot be applied in between Op1 and Op2 . Second, due to the GSE condition, the NPI cannot QR to the sandwiched place between Op1 and Op2 . (104) [S ... Op1 Op2 [S ... NPI...]]

4. Overt only versus covert O So far I have shown that all the problems with Wagner (2006) and the G-view on the NPI-licensing effect of only can be overcome by incorporating F-movement into the G-view. Adopting the Gview and adding covert Os-operators to the LF, we now need to address the contrasts between the overt focus particle only and its covert counterpart O with respect to PI-licensing and PIunlicensing. In section 1, I have described three relevant contrasts: first, overt only licenses NPIs, but covert O does not, as shown in (105); second, the NPI any alone can be associated with a covert O across negation, but not with overt only, as shown in (106); third, the FCI any alone can be associated with a covert O across a weak modal, but not with overt only, as shown in (107). (105)

a. Everyone slept the day away, only/*O JOHNF read any paper. b. Mary only/*O gave any funding to JOHNF .

(106)

a. *John only didn’t read ANYF paper. b. John O didn’t read ANYF paper.

(107)

a. *You are only allowed to read ANYF paper. 27

b. You are O allowed to read ANYF paper. This section will show that the first two contrasts can be immediately predicted by the distinctive lexical entries of only and O, and that the last contrast can be reduced to the unique preexhaustification use of the covert O. 4.1. The lexical entry of only The lexical entry of only used in the last section strictly follows Horn (1969), which says that only asserts an exhaustivity inference and presupposes the truth of its prejacent. In this section, further, I will argue that only also presupposes an additive inference, namely that some alternative in the quantificational domain of only is excludable.14 Consider the dialogue in (108) for an illustration of the additive presupposition. The whichquestion with a restricted domain ensures that the quantificational domain of only contains exactly three members, namely I will invite John, I will invite Mary, and I will invite both John and Mary. The answer (108b) is infelicitous because the prejacent is the strongest one among the alternatives, which therefore makes the additive presupposition of only unsatisfied. In contrast, the answer (108c) is fully acceptable, because a covert O does not have an additive presupposition. (108) Which of John and Mary will you invite? a. Only JOHNF , (not Mary/ not both). b. # Only BOTHF . c. BOTHF . The lexical entries of the exclusive focus particle only and the covert exhaustivity operator O are defined as in (109) and (110), respectively. For simplicity, all alternatives are represented in a propositional form. (109) onlyc (p) 14 The

additive presupposition, as suggested by Martin Hackl (p.c.), can be reduced to a more general economy condition that an overt operator cannot be semantically vacuous. In this sense, the additive presupposition of only can be understood as a part of Al Khatib’s (2013) “non-vacuity presupposition”, which says that some excludable alternative is such that its negation is not entailed by the assertion, as schematized in (1a). Another way to characterize this non-vacuity presupposition is as in (1b), which says that there is some alternative such that the prejacent entails neither this alternative nor the negation of this alternative, (1) Non-vacuity presupposition of only: a. only (p) presupposes ∃q ∈ E xcl(p)[p 6⊆ ¬q]

b. only (p) presupposes ∃q ∈ ALT(p)[p 6⊆ q∧ p 6⊆ ¬q ]

The boxed part in (1b) is needed for predicting the infelicity of the answer in (2b): the prejacent φEVERY does not entail the alternative φNO itself but entails its negation (¬φNO = φSOME ). But for the purpose of explaining the contrasts between only and O with respect to PI-(un)licensing, the additive presupposition would be enough. I will ignore cases like (2) for simplicity. (2)

a. A: Did John see every student, or did he see no student(s)? b. B: # He only saw [every student]F .

28

a. Assertion: ∀q ∈ ALT(p)[p 6⊆ q → ¬q] b. Prejacent presupposition: p c. Additive presupposition: ∃q ∈ ALT(p)[p 6⊆ q]

(110) O(p) = p ∧ ∀q ∈ ALT(p)[p 6⊆ q → ¬q]

Accordingly, the overt particle only asserts an exhaustification inference, presupposes the truth of the prejacent and the existence of an excludable alternative.15 In contrast, the covert O is nonpresuppositional: it asserts an exhaustification inference and the prejacent inference; and it has no additive inference. 4.2. O has no NPI-licensing effect Section 3 has shown how an integrated account of exhaustification and F-movement explains the NPI-licensing effect of only. In this subsection, I will explain why an NPI is not licensed when the semantic focus is associated with a covert O, as exemplified below. (111)

a. Only JOHNF read any papers. b. *JOHNF read any papers.

