Polarity in the Semantics of Natural Language
Summary and Keywords
This paper provides an overview of polarity phenomena in human languages. There are three prominent paradigms of polarity items: negative polarity items (NPIs), positive polarity items (PPIs), and free choice items (FCIs). What they all have in common is that they have limited distribution: they cannot occur just anywhere, but only inside the scope of licenser, which is negation and more broadly a nonveridical licenser, PPIs, conversely, must appear outside the scope of negation. The need to be in the scope of a licenser creates a semantic and syntactic dependency, as the polarity item must be c-commanded by the licenser at some syntactic level. Polarity, therefore, is a true interface phenomenon and raises the question of well-formedness that depends on both semantics and syntax.
Nonveridical polarity contexts can be negative, but also non-monotonic such as modal contexts, questions, other non-assertive contexts (imperatives, subjunctives), generic and habitual sentences, and disjunction. Some NPIs and FCIs appear freely in these contexts in many languages, and some NPIs prefer negative contexts. Within negative licensers, we make a distinction between classically and minimally negative contexts. There are no NPIs that appear only in minimally negative contexts.
The distributions of NPIs and FCIs crosslinguistically can be understood in terms of general patterns, and there are individual differences due largely to the lexical semantic content of the polarity item paradigms. Three general patterns can be identified as possible lexical sources of polarity. The first is the presence of a dependent variable in the polarity item—a property characterizing NPIs and FCIs in many languages, including Greek, Mandarin, and Korean. Secondly, the polarity item may be scalar: English any and FCIs can be scalar, but Greek, Korean, and Mandarin NPIs are not. Finally, it has been proposed that NPIs can be exhaustive, but exhaustivity is hard to precisely identify in a non-stipulative way, and does not characterize all NPIs. NPIs that are not exhaustive tend to be referentially vague, which means that the speaker uses them only if she is unable to identify a specific referent for them.
1. The Landscape of Polarity Items: Negative Polarity, Positive Polarity, Free Choice
Polarity is a pervasive phenomenon in natural language, and has received considerable attention since Klima’s (1964) seminal work on English negation. The polarity-sensitive item, or ‘polarity item’ (PI) for short, is an expression that requires negation when it appears. The following is a classic contrast:
PIs exhibit limited distribution: the grammatical sentences with anything, ever contain negation; the ungrammatical sentences (indicated by *) lack negation. Anything and ever are labeled ‘negative polarity items’ (NPIs) because they need negation in order to be grammatical.
Polarity, then, illustrates a semantically driven grammatical constraint, and appears to be a universal of natural language. PIs are found in virtually every human language we consider, but artificial languages appear to lack PIs. From a purely logical perspective, polarity is an anomaly: why couldn’t Nicholas said anything be used to convey Nicholas said something or Nicholas said everything? Why can’t *Nicholas has ever talked to Ariadne be used to say Nicholas has once (or: always) talked to Ariadne? PIs, logically superfluous or redundant, are abundant in the world’s languages, and have featured quite prominently in linguistic theory.
In earlier works (Klima, 1964; Fauconnier, 1974; Horn, 1972; Baker, 1970; Ladusaw, 1980; Linebarger, 1980), the focus was on English NPIs; crosslinguistic studies in the ’80s and ’90s extended the empirical domain of polarity, and revealed a complexity that in the earlier works had gone unnoticed. Influential works were Giannakidou (1994, 1995, 1997, 1998, 1999, 2001) on Greek NPIs and free choice items; Zwarts (1981, 1986, 1995), Hoeksema (1994, 1999), and van der Wouden (1994) on Dutch NPIs; Lin (1996) on Mandarin NPIs; and Lahiri (1998) on Hindi NPIs. Haspelmath (1997) presented a study of indefinites in forty languages revealing the rich landscape of indefinites, including limited distribution NPIs.
Below are examples from Greek and Dutch—which will be, along with English, the main languages of illustration:
Ook maar iets and tipota are the Dutch and Greek NPI equivalents of any, respectively. Ook maar iets contains even (though the even component often doesn’t get interpreted literally, as shown in Giannakidou & Yoon, 2016). Giannakidou (1997) talks about the landscape of polarity items, to emphasize the breadth and variation involved in paradigms of polarity items—which is not confined to sensitivity to negation. Our discussion in this chapter will reveal some crucial aspects of this variation.
NPIs are sensitive to the presence of negation, and this means that they need negation to be licensed (Ladusaw, 1980; Giannakidou, 1997). Licensing is two things: (a) the semantic requirement that there be a negation (the licenser) in the sentence, and (b) the syntactic requirement that the NPI be in the scope of negation, which translates into a need for the NPI to be c-commanded (Reinhart, 1976) by negation:
Any student can only be interpreted in the logical scope of negation (8a)—the scoping in (8b), where there is one person such that Bill didn’t see (but others that he possibly saw), is impossible. Furthermore, appearance of the NPI to the left of negation is generally prohibited (7b). Hence, there is a mapping between the narrow-scope condition and the syntactic requirement of c-command (see Giannakidou, 1997, 1998 for extensive discussion; also Uribe-Echevarria, 1994; De Swart, 2000 for empirical refinements of the c-command condition still in line with narrow scope). The example below shows more effects of c-command:
No student licenses any in (9b) but not in (9a), despite its linear precedence, because it does not c-command the NPI. NPIs manifest a dependency in both semantics and syntax, and thus present a prime case for studying the interaction between these two levels of grammatical representation. The literature, since Klima (1964), Ladusaw (1980), and Linebarger (1980) typically marks NPI failures with * and not #, reflecting the judgment that the NPI failure is not a mere infelicity or lexical anomaly. NPI-licensing, then, illustrates a synergy between semantics and syntax, and raises the question of well-formedness that is determined by both.
In the early literature, NPIs were thought to be duals of positive polarity items (PPIs). In an apparent reversal of the NPI’s need to be in the scope of negation, PPIs are ‘repelled’ by negation and tend to escape its scope. PPIs were first identified as a class in Baker (1970), and are discussed more recently in Szabolcsi (2004), Nilsen (2003), Ernst (2009), Giannakidou (2011), and Iatridou and Zeijlstra (2013). Expressions like some, already, would rather, and speaker-oriented adverbs such as unfortunately have been identified as PPIs:
As shown, some books exhibits the scope outside negation that any lacks, and only that. Would rather and already are odd with negation, and likewise unfortunately, an evaluative adverb. Metalinguistic denial (Horn, 2001), however, can rectify PPIs (see Ernst, 2009 for discussion): John isn’t here ALREADY, we are still waiting for him; hence ‘#” reflects that the PPI is not ungrammatical, but infelicitous in the scope of negation. PPIs exhibit limited interpretation, whereas NPIs have limited both interpretation and distribution (Giannakidou, 2002, 2011). A failed NPI is ungrammatical, but a failed PPI is only infelicitous, and its failure could be fixed. The intended duality between NPIs and PPIs is therefore not an exact parallel, involving the same grammatical mechanism, but a handy metaphor to express the duality of relation with respect to negation: the NPI is attracted to negation, but the PPI avoids it. Krifka (1995) offers a Gricean explanation stating that since under the scope of negation the specific form NPI is necessitated, using another form creates the implicature that the alternative scope is intended.