Recall the proposed LF for the only-sentence (111a), repeated below: (112) OD [[ only [JOHNF,i]] [ti read anyD papers]] Taking the LF (112) as a baseline, to explain the ungrammaticality of the corresponding O-sentence (111b), we just need to check the viability of the LFs in (113).16 15 Note

that there is no need to propose any kind of existential inference for only, because this inference can be derived as a logical consequence of the prejacent inference or the additive inference. In (1) and (2), the prejacent presupposition entails the existential inference. In (3), the additive presupposition together with the assertion also entails the existential inference. (1) Only JOHN saw Mary. a. John saw Mary. b. ⇒ Someone saw Mary.

Prejacent

(2) Not only JOHN saw Mary. a. John saw Mary. b. ⇒ Someone saw Mary.

Prejacent

(3) Only JOHN didn’t see Mary. a. In the context, there is some x other than John. For every x other than John, it is not the case that x didn’t see Mary. b. ⇒ Someone saw Mary. 16 The

Additive Pres Assertion

following two LF can be excluded immediately. The LF (1a) is not syntactically well-formed, because the O-operator does not c-command any, making the [D] feature of any unchecked. The LF (1b) can be ruled out based on the discussion in section 2.2.4, namely that interpreting focus inside the VP would make F-alternatives propositional, which therefore would make the projection of OF non-monotonic with respect to the NPI any. (1)

a. *[OF,D [JOHNF,i ]] [ti read anyD papers] b. # OD OF [JOHNF read anyD papers]

29

(113)

a. OD [[OF [JOHNF,i]] [ti read anyD papers]] b. OD,F [JOHNF read anyD papers]

In the LF (113a), the focus takes an overt F-movement, and the focus particle only is replaced with a covert OF -operator. This OF is a two-place function that takes the semantic focus as its syntactic restrictor and the remnant VP as its scope. In the LF (113b), the semantic focus does not take any overt or covert movement, and a single covert O-operator checks off both [F] and [D] features. In the following, I will show that both of the LFs yield a contradiction. Under the LF in (113a), according to the lexical entry of O defined in (109), the prejacent inference is asserted by the covert OF -operator, as schematized below. Thus, when the OD -operator is applied, the prejacent inference will also enter into the assessment of the [D] feature, contrary to the case of the only-sentence (111a). Crucially, the prejacent inference (the foxed part) and the exhaustivity inference (the rest part) are UE and DE with respect to the NPI any, respectively; thus overall the complement of OD is non-monotonic with respect to the NPI any. (114) OD [[OF [JOHNF,i]] [ti read anyD papers]] = OD [[ ∃y ∈ D[P(y) ∧ R( j, y)] ∧∀x ∈ De [∃y ∈ D[P(y) ∧ R(x, y)] → j ⊆ x]] = ⊥ (OD [John and only John read a paper in the total domain D]) Alternatively, if the O-sentence (111b) takes the LF in (113b), then the [F] and [D] features will be checked off simultaneously, generating a set of alternatives via the point-wise functional application (Hamblin 1973), as schematized in (115b). Applying O affirms the prejacent and negates all the alternatives except the prejacent itself, yielding a contradiction. (115) OD,F [JOHNF read anyD papers] a. Prejacent: ∃y ∈ D[P(y) ∧ R( j, y)] b. ALT = {∃y ∈ D′ [P(y) ∧ R(x, y)] | D′ ⊆ D, x ∈ De } c. OD,F [∃y ∈ D[P(y) ∧ R( j, y)]] = ⊥ The following model illustrates why the meaning of (115c) is contradictory. Let j and m be the only possible readers, and let a and b be the only relevant books. Applying O negates all the alternatives except the one equivalent to the prejacent, yielding a contradictory inference (the underlined part in (116e)), namely # John read a or b, and he didn’t read a, and he didn’t read b. (116)

a. b. c. d. e.

De = { j, m} D = {a, b} Prejacent: R( j, a ∨ b) ALT = {R( j, a ∨ b), R( j, a), R( j, b), R(m, a ∨ b), R(m, a), R(m, b)} OD,F [R( j, a ∨ b)] = R( j, a ∨ b) ∧ ¬R( j, a) ∧ ¬R( j, b) ∧ ¬R(m, a ∨ b) ∧ ... = ⊥

4.3. The NPI-unlicensing effect of only Recall Chierchia’s (2006) assumption that the lexicon of any contains a [D] feature which must be checked by a covert c-commanding OD -operator, as schematized in (117b). This O, although has a meaning akin to only, cannot be spelled-out as only, as shown in (117c). In this subsection, I will 30

show that the ungrammaticality of (117c) can be reduced to the failure of satisfying the additive presupposition of only. (117)

a. John didn’t read any papers. b. OD not [John read anyD papers] c. *John only didn’t read ANYD,F papers.

The set of F-alternatives in (117c) contains only propositions of the following two forms: (i) it is not the case that John read some paper in D′ (D′ ⊆ D); (ii) it is not the case that John read most/all/... the papers in D. I argue that the ungrammaticality of (117c) relates to the oddness of (108b), repeated below in (118b): in these two sentences, the additive presupposition of only is not satisfied, because all the alternatives are entailed by the prejacent and not excludable. (118) Which of John and Mary are you going to invite? a. Only JOHN, (not Mary/ not both). b. # Only BOTH. c. BOTH. For sake of comparison, consider the following two conversations. The only-sentences in (119b) and (120b), where only is associated with the entire anyP and the NP complement PAPERS, respectively, are more acceptable than (117c). (119)

a. “I heard that John didn’t do any readings.” b. “No, he only didn’t read [anyD papers]F , he did read some of the books.” only [OD ¬ [he read [anyD papers]F ]]

(120)

a. “I heard that John didn’t read any papers or any books.” b. “No, he only didn’t read anyD PAPERSF .” only [OD ¬ [John read anyD PAPERSF ]]

The reason is that the additive presupposition of only is satisfied in the two cases above. In (119a), the F-alternative set activated by the wide focus [any paper]F is richer than the one activated by the narrow focus ANYF . In particular, in addition to the two forms of alternatives seen in (117c), this F-alternative set from the wider focus also includes propositions like John didn’t read some of the books. Alternatives of this form are excludable, making the additive presupposition of only be satisfied. Likewise in (120b), the F-alternative set includes excludable alternatives like John didn’t read any books. 4.4. The FCI-unlicensing effect of only Recall the fact that the emphatic item any can take an FC reading when appearing under a weak modal, as exemplified in (121). (121) John is allowed to read any paper.

31

The G-view of exhaustification also provides an explanation to the licensing condition of the FCI any. Chierchia (2006, 2013) assumes that the [D] feature in the lexicon of any activates either a set of regular D-alternatives, as discussed above, or a set of “pre-exhaustified” D-alternatives. To tell them part in the LF, he assumes that the latter set is used by a pre-exhaustified operator OD-Exh , as in (122a). Exercising an OD-Exh -operator negates all the pre-exhaustified D-alternatives in (122b), giving rise to the inference in (122c). Further, Chierchia (2006, 2013) assumes that any is a weak scalar item with an obligatory scalar implicature.17 Thus, (122a) obligatorily implicates (122d). Crucially, the exhaustivity inference (122b) and the scalar implicature (122d) contradict to each other, making the FCI any unlicensed. (122)

a. OD-Exh [John read anyD paper] b. Exh-DALT = {O∃x ∈ D′ [P(x) ∧ R( j, x)] | D′ ⊆ D} c. ∀D′ [D′ ⊂ D → ∃x ∈ D′ [P(x) ∧ R( j, x)]] (For all the proper sub-domain D′ , John read some paper in D′ ) d. scalar implicature: ¬∀x ∈ D[P(x) → R( j, x)] (John did not read all the papers in the total domain D)

The contradiction between (122b) and (122d) is avoided when the OD-Exh -operator is applied over a weak modal. For instance in (123), applying OExh yields the inference in (123e), which is compatible with the modalized scalar implicature, giving rise to an FC reading. (123) John is allowed to read any paper. a. OD-Exh ✸ [John read anyD paper] b. Assertion: ✸∃x ∈ D[P(x) ∧ R( j, x)] (John is allowed to read a paper in the total domain D) c. scalar implicature: ✸¬∀x ∈ D[P(x) → R( j, x)] (John is allowed not to read all the papers in the total domain D) d. Exh-DALT = {O✸∃x ∈ D′ [P(x) ∧ R( j, x)] | D′ ⊆ D} e. ∀D′ [D′ ⊆ D → ✸∃x ∈ D′ [P(x) ∧ R( j, x)] (For all the sub-domains D′ , John is allowed to read a paper in D′ .) f. J(123a)K = ✸∃x ∈ D[P(x) ∧ R( j, x)] ∧ ∀D′[D′ ⊆ D → ✸∃x ∈ D′ [P(x) ∧ R( j, x)] (John is allowed to read a paper in the total domain D, and he is allowed to read a paper in any sub-domain D′ .) Note that in a DE-context the emphatic item any has to take an NPI reading no matter whether its [D] feature is checked by a regular OD or by a pre-exhaustified OD-Exh . Let’s assume that the basic negative sentence (124a) can take the LF in (124b), where the [D] feature of any agrees with an OD-Exh -operator and activates a set of pre-exhaustified D-alternatives. For instance, let D = {a, b}, the pre-exhaustified D-alternative set would be like (124d). For each of the pre-exhaustified proper D-alternatives, its negation is entailed by the prejacent. Therefore, the OD-Exh -operator is semantically vacuous, just like the regular OD -operator. 17 Chierchia