Recently, the NPI-PPI metaphor has been extended to characterize the way modal verbs interact with negation:
Iatridou and Zeijlstra (2013) characterize must as a PPI and need as an NPI; German and Dutch also have NPI need-equivalent modals—brauchen (German) and hoeven (Dutch; van der Wouden, 1994). The discussion of the polarity of modal verbs relates, crucially, to the quantificational force of the modal: the PPI modals are generally universal (must, will, and their equivalents; see Giannakidou & Mari, 2017 for capitalizing on this fact). A Gricean explanation could also be given in view of the fact if the NPI-modal is not used, the hearer is forced to conclude that the alternative wide scope of the modal is intended.
The contrasting behavior of NPIs and PPIs prompted analyses of PPIs as anti-licensed by negation (Ladusaw, 1980; Progovac, 1994; Giannakidou, 1997, 1998; Postal, 2000). Giannakidou (1997) formulates the contrast in the following way:
As indicated, licensing requires that α be in the scope of β, and #R is the opposite condition that α avoid the scope of β, or anti-scope. β is for now negation, but as will be seen, the set of licensers exceeds negation. The anti-licensing condition is merely an indicator about where the PPI cannot occur, that is, inside the scope of negation. The condition says nothing about environments besides negation, and PPIs are generally fine in many non-negative environments, often alternating with NPIs (e.g., in questions, with modals, etc; see Giannakidou, 1997, 2011; Szabolcsi, 2004 for more detailed exhibition).
As just alluded to, limited distribution of polarity items goes beyond the polar opposition. There is a class of PIs known as free choice items (FCIs), which require typically modal and quantificational licensers, and which are blocked in the scope of negation if such a licenser is lacking. This is the case with simple past sentences, where reference is made to a single event. Giannakidou (1997) calls this the anti-episodicity constraint. Below, examples with Greek (Giannakidou, 1997, 1998, 2001), Spanish, and Catalan NPIs (Quer, 1998, 1999) are given to illustrate the constraint:
FCIs express what Vendler (1967) called freedom of choice, a property manifested in the typical FCI use of any in generic sentences and with modal verbs, as we see. The ungrammatical sentences are episodic due to simple past tense, which forces reference to a single event. This property blocks FCIs. In Greek, Spanish, and Catalan, FCIs are distinct lexically from NPIs (for more on Greek FCIs, see Vlachou, 2007; Lazaridou-Chatzigoga, 2009), but in English they two forms are collapsed in the word any.
FCIs tend to combine a wh-component with ‘free choice’ marking, which may contain focus particles (Greek dhipote, Dutch ook maar), volitional items (vol, quiera in Spanish, Catalan), or disjunction (Korean na).
A similar composition is found in the English whatever series, which appears in free relative structures (for discussion of the differences between FCIs and free choice free relatives, which are not subject to licensing, see Giannakidou & Cheng, 2006). Some FCIs can be wh-indeteminates, that is, they are wh-expressions, as in Korean above, that receive free choice but also interrogative and NPI use when combined with different particles. Another well known case is Mandarin shenme:
East Asian languages are particularly keen on using wh-indeterminates for question words, NPIs, and FCIs, prompting analyses based on interrogative semantics (Kratzer & Shimoyama, 2002; see Giannakidou & Cheng, 2006; Cheng & Giannakidou, 2013 for criticism). FCIs, in European languages at least, do not have NPI or interrogative use (Giannakidou & Quer, 2013):
FCIs are not just unusable as question words, they are simply bad in questions. Moreover, in Greek, the FCI wh-word must contain the definiteness marker o (homophonous to the definite article in Greek). The bare wh-word does not serve as the source for free choice, as the contrast below shows (Giannakidou & Cheng, 2006; Giannakidou & Quer, 2013):
These asymmetries challenge the derivation of FCIs directly from question meaning, or at least challenge its generalizability to all wh-based FCIs. In any case, it is clear that NPIs, FCIs, and any belong to the same landscape; with any, free choice and NPI are collapsed into the same form, which is morphologically unmarked for either.
As said earlier, FCIs express freedom of choice, a reading akin to “it doesn’t matter who” seen in the typical examples in (18, 19). Unlike NPIs, however, FCIs are not attracted to negation but to modal, generic, and similar contexts. It is important to note that NPIs also appear in these contexts, as can be seen below:
The NPI kanena vivlio gets interpreted with a similar ‘choice’ flavor, that is, it doesn’t matter which book Ariadne reads. But unlike any, the choice is weaker, akin to some or other. This reading differs from the FCI reading Ariadne can read any book, which is a permission to read any book whatsoever, infelicitous as an answer to the question above. NPIs and FCIs thus share environments while having distinct semantics. This point will be elaborated on in section 6.
Overall, NPIs and FCIs raise the question of well-formedness that is determined by both syntax and semantics. The intuition is that sentences with failed NPIs, for example, *Bill brought any presents, *Bill talked to John either, are not generated by the grammar. This distinguishes them from mere lexical mismatches or contradictions which are anomalous or infelicitous, but nevertheless grammatical sentences:
The sentences are anomalous, although it is possible to figure out what they would mean if felicitous: for example, If Jason were a city, then it would have the population of 3 million. And even with the contradiction, which is a fine sentence, a hearer will try to make something out of it, for example, tall in one sense but not tall in another. Ill-formed NPIs and FCIs, however, are not generated by the grammar (see Ladusaw, 1980; Giannakidou, 1997, 1998; Giannakidou & Quer, 2013). Since Chomsky (1957, 1964), the field has accepted that speakers’ reactions to, and intuitions about, “odd” and “ungrammatical” sentences differ, and negative polarity, in virtually all accounts, is a grammatical constraint.
How does the semantico-syntactic integration exhibited by NPIs and FCIs differ from infelicity and mere lexical anomaly? It is important to raise this question because often the difference is intentionally blurred. The contribution of experiments and quantitative data has been instrumental in strengthening the argument from intuition. Processing evidence reveals patterns suggestive of syntactic-semantic integration which is a P600 effect (Saddy et al., 2004; Drenhaus et al., 2006; Steinhauer et al., 2010; Xiang et al., 2013, 2016). Overall, the literature reveals P600 and N400 as physical (neural) correlates of what can be thought of as call the ‘integration judgment’, which is the judgment typical of interface phenomena that rely on integrating multiple levels of grammatical representation. Reduced N400 can be understood as the physical correlate of semantic licensing, i.e. as a matching relation between the NPI and its licenser, and P600 indexes semantico-syntactic integration. Remember, finally, that PPIs do not involve grammatical constraints; experimental results could shed additional light on this difference between NPIs and PPIs.