(2006, 2013) assumes that the lexicon of any also carries an scalar implicature feature [σ ], which obligatorily activates a scalar-alternative (John read all the papers in the total domain D). This feature is not crucial for the goals of this paper and was ignored in the previous sections.

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(124)

a. b. c. d. e.

John didn’t read any papers. OD-Exh not [John read anyD papers] Assertion: ¬R( j, a) ∧ ¬R( j, b) Exh-DALT = {O¬R( j, a), O¬R( j, b)} = {¬R( j, a) ∧ R( j, b), ¬R( j, b) ∧ R( j, a)} J(124a)K = ¬R( j, a) ∧ ¬R( j, b) ∧ ¬[¬R( j, a) ∧ R( j, b)] ∧ ¬[¬R( j, b) ∧ R( j, a)] = [¬R( j, a) ∧ ¬R( j, b)] ∧ [R( j, a) ∨ ¬R( j, b)] ∧ [R( j, b) ∨ ¬R( j, a)] = ¬R( j, a) ∧ ¬R( j, b)

Recall the problem that the OD-Exh -operator used in the LF (123a) cannot be spelled-out as only, as shown in (125). In section 1, I described this problem as a contrast between O and only with respect to FCI-unlicensing: the overt particle only unlicenses the FCI any across an FCI-licenser (e.g., a weak model), while a covert O does not. (125) *You are only allowed to read ANY paper. In response to the ungrammaticality of the only-sentence in (125), I assume that the overt particleonly cannot take the role of the OExh -operator. In other words, overt only does not have a pre-exhaustification use in the sense of Chierchia (2006, 2013), or say, it cannot be applied recursively in the sense of Fox (2007). This assumption is supported by observations on the disjunctive or, another prototypical FCI. Consider the conversation in (126). Relevant alternatives are, the pre-exhaustified D-alternatives (namely, you are only allowed to have some ice cream, and, you are only allowed to have some cake), the scalar alternative (namely, you are allowed to have both), and possibly some ad hoc alternatives (e.g., you are allowed to have some cookies). In (126b-c), overt only can be used felicitously, negating some alternative of the latter two kinds. (126)

a. Am I allowed to have some ice cream and cake? b. You are (only) allowed to have some ice cream OR cake, not both. c. You are (only) allowed to have some [ice cream or cake]F , nothing else.

In contrast, under the following conversation, using only in the answer is quite odd. This oddness is expected if we assume that overt only does not have a pre-exhaustification use. The question has explicitly excluded the scalar alternative and restricted the domain (D = {ice cream, cake}), only the pre-exhaustified D-alternatives are relevant and potentially excludable. Under the assumption that only cannot deal with pre-exhaustification D-alternatives, we can attribute the oddness of using only in (127b) to failure of satisfying the additive presupposition. (127)

a. Which one of these two (i.e. ice cream and cake) am I allowed to have? b. You are (# only) allowed to have either of them.

Turn back to the case of the FCI any. Under the assumption that only has no pre-exhaustification use, the LF for (125) should be structured as (128), where only checks off just the [F] feature of the focused item, leaving the [D] feature of any agree with another covert OD-Exh -operator. (128) # Only OExh-DA ✸ [you read anyD,F paper ] 33

We can now capture the ungrammaticality of the only-sentence (125) the in the way stated for the disjunctive sentence (127b): the additive presupposition of only is not satisfied in (125); none of the F-alternatives (e.g., you are allowed to read some/most/all/... paper(s)) is excludable.18 Consider the only-sentence (129) for comparison, where only associates with merely the NP complement of any. (129) You are only allowed to read any PAPERF , you are not allowed to read any book. (129) appears to be much more acceptable than (125), due to the satisfaction of the additive presupposition: the narrow focus activates some excludable alternatives in the form of you are allowed to read any book/magazine/..., which therefore satisfy the additive presupposition of only.

5. Conclusions The goals of this paper have been to explain the NPI-licensing effect of the overt exclusive focus particle only and to explain the distinctions between only and covert exhaustification operator O with respect to PI-licensing and PI-unlicensing. To address the NPI-licensing effect of only, I incorporated F-movement into the G-view of exhaustification with a simple assumption that F-movement is motivated by the requirement of avoiding contradictions. This integrated analysis not only inherits the advantages of both theories on explaining the NPI-licensing effect of only, but also addresses the major problems with both theories, such as the island-insensitivity of multi-foci constructions, the unconventional interpretation of only, the “Head Restriction”, the NPI-unlicensing effect of internal negation, and so on. To explain the distinctions between only and O, I re-evaluated the meaning and the usage of overt only and compared it with its covert counterpart, finding that only has an additive presupposition and no pre-exhaustification use. Accordingly, I argued that the NPI-unlicensing and FCIunlicensing effect of only could be attributed to the failure of satisfying its additive presupposition.

Appendix: Move to complement or to specifier? In the case of VP-only association, it remains controversial whether the associated focus (or the F-contained island) moves to the complement of only (Chomsky 1976, Wagner 2006), as illustrated above in (68a), or to the specifier of onlyP (Drubig 1994), as illustrated in (130). I call the former a “moving-to-complement account” and the latter a “moving-to-specifier account”. In this 18 Recall

Chierchia’s (2006, 2013) assumption in footnote 17 that the lexicon of any contains a scalar feature [σ ] which obligatorily actives a scalar-alternative. One possible concern for the present analysis is that the scalaralternative is excludable, which therefore might be able to feed the additive presupposition of only. The existence of scalar-alternative, however, is not a threat to the present analysis. As Chierchia (2013: section 2.4) indicates, the scalar-alternative must have been used before the OD-Exh -operator is applied. Therefore, if the scalar-alternative is taken into consideration, the LF of (125) should be structured as follows, which still does not satisfy the additive presupposition of only. (1) # Only OExh-DA Oσ ✸ [you read anyD,F,σ paper ]

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appendix, I will provide arguments and schematic compositions for both accounts without passing any judgements. (130) Mary only gave any funding to JOHNF . OD

onlyP

JOHNF,i only

VP

Mary gave anyD funding to ti Let us start with arguments for the moving-to-complement account. Crniˇc (2014b) observes that VP-only does not always take a rigid scope (cf. Taglicht and Quirk 1984, Rooth 1985, Bayer 1996). Consider the example in (131a), where the VP-only is associated with an element hosting an antecedent contained deletion (ACD henceforth). Intuitively, (131a) can be interpreted as in (131b), where only takes scope over the matrix clause. (131)

a. The dean demanded that we only be on [the COMMITTEES that I thought he would]F . b. The dean only demanded that we be on [the COMMITTEES that I thought he would]F .

Considering that only can form a constituent with its complement, but not with its specifier or any item at a distance, Crniˇc (2014b) proposes that the wide scope interpretation of only is achieved by moving focus to the complement of only, forming a quantifier, and then moving the whole only-DP to the matrix clause. A step-by-step syntactic derivation for the sentence (131a) is given below. (132) F-association via moving-to-complement [only (the COMMITTEES λ x [I thought he would ])F ] λ y [the dean demanded that we be on y] a. Embedded Clause: [only [we be on the committees λ x [I thought he would ]] b. Move Focus: [only (the committees λ x[I thought he would ])F λ y[we be on y]] c. Merge Matrix: [the dean demanded that [only (the committees λ x [I though he would ])F λ y [we be on y]]] d. Move only-DP: [only (the committees λ x[I though he would ])F λ y[the dean demanded that we be on y]] e. ACD: [only (the committees λ x[I though he would ])F λ y[the dean demanded that we be on y]]

Under this account, only would firstly compose with the moved phrase and then with the remnant VP. Taking the sentence (67a) for example, I schematize its semantic composition steps as the following. 35

(133) Mary only gave any funding to JOHNF . [Mary λ x [OD [only (JOHNF ) λ y [x gave any funding to y]]]] a. b. c. d. e. f. g.

h. i. j. k.