The early literature postulated polarity conditions as global, composition external filters on sentences or grammatical representations like, for example, binding theory. Ladusaw (1983) talks about semantic filtering: a syntactically well-formed structure with any is filtered out semantically. But what in the lexical entry of any necessitates that it be subject to semantic filtering? In current theorizing, the idea of global semantic filtering is unsatisfactory because it is stipulative; it seems preferable to derive the limited distribution from the lexical makeup and featural specification of the NPI or FCI. Early pioneers in this direction were Kadmon and Landman (1993), Israel (1996), Giannakidou (1997, 1998), Tovena (1998), Krifka (1995), and Lahiri (1998). Giannakidou posits sensitivity features on NPIs and FCIs which are morphological features such as the FCI marking noted earlier, intonational features for example, in the Greek emphatic NPIs, or abstract morphological features like Chierchia’s +σ feature, or [neg] in Lin (2015) and Lin et al. (2015).
Core issues in polarity literature will now be discussed. There is no historical survey; the reader can consult the Oxford Bibliography for that, and the references indicated in the Further readings section of this article. The focus is rather on current research, with emphasis on important key questions that have emerged in the more than forty years of study, and what has been achieved in our answering these questions thus far. Section 2 presents the distribution of NPIs in contexts beyond negation; section 3 studies nonveridicality and negation, the two major licensers of NPIs and FCIs; section 4 discusses what makes a polarity item sensitive and scalar NPIs; section 5 discusses NPIs and FCIs containing dependent variables; and section 6 addresses the issue of exhaustification and distinguishes it from referential vagueness, which is shown to characterize an important number of NPIs.
2. Polarity Items: What Licenses Them Besides Negation?
NPIs belong to various syntactic categories: there is nominal any, any boy, but there are also NPI adverbs and adverbials (ever, Dutch ooit; Hoeksema, 1999; see (28, 29)), verbs (hoeven, brauchen (31), modal infinitives in a Pontic dialect of Greek (Sitaridou, 2014), focus particles (Greek oute (32), Giannakidou, 2007; English either (30)), even negation itself (Greek me, Chatzopoulou, 2012). There are also minimizers, NPIs denoting minimal amount making idiom-like statements:
Thus, the term NPI is a descriptive label saying that a linguistic expression needs the presence of negation. But NPIs appear also without negation in questions:
What do negation and questions have in common? The answer is that they are both nonveridical (Giannakidou, 1994, 1997; Zwarts, 1995), but it took a few years for this discovery to come about; the first approaches focused on the role of negation, and could not handle NPIs in questions. Any in modal and generic contexts was dismissed as an FCI, thus at that time irrelevant for negative polarity (Ladusaw, 1980).
2.1 Negation, Downward Entailment
Negation emerges as the crucial licenser in Baker (1970), Fauconnier (1974), and Linebarger (1980, 1987, 1991). If there is no negation in the sentence, as with only, emotive verbs, and long after, negation is implicated:
Only Ariadne said anything says both that Ariadne said something and that nobody other than Ariadne did. Likewise, Ariadne regrets that she said anything triggers an inference that Ariadne wishes she had not said anything. Questions with any, it must be noted, do not trigger negative inference (Ladusaw, 1980).
Ladusaw (1980) makes the discovery that any appears also with few and in the restriction of every, and proposes the following licensing condition:
Here is the definition of DE:
DE functions reverse the order of entailment, and support inference from sets to subsets, as in (40). Order preserving inference, as in (39), is upward entailing:
Few and the restriction of every validate DE. Thus DE initiated a fruitful research program (Hoeksema, 1986; Zwarts, 1986, 1998; van der Wouden, 1994; Kas, 1993; Dowty, 1994, among many others), the most exciting part of which was that a semantic property such as monotonic (upward or downward) inference is relevant for a grammatical phenomenon. Prior to the emergence of DE, the best generalization was Klima’s postulate that NPI contexts contain a syntactic feature [affective], without a semantic characterization of what ‘affective’ meant.
Zwarts (1998) further makes an important contribution by establishing a relation between DE and negativity. For Zwarts, DE is minimal negation, the threshold of negativity: it satisfies two of the de Morgan relations as indicated in (42), and serves as the criterion for being negative. Classical negation, on the other hand, is DE plus a third law (antiadditivity) and antimorphicity, which satisfies the full negation laws. This is the case with sentential negation, the strongest negation.
Few and the restriction of every satisfy only the DE relations, they are therefore only minimally negative; but nobody and not are anti-additive and antimorphic respectively. Zwarts’s theory allows negativity to be viewed as a gradient property, as a scale of strength: the more negative laws an expression satisfies, the more negative it will be. The stronger the negation, the more stereotypical it is.
NPIs can be likewise weaker or stronger depending on whether they are licensed by mere DE or stronger negation. Any is weak because it is licensed by few/every, but the Dutch ook maar iets appears strong—as mere DE weinig ‘few’ does not suffice for licensing, it needs niemand ‘nobody.’ The Greek NPI kanenas follows a similar pattern:
2.2 Strong NPIs: Classical Negation Dependent
Strong NPIs—or strict NPIs, as Giannakidou (1998, 2000) calls them—are NPIs that are narrowly licensed by classical negation (including without, which is at least anti-additive; Giannakidou, 1999). Such NPIs do not appear in questions or with DE quantifiers.
English contains one word even, but Rooth (1985) hypothesized that there is an NPI-even with negation. NPI-even is found in many languages: for example, Spanish nisiquiera (Herburger, 2003), German (einmal; Zwarts, 1995), Korean to (Lee, 2010; Giannakidou & Yoon, 2016), and Greek (oute; Giannakidou, 2007). Below are examples from Greek illustrating that the Greek NPI-even is not licensed by DE:
This constraint is largely shared by the other NPI-evens mentioned above.
2.2.2 Minimizers in Greek, Japanese, and Korean
Minimizers in Greek, Japanese, and Korean also show very narrow distribution (in contrast to English minimizers), and may contain NPI-EVEN. (For Japanese data, see Yoshimura, 2007; for Korean, Giannakidou & Yoon, 2014, 2016; Lee, 1997, 1999).
Minimizers involve focus and minimal amount expressions (Giannakidou, 1997, 1998; Israel, 2011), hence the use of an even word is not unexpected. Albanian further employs EVEN with its strong NPIs (Xherija, 2014), a strategy in common with other languages.
2.2.3 N-Words in Strict Negative Concord
Negative concord is the phenomenon of apparent multiple negative exponents that are interpreted as one semantic negation (53). N-words can be marked with n- or intonation (Greek n-words, Giannakidou, 1997; Chatzikonstantinou, 2016). In addition, n-words require negation to be in the same clause, unlike any, which is not as restrictive (see Zanuttini, 1991; Haegeman & Zanuttini, 1991; Giannakidou, 2006; Giannakidou & Zeijlstra, 2017 for overviews of the data and the various analyses of negative concord):
To sum up, there are weaker NPIs (any, kanenas, ook maar iets) with broader distribution in mere DE (few, every) contexts, questions, and modal contexts, and stronger NPIs requiring classical negation.
2.3 NPIs and FCIs in Modal Contexts and Non-Assertions
NPIs appear in imperatives, with modal verbs, subjunctive complements of propositional attitudes, habituals, if-clauses, and disjunctions (Giannakidou, 1994, 1995, 1998, 1999, 2006). This is illustrated with Greek and English any to keep things simple, but similar observations are reported for NPIs in Salish (Matthewson, 1998), Chinese (Lin, 1996; Giannakidou, 2013; Lin et al., 2015), Navajo (Fernald & Perkins, 2006), Russian (Haspelmath, 1997; Pereltsvaig, 2000), Ossetic (Haspelmath, 1997), Hindi NPIs (Lahiri, 1998), Korean NPIs (Lee, 1999; Giannakidou & Yoon, 2014, 2016), Albanian (Xherija, 2014), Benghali (Ullah, 2016), and other languages. In these contexts FCIs can also appear. English has any.
NPIs and FCIs are distinct semantically in these contexts, a point further discussed in section 6. Modal environments are not negative or order reversing, yet they license NPIs and FCIs.
In the face of the Greek-type NPI—namely, the NPI that has a distribution similar to any, but lacks free choice reading—one may attempt to think of it as ‘not proper’. But there is no empirical basis for treating the latter as exceptional. The only reason one might think of any as ‘more proper’ than kanenas, shenme and rato-NPI is historical accident: the NPI literature started with, and focused for many years on any (since Klima’s 1964 seminal work); it was only in the mid-nineties that the Greek and Mandarin NPIs facts became known, approximately at the same time (Giannakidou, 1994, 1995, 1997; Lin, 1996, Wang, 1996). Thirty years of English-based polarity doctrine may have created the illusion that only any deserves the moniker of ‘proper’ NPI; but treating the newly discovered NPIs as ‘not proper’ would represent nothing but a highly normative stance—especially given that both any and the Greek, Mandarin and Korean NPIs appear in the same contexts,
2.4 NPIs and FCIs in Conditionals
Here again there are both NPIs and FCIs:
If-clauses are not monotonic, as pointed out by Heim (1984): If you go to Spain you will have a good time does not entail that If you go to Spain and have an accident you will have a good time. Von Fintel (1999) proposes the notion of Strawson-DE as a way to produce DE inference by strengthening the meaning, but Giannakidou (2006) shows that this causes empirical overgeneralization. Strengthening and Strawson-DE also don’t help with NPIs in questions, with modals, generics, and imperatives seen earlier, since these are not Strawson-DE.
2.5 NPIs and FCIs in Habituals
Similar data have been reported for Dutch (Hoeksema, 1999), Mandarin, and the other languages mentioned earlier.
NPIs and FCIs occur in disjunctions (Giannakidou, 1998):
Disjunction is nonveridical, but conjunction is veridical (it requires that both conjuncts be true; Zwarts, 1995).
2.7 Summary: Overall Distribution of NPIs and FCIs
Here are summarized the distributions of the four major polarity item types: Greek-style weak NPIs, strong NPIs, FCIs, and any.
Table 1. Distributions of Weak NPIs (Any, Greek NPIs), Strong NPIs, and FCIs
Greek kanenas NPI
3. Conditional (if-clause)
4. Restriction of every/all
5. Downward entailing Quantifier
6. Modal verbs
7. Nonveridical verbs (e.g., want)
11. prin/before clauses
13. Affirmative past sentences
14. Affirmative existential
The last two rows are the positive contexts where all PIs are excluded; the rest are the polarity contexts. In bold are the contexts that are not predicted by the negativity scale.. A comprehensive theory of polarity sensitivity must explain what the semantic property is that all polarity contexts share.
3. Polarity Contexts Are Nonveridical
The formal property that all polarity contexts share is nonveridicality. Nonveridicality allows us to unify non-negative with negative (minimally and classically) licensers, which are characterized as anti-veridical.
3.1 Nonveridicality, Negation, and Uncertainty
Montague (1969) discusses veridicality relying on existence with reference to perception verbs such as see; Giannakidou, Zwarts, and more recently Giannakidou and Mari (2017) define it in terms of truth entailment; Giannakidou, 2013, 2014, establishes a relation between existence, truth, and inquisitiveness. Bernardi (2002) generalizes veridicality to a variety of types.
A veridical context is one that allows the speaker to infer the truth of a sentence; a nonveridical context is one where truth inference seems to be suspended. Consider the difference below between adverbs such as yesterday/(un)fortunately, which create veridical contexts, and modal adverbs, which create nonveridical contexts.
A veridical expression allows inferencing to the actual truth of the sentence: yesterday and unfortunately are thus veridical. Unfortunately is called sometimes factive because it appears to presuppose the truth of the embedded sentence; factivity can therefore be understood as veridicality. Modal elements, on the other hand, are nonveridical: under a modal adverb or verb, it is unclear whether p is true. From Mary possibly/ probably saw a snake, it doesn’t follow that she did or did not see a snake. A speaker uses Modal p if she is not (absolutely) certain that p is true. For this reason, modal adverbs and verbs have been characterized in the literature as weak (Karttunen, 1971; Kratzer, 1991; Giannakidou, 1997, 1999; Giannakidou & Mari, 2017, 2017; Portner, 2009). Giannakidou and Amri in fact argue that, by using a modal, a speaker signals that she does not know p.
Context means minimally a sentence S that denotes a proposition p embedded under a sentential operator F, as above. (Non)veridicality is about whether Fp entails or presupposes p; Zwarts (1995) and Giannakidou (1997, 1998, 1999) define it as follows:
Veridicality can also depend, as I alluded to, on what the speaker knows or believes to be the case, as typically observed with modals. In this case, veridicality is relative, or subjective (Giannakidou, 1994, 1998, 1999, 2013; Giannakidou & Mari, 2017, 2017). Subjective veridicality is needed also for discussing propositional attitude verbs, mood choice, predicates of personal taste, evidentials, and similar phenomena—while the role of knowledge or belief in assessing truth is apparent even in unembedded sentences; for example, Harris and Potts (2009) assert that all sentences are perspectival. Giannakidou, as well as Giannakidou and Mari, define veridicality subjectively as follows:
In the subjective definitions, it becomes clear that veridicality refers to epistemic states that universally support p (veridical: knowledge and belief, but also private states such as imagination, dream, and the like); nonveridicality refers to non-homogenous partitioned states that only partially support p, and which also allow non-p worlds. Modal bases of modals, disjunctions, subjunctives, and imperatives are such contexts; hence it is no surprise that they license NPIs and FCIs. Questions are also nonveridical spaces: Did Ariadne talk to anybody? presupposes an epistemic state of the speaker with worlds where Ariadne saw somebody and worlds where she didn’t. Giannakidou (2013) bring together modal assertion and questions as nonveridical inquisitive spaces. Nonveridicality gives the good result of being able to account for a long-standing problem, namely why questions and modals are a core NPI environment.
How about negation? Negation does not validate the veridicality schema Fp ⇒ p, and it is therefore nonveridical; at the same time, negation entails not p. This is labelled ‘antiveridicality’:
Antiveridicality is the reversal of veridicality, the strengthening of the uncertainty into certainty that not p. Apart from negation and negative quantifiers, the connectives without and before also allow antiveridical inference, as in John worked without having any break, or John died before he saw any of his grandchildren. For the nonveridicality of before, see Sanchez-Valencia, van der Wouden, and Zwarts (1993), Giannakidou (1997), and Xherija (2016), who proposes that before contains disjunction.
Nonveridicality, therefore, appears to characterize the contexts where NPI and FCIs appear, as formulated in the thesis below. A pictorial depiction is also given in Figure 1.
As can be seen, nonveridicality is a conservative extension of negation, allowing a wider distribution of NPIs in non-negative contexts. For a proof that all DE environments are nonveridical, see Zwarts (1995). Polarity sensitivity emerges empirically as a phenomenon that has to do not just with polar opposition, but also with truth undecidedness—and negative and non-negative licensers can be unified, something that was previously impossible. Nonveridicality also plays a decisive role in the selection of subjunctive mood and other non-assertive moods (see Giannakidou, 1995, 1998, 2009); it appears therefore to be a logical category with broader applications in grammar.
The veridicality judgment lies at the foundation of cooperative communication, as is revealed by the significance of Grice’s maxim of quality (be truthful). It is therefore not surprising that expressions exist in language (NPIs, FCIs) that are sensitive to it. Negative inference is also pretty basic: it is the ability to reverse the truth value (Horn, 2001). Nonveridicality links logically uncertainty with negation, and in so doing it unifies NPI-licensers as a natural class—a remarkable achievement that is available with no other theory.
3.2 Veridicality Conflict and Secondary Licensing of NPIs
Some NPIs, most notably any and English minimizers, appear in contexts that exhibit veridicality conflict. The data have been known since Baker and Linebarger, as mentioned earlier, and have been treated in terms of implicit negation. More examples:
English minimizers are weak NPIs, but have been referred to as strong.1 The data with only and emotives are challenging, since emotives and only allow veridical inference and are not DE (Atlas, 1993, 1996; for recent overview, see Beaver & Clark, 2003):
Von Fintel (1999) and Hoeksema (1986) weaken the DE inference to deal with the problem. If it is known in the context that John ate spinach, then from Only John ate a vegetable (which presupposes that John ate a vegetable) it can be inferred that Only John ate spinach. Von Fintel calls this Strawson-DE. Giannakidou (2006) criticizes Strawson-DE as overpredicting NPIs, for example, also in positive sentences: if it is known that John ate spinach, then the assertion John ate a vegetable allows one to infer that John ate spinach. But this will not suffice to legitimize NPIs, as *John ate any vegetables remains ungrammatical.
Giannakidou also points out that Greek-style NPIs, weaker and stronger, are blocked from only and emotives. The same holds for Spanish and Catalan (as well as Korean and the other NPIs mentioned at the beginning that pattern with Greek). Notice below that contrasts with English (the data are from Giannakidou, 2006):
This crosslinguistic variation suggests that only and emotives are not typical licensers. Unlike the regular licensers, only and emotives combine a veridical (69) and a nonveridical component seen below, thus creating veridicality conflict.
The negative clause is an entailment with only, and an implicature with emotives (Linebarger, 1980). Giannakidou (2006) argues that in veridicality conflict situations, NPIs are not licensed, strictly speaking, but rescued (previously called indirect licensing; Giannakidou, 1997, 1998):
Rescuing is a secondary mode of licensing that relies on inferencing of the global context, that may include presuppositions and implicatures. The positive presupposition of only blocks NPIs in Greek, Spanish, and Catalan, and the negative implicature of emotives (wish/expect that NOT) licenses any. Horn (2002) further structures the global context with assertoric inertia: one component becomes assertorically inert, and another becomes salient. If the salient component contains negation, NPIs will be licensed. Compare, for instance Ariadne barely said anything—where Ariadne didn’t say much is salient, but the positive Ariadne said something is inert—to *Ariadne almost said something, where the inert part is the negative Ariadne didn’t say anything, therefore unable to license any. Assertoric inertia is helpful in constraining when rescuing will be successful.
Importantly, recent experimental evidence (Xiang et al., 2016) confirms indeed that, at least with emotive verbs, the neurophysiological status of NPIs differs from that found in nonveridical contexts; and Chatzikontantinou et al. (2015) further show that the judgment for emotives borders the ungrammatical judgment for NPIs in Greek. Duffley and Larivée (2015), finally, in their corpus study show that NPIs with emotives are rare compared to negations or questions. These observations support the view that NPI rescuing is qualitatively different from licensing, and that NPIs differ in their ability to be sanctioned by the secondary mechanism.
4. Lexical Semantics of Polarity: Scalarity
It has been established that polarity as a phenomenon of natural language reveals sensitivity to negation and nonveridicality. Now it is time to ask the question: what triggers this sensitivity? This question needs to be addressed individually for each NPI and FCI, but some general patterns of lexical meaning have been shown to play a major role. One such pattern is scalarity; the other is dependent variable. These will be discussed in turn.
Many NPIs are scalar operators and affect rhetorical structure. Israel (1996, 2004, 2011) presents the most recent and comprehensive version of this idea. NPIs trigger pragmatic ordering, which, with negation, results in rhetorically strong statements if the value of the NPI is minimal (He didn’t say a word). NPIs can also create rhetorically weaker, attenuating statements; this happens if the NPI value is high (He didn’t read much, vs. *He read much). In both cases there is a correlation between the informational value of the NPI, ordered along a pragmatic scale, and negation. Scalar NPIs thus depend crucially on negation and negative inferencing. This observation is borne out by any for the most part, minimizers, and the other English scalar NPIs discussed by Israel.
As pointed out at the beginning of the paper, however, the Greek kanenas, Mandarin shenme, and Korean rato-NPIs are not scalar (Giannakidou, 1998, 2011; Giannakidou & Quer, 2013; Lin, 1996; Giannakidou & Yoon, 2014, 2016). Non-scalar NPIs do not affect rhetorical structure, but appear to express indeterminacy of reference—what Giannakidou and Quer call referential vagueness. Scalar and non-scalar NPIs both appear in nonveridical contexts, but obviously for different reasons. Many non-scalar NPIs contain dependent variables. Any, Giannakidou argues, is both scalar and with a dependent variable.
4.1 Scalarity and Widening
The scalar analysis originates in Fauconnier’s (1974) discussion of superlatives and minimizers:
A single thing and the slightest sound designate the lower end of a (pragmatic) scale, where for example sounds are ordered based on how strong they are. If one cannot hear the slightest or one single sound, it follows that one cannot hear the sounds above the slightest on the scale, thus one cannot hear anything.
In questions—Did John hear a single thing?—negative bias is produced: the question becomes rhetorical, expecting a negative answer. Any, however, does not have negative bias in questions (Ladusaw, 1980): Did you see anything? is a genuine information question. So there is an asymmetry between minimizers and any (though see Lee & Horn, 1994 for an attempt to unify the two by positing even in any). Hence the explanation invoked for negation cannot be extended to the second most prominent NPI environment for NPIs.
Kadmon and Landman (1993) and Krifka (1995) develop further the scalar approach of any. Kadmon and Landman (1993) say that any contributes widening. Widening is felicitous only if it produces strengthening. This is what licenses any:
The idea is that widening has the purpose of strengthening the any statement—but this does not appear to be a property of all scalar NPIs, since attenuating NPIs also exist as we know from Israel’s work (I don’t like him much). Hence widening cannot extend to NPIs as a class, even if it were to be posited for any.
Strengthening, the claim goes, is satisfied in a negative context, but not in a positive one:
Without negation, the widened statement does not entail the c statement, and strengthening fails, ruling out any. Strengthening is satisfied with negation, so any is fine. This reasoning could generalize in order reversing environments—but recall that any appears in non-monotonic contexts such as questions, modals, generics, imperatives, and disjunctions.
In a domain that consists of three boys, any boy quantifies over subdomains that contain one boy, two boys, and all three boys. These alternatives are said to be “active” with any, and to enrich plain meaning. The domain of individuals is not ordered, and in choosing among alternatives, speakers tend to go for the strongest one they have evidence for. In the case above, even the most broad choice of D makes the sentence true: “the base meaning will acquire an even-like flavor” (Chierchia, 2006, p. 556). In Chierchia (2006, 2013) positive sentences with any are ruled out as contradictions. However, any needs to be licensed grammatically, a fact that does not follow from this kind of reasoning.
4.2 Problems with Widening Accounts
In all widening approaches, the failure of an NPI in a positive veridical sentence is of pragmatic nature. The first, rather obvious, problem lies in the fact that the ill-formedness that such an explanation predicts is weak: sentences with failed any do not have the same status as infelicitous sentences—that is, uninformative or contradictory sentences—none of which is judged ungrammatical. One can say I talked to every student in the universe last night, or Ariadne kicked and ball and Ariadne didn’t kick the ball. These would be odd things to say, but the grammar doesn’t rule them out.
Chierchia acknowledges the insufficiency of the pragmatic explanation, and proposes a syntactic account of licensing: any has an uninterpretable syntactic feature [+σ] (Chierchia, 2006, p. 559) that must be checked against an operator that bears it. Negation and DE have the feature [+σ], but it is unclear if non-negative nonveridical operators have it. For more critical points, see Giannakidou (2011, 2016). Here it is pertinent to note that in Chierchia the semantics alone is not enough to deliver grammaticality in nonveridical contexts.
An additional problem with widening is that it is simply not true that any enlarges the domain. Below, any occurs with a partitive phrase:
With these cards, the use of any does not make us think of additional cards. Clearly, there is an intuition about exhausting the domain with any—shared with FCIs, as will be shown in section 6—but exhausting the domain is different from widening it. The literature has therefore been critical of the idea of widening as formulated in Kadmon and Landman, and uses instead the concept of exhaustivity (for some more point against widening, see Arregui, 2008; Giannakidou, 2011, Giannakidou & Quer, 2013).
5. Dependent Variable NPIs and FCIs: Semantics and Syntax
Giannakidou (1998, 2001, 2011) and Giannakidou and Quer (2013) propose that NPIs may contain a dependent variable. The Greek, Mandarin, and Korean NPIs belong to this class (for recent discussion of Mandarin shenme and the role of dependent variable in acquisition, see Lin, 2015). By acknowledging dependent variables, the “anomalous” character of NPIs becomes part of referential dependencies that exist in grammar, for instance, with anaphoric nominals, anti-specific and obligatorily narrow-scope indefinites, the genitive of negation in Russian (Partee, 2008; Partee & Borschev, 2004), English bare plurals (Carlson, 1977), and distributivity markers that need higher plurals to distribute over (Farkas, 1998; Pereltsvaig, 2008; Henderson, 2014). Here are two well-known English examples:
Each requires that there be a c-commanding plural to distribute over, and himself needs a c-commanding male antecedent. These syntactic needs are motivated semantically: each is distributive and a singular can’t distribute; himself cannot refer by itself, it acquires reference from an antecedent. These semantic needs translate into syntactic requirements (c-command) with each and himself, resulting in ungrammaticality if the requirement is not met. The idea of dependent variable for NPIs renders them part of this class of semantically driven syntactic dependencies. Progovac (1994) was the first to suggest a similarity between pronouns and NPIs, and offered an account of NPIs in the style of binding theory.
Giannakidou and Giannakidou and Quer frame the issue in terms of an isomorphism between semantics and syntax. There are two kinds of variables in natural language, dependent and non-dependent. Dependent variables are lexically deficient, and can only be well-formed if they are found in an appropriate structural relation with another expression that will value them. The presence of a dependent variable therefore creates limited distribution. The dependent variable class includes NPI and FCI variables, but also the non-polarity variables mentioned earlier, as well as the temporal variable of the subjunctive mood (‘temporal’ polarity in Giannakidou, 2009), subjects of control verbs such as try, manage, etc. (Grano, 2011). What all these variables have in common is that they cannot be free; in order for them to become licit they need to be bound or identified with antecedents:
This framework imposes an isomorphism between semantics (dependent variable that cannot remain free) and morphosyntax (a dependent variable being a distinct syntactic object from a non-dependent variable). The dependent variable creates a semantico-syntactic dependency at the logical form, and therefore leads to grammatical, and not simply interpretative, failure. As seen earlier, himself is ungrammatical because the anaphor contains a dependent variable that needs to be identified with a c-commanding antecedent, and the sentence lacks such an antecedent. Likewise, in *The student each ate an apple each the word each creates a problem because it is a dependent distributive variable necessitating a plural nominal to distribute over.
In other words, the dependent variable is an element that establishes a syntactic narrow scope or co-dependency that is motivated semantically. Giannakidou (1998) argues that NPIs and FCIs contain dependent variables which cannot introduce a discourse referent. One can think of these variables as non-deictic:
A non-deictic variable cannot be used to introduce a discourse referent if unembedded. These restrictions, which can be viewed as presuppositions on the interpretation of the variable, ‘trap’ NPI variables in nonveridical contexts. This derives the narrow-scope property of NPIs without further qualifications or a special NPI constraint. Semantic licensing—the ‘be in the scope of’ condition—and syntactic licensing (be in the c-command domain) become isomorphic. Nonveridical contexts are appropriate for non-deictic variables because in those contexts NPIs are not forced to introduce discourse referents. Giannakidou designates the dependent variable of the Greek NPI kanenas as xd and xni:
Under negation, ∃-closure of xd will be fine because xd does not introduce a discourse referent under negation; the scope above negation is impossible, because it would force introduction of a discourse referent. Den Dikken and Giannakidou (2002) analyze further any and wh-the-hell phrases as NPIs along this line.
The free choice determiner contributes a dependent variable of type s—wd—and this variable brings about the anti-episodicity effect we observed: it rules out FCIs in episodic contexts because they do not contain a w binder (Giannakidou, 1998, 2001). The wd renders FCIs intensional indefinites, necessitating the presence of modals, generics, and other quantificational binders, thus capturing successfully their distribution. FCIs have, in addition, a presupposition of exhaustive variation, which requires that they exhaust all values in the domain. This property is responsible for the quasi-universal flavor of free choice, and in some theories exhaustive variation is implemented by adding an actual universal quantifier (e.g., Kratzer & Shimoyama, 2002; Aloni, 2007; Menéndez-Benito, 2010). Any appears to convey, in most (but not all) FC uses, exhaustive variation—but the NPI use is never paraphrasable by a universal:
The dependent vs. non-dependent variable contrast can be seen as type difference or as variables belonging to different systems. In such framing, the idea of colored variables (Gardent & Kolhase, 1996) may be useful. In Giannakidou’s work and in Giannakidou and Quer (2013), the constraint that a variable cannot remain free was a presupposition, so the failures are presupposition failures. Presupposition failures do not generally lead to ungrammaticality, but a failure of this kind does—just as with anaphors, distributivity markers, etc.—because the presupposition failure translates syntactically into a syntactic relation between NPI and licenser (checking, matching, or binding). NPIs and FCIs thus exhibit a true semantico-syntactic dependency, as suggested also by experimental accounts we mentioned at the beginning.
6. Exhaustification and Referential Vagueness
This last section addresses the debate about the alleged exhaustivity of NPIs, as expressed in the view below:
This view surfaced recently in a number of works (Chierchia, 2006, 2013, and works following). Exhaustification is stipulated without empirical justification as the defining ingredient in all NPI/FCI classes. Giannakidou (2016), Lin and Giannakidou (2016), and Giannakidou and Yoon (2016) criticize this view, and defend the thesis that not all NPIs are exhaustified. Evidence again from Greek, Korean, and Mandarin NPIs is presented in those works showing that these NPIs contrast empirically in a number of significant ways with the intended exhaustified NPI any. Giannakidou (2016) further argues that it is not even clear what exhaustification means any. This brief article cannot go into detail, but will give an idea of the empirical differences between any and the Greek, Mandarin, and Korean NPIs. These differences can serve as useful diagnostics for distinguishing these two types of NPIs.
Technically, Chierchia’s exhaustification uses two covert syntactic devices: O(nly) and the [+σ] feature that we talked about earlier. Both are posited ad hoc—a point for which the theory has been criticized also by Geurts (2009, 2010). Granting for the moment that any is the exemplar of ‘exhaustified,’ and without any additional stipulations, exhaustification predicts behavior akin to any. Here are the core properties of any, observed in non-negative contexts where the FC reading is triggered:
1. Any has reduced tolerance to exceptions.
2. Any has free choice readings with modals, conditionals, and imperatives.
3. Any appears with a relative clause in an otherwise veridical sentence. In this case again a free choice reading arises.
4. Any has supplementary uses.
5. Any and FCIs are implausible with universal modal verbs.
Most of these facts are typical also for FCIs. Giannakidou (1998, 2001) was the first to propose that FCIs have a presupposition of exhaustive variation which is responsible for their universal-like reading. The question, when it comes to NPIs, is: do all NPIs behave like any with respect to the above—and if not, what is the analytical advantage of maintaining exhaustification for all NPIs?
Here are a number of asymmetries within the NPI classes represented by any and the Greek NPI respectively. Consideration is limited to the Greek NPI, but see Giannakidou and Yoon (2016) and Lin and Giannakidou (2016) for the respective Korean and Mandarin data.
6.1 Greek NPI Tolerates Exceptives
Any does not combine with exceptive phrases, but the Greek NPI does:
In the modal context, any receives free choice reading, which excludes the exceptive. The Greek NPI lacks this reading and tolerates exceptives.
6.2 Greek NPI Gets Non-Free Choice in Imperatives
The Greek NPI tolerates exceptions also in the imperative. In fact, the imperatives with Greek NPIs and FCIs are substantially different:
The Greek FCI and any induce a reading where the addressee comes to the dessert table with a great appetite, and the speaker invites her to try every option if she wishes to. By contrast, the Greek NPI invokes a context with average or little appetite, and is a suggestion to eat some cookie or other. In a context where some cookies are off limits, the NPI versions are good, but any/FCIs are bad (see Lin and Giannakidou, 2016 for more discussion, including Mandarin data):
6.3 No Indiscriminative Reading of Greek NPI in Conditionals
If-clauses are good environments for NPIs and FCIs. The latter trigger the so-called indiscriminative, just any reading (see Haspelmath, 1997; Duffley & Larivée, 2010), and here is variant of an example due to Larry Horn (2005). The Greek NPI, as we see, cannot convey the indiscriminative reading, but FCIs can.
6.4 No Subtrigging of the Greek NPI
In veridical simple past sentences, all NPIs are ungrammatical. This is the defining feature of both NPIs and FCIs, but any improves with a relative clause—a phenomenon called subtrigging (LeGrand, 1975). In subtrigging, any is interpreted with free choice (Dayal, 1998; Giannakidou, 2001; Horn, 2005). The Greek NPI kanenas cannot be subtrigged:
FCIs, like any can be subtrigged:
Hence, the subtrigging diagnostic reveals another difference between the Greek NPI and any that doesn’t follow from the assumption that they are one class.
6.5 No Supplementary Use for the Greek NPI
Any and FCIs exhibit supplementary use (Horn, 2005), but the Greek NPIs do not:
The effect is similar to the tolerance of exceptions noted earlier. It is again difficult to imagine how the contrast can follow from idea that any, opjondihopote, and kanenas are all due to the same mechanism as exhaustivity for all would have it.
6.6 Greek NPIs Are Fine with Universal Modal Verbs
Finally, any and FCIs are implausible with universal modal verbs, but Greek NPIs are fine:
Overall, then, there are six asymmetries between Greek NPIs and any that are due to the fact that the Greek type of NPI lacks free choice. These asymmetries can serve as diagnostics for other NPIs as well. If any is the exemplar of ‘exhaustified’ NPI, it is hard to imagine how the kanenas-NPI can be exhaustified too.
6.7 Alternatives Need Not Be Exhaustified: Referential Vagueness
Considerable differences have been found between the Greek type of NPI and any that do not follow if a unified analysis is assumed. One could, of course, axiomatically hold on to uniformity and add a panoply of ad hoc stipulations, resulting to a proliferation of rules. Most researchers would be led to the conclusion that a system without these stipulations is superior to the Rube Goldberg contraption that such an analysis would end up constructing around itself. The alternative would be to simply to take the above differences at face value as indicating that not all NPIs are exhaustified. This is the avenue taken by Giannakidou and coauthors. They argue that some NPIs have a presupposition not of exhaustivity, but of referential vagueness:
(The epistemic state of the speaker is modeled standardly as a set of worlds M(speaker) compatible with what the speaker knows or believes in the base world w). Referential vagueness, like free choice, expresses indeterminacy regarding the value of α; the speaker does not have a particular object in mind. Free choice and referential vagueness are both manifestations of anti-specificity (Giannakidou & Quer, 2013). With referential vagueness, however, the speaker is not making claims about the entire domain, unlike with free choice. Hence in both cases there is presupposed variation, but only with free choice is there exhaustive variation. Given the numerous NPIs crosslinguistically that behave similarly to Greek, a comprehensive understanding of polarity cannot ignore referential vagueness. Finally, referential vagueness is not a stipulated property of NPIs, but is independently shown to describe anti-specific, narrow-scope indefinites such as Spanish and Catalan algun (see also Alonso-Ovalle & Menendez-Benito, 2010), Greek kapjos, and similar items, which are not polarity sensitive.
This brief survey has explored the rich landscape of NPIs and FCIs and isolated some of the clearest and best-studied patterns. As noted at the beginning, polarity is a pervasive phenomenon in human language, but from a purely logical perspective, it is an anomaly: since there are “regular” quantifiers, why are polarity-sensitive versions of them needed?
The preceding discussion allows several answers to this question. As dependent variables, NPIs and FCIs manifest referential deficiency observed also in other areas of grammar—for instance, with anaphors, question words, and narrow-scope indefinites. From this perspective, NPIs and FCIs exist for the same reasons as these devices: to encode linguistic dependencies that reveal the speaker’s epistemic judgment about whether a potential referent is or is not known to her. At the same time, FCIs and some NPIs can be scalar, that is, manipulators of rhetorical force, as Israel (2011) succinctly puts it. Overall, scalarity and referential dependency appear to be properties that language systematically encodes in the polarity system, but also elsewhere in grammar.
NPIs and FCIs emerge as expressions sensitive to nonveridicality and negation. Nonveridicality is uncertainty about truth. The veridicality judgment, that is, how speakers extract inference from texts or speech to be certain or uncertain about truth, can actually be quiet complex, as shown in recent work by de Marneffe et al. (2012); but conceptually and cognitively, reasoning about the truth of sentences is a very basic property of human communication. The fact that there are linguistic expressions sensitive to nonveridicality, then, is hardly a surprise. Other linguistic devices sensitive to nonveridicality are the grammatical moods (subjunctive-indicative), modal verbs, and generally non-assertive devices such as the imperative, questions, and counterfactuals. NPIs and FCIs appear routinely in these contexts.
The negative judgment emerges, in this context, as a special case of nonveridical judgment. That NPIs are sensitive to negation, and some strictly require it, should again not come as a surprise, since negation is cognitively quite basic, and in a fundamental way is a hallmark of human language (Horn, 2001). While nonveridicality is uncertainty about truth, negation is the strengthening of uncertainty to certainty that not. Finally, it is worth repeating that the category of minimal negation—that is, mere downward entailment—plays very little role, by itself, in the licensing of PIs. I do not know of any language that has NPIs that appear with few and in the restriction of every, but are excluded with not. And for well-known NPIs that appear in nonveridical contexts—such as Greek kanenas and Dutch ook maar iets—minimal negation is sometimes not enough to license them.
Many thanks to Jack Hoeksema for his detailed comments on the paper, and to the reviewers and editors of the Oxford encyclopedia. I am very grateful for the opportunity to write this paper, and hope that the reader will enjoy this brief journey into the landscape of polarity items in language.
Collections on Negation and Polarity: Syntax-Semantics
Forget, D., Hirschbühler, P., Martineau, F., & Rivero, M. L. (Eds.). (1997). Negation and polarity: Syntax and semantics (pp. 209–230). Amsterdam: John Benjamins.Find this resource:
Hoeksema, J., Rullmann, H., Sánchez-Valencia, V., & van der Wouden, T. (Eds.). (2001). Perspectives on negation and polarity items. Amsterdam: John Benjamins.Find this resource:
This volume comprises papers from the Groningen Workshop on Polarity that was held at the University of Groningen in 1996, and contains syntax-semantics, pragmatics, and corpus studies of NPIs. Corpus studies started emerging around that time, mostly due to Jack Hoeksema’s work on Dutch NPIs.
Horn, L. R., & Y. Kato. (2000). Negation and polarity: Syntactic and semantic perspectives. Oxford: Oxford University Press.Find this resource:
A collection of articles with emphasis on English and Japanese, including historical data.
Penka, D., & Zeijlstra, H. (Eds.). (2010). Negation and polarity items. Natural Language and Linguistic Theory, 28, 4.Find this resource:
This collection is in a thesis-response format, and contains research in syntax, semantics, and historical developments of NPIs.
Horn, L. (Ed.). (2010). The expression of negation. Berlin: De Gruyter.Find this resource:
This work combines theoretical with typological approaches, along with data from corpus linguistics (e.g., Hoeksema’s paper mentioned in the overviews above). Horn offers also an updates and quite comprehensive bibliography: “Negation in the new millennium: a bibliography,” pp. 289–232.
Negation, Negative Concord, Neg-Raising
Collins, C., & Postal, P. (2014). Classical Neg-raising. Cambridge, MA: MIT Press.Find this resource:
This is an updated syntactic approach to Neg-raising.
Horn, L. (1978). Remarks on neg-raising. In P. Cole (Ed.), Pragmatics (pp. 129–220). Syntax and Semantics 9. New York: Academic Press.Find this resource:
In this classic and much-cited paper, Horn identifies the phenomenon of Neg-raising and offers a pragmatic explanation of it within his theory of Q and R-implicature.
Gajewski, J. (2007). Neg-raising and polarity. Linguistics and Philosophy, 30, 289–328.Find this resource:
This paper discusses NPI-licensing in Neg-raising contexts. Specific features of presupposition projection are used to explain the licensing of strict NPIs under Neg-raising verbs.
Giannakidou, A., & Zeijlstra, H. (2017). The landscape of negative dependencies: N-words and negative concord. In the Blackwell Companion to Syntax, 2d ed.Find this resource:
This is a detailed overview article of n-words and negative concord.
Penka