Jx gave any funding to yK = ∃z ∈ D[F(z) ∧ G(x, z, y)] Jλ y [x gave any funding to y]K = λ y.∃z ∈ D[F(z) ∧ G(x, z, y)] JJOHNF K0 = j JJOHNF K f = De JMaryK = m JonlyK = λ gα .λ f .∀g′ ∈ JgK f [ f (g′) → JgK0 ⊆ g′ ] Jonly (JOHNF )K = λ f .∀g′ ∈ JJOHNF K f [ f (g′ ) → JJOHNF K0 ⊆ g′ ] = λ f .∀g′ ∈ De [ f (g′ ) → j ⊆ g′ ] Jonly (JOHNF ) λ y [x gave any funding to y]K = ∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(x, z, g′)] → j ⊆ g′ ] JOD [only (JOHNF ) λ y [x gave any funding to y]]K = ∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(x, z, g′)] → j ⊆ g′ ] Jλ x [OD [only (JOHNF ) λ y [x gave any funding to y]]]K = λ x.∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(m, z, g′)] → j ⊆ g′ ] JMary λ x [OD [only (JOHNF ) λ y [x gave any funding to y]]]K = ∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(m, z, g′)] → j ⊆ g′ ]

Next, move on to arguments for the moving-to-specifier account. First, the operation of moving focus to the complement of only violates the Extension Constraint (Chomsky 1995), that all movement operations extend the rooth of the structure that they apply to. What’s more, the wide scope reading of only in (131a) can be achieved alternatively via an operator-movement of only: only moves alone to the matrix clause and then associates with the focus either via moving the focus to the specifier of the higher onlyP, as in (134), or at a distance, as in (135). (134) F-association via moving-to-specifier: [ (the COMMITTEES λ x [I thought he would ])F only λ y [the dean demanded that we be on y] a. Embedded Clause: [only [we be on the committees λ x [I thought he would ]] b. Merge Matrix: [the dean demanded that [only [we be on the committees λ x [I thought he would ]] c. Move Only: [only [the dean demanded that [we be on the committees λ x [I thought he would ]]] d. Move Focus: [(the committees λ x [I thought he would ]) only λ y [the dean demanded that we be on y]] e. ACD: [(the committees λ x [I though he would ) only λ y [the dean demanded that we be on y]]

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(135) F-association at a distance: [only [the dean demanded that we be on [the COMMITTEES λ x [I thought he would ]]F ]] a. Embedded Clause: [only [we be on the committees λ x [I thought he would ]] b. Merge Matrix: [the dean demanded that [only [we be on the committees λ x [I thought he would ]]]

The derivation in (134) is slightly unconventional, as it isolates the lambda-abstractor λ y from the corresponding F-moved phrase. This unconventional manipulation is needed for semantic composition, as schematized in (136). One way to justify the lambda-expression λ y, as suggested by Gennaro Chierchia (p.c.), is that only is co-indexed with the focused constituent at its specifier. In particular, the index on only is interpreted as the λ -abstractor on the VP, while the index on the focused constituent is vacuous. Contrary to the composition in (133), under the moving-to-specifier account, only would firstly compose with the remnant VP and then with the F-moved part. (136) Mary only gave any funding to JOHNF . [Mary λ x [OD [JOHNF [only λ y [x gave any funding to y]]]] a. b. c. d. e. f. g. h. i. j. k.

Jx gave any funding to yK = ∃z ∈ D[F(z) ∧ G(x, z, y)] Jλ y [x gave any funding to y]K = λ y.∃z ∈ D[F(z) ∧ G(x, z, y)] JJOHNF K0 = j JJOHNF K f = De JMaryK = m JonlyK = λ f .λ gα .∀g′ ∈ JgK f [ f (g′) → JgK0 ⊆ g′ ] Jonly λ y [x gave any funding to y]K = λ gα .∀g′ ∈ JgK f [∃z ∈ D[F(z) ∧ G(x, z, g′)] → JgK0 ⊆ g′ ] JJOHNF [only λ y [x gave any funding to y]]K = ∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(x, z, g′)] → j ⊆ g′ ] JOD [JOHNF [only λ y [x gave any funding to y]]]K = ∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(x, z, g′)] → j ⊆ g′ ] Jλ x [OD [JOHNF [only λ y [x gave any funding to y]]]]K = λ x.∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(x, z, g′)] → j ⊆ g′ ] JMary λ x [OD [JOHNF [only λ y [x gave any funding to y]]]]K = ∀g′ ∈ De [∃z ∈ D[F(z) ∧ G(m, z, g′)] → j ⊆ g′ ] 37

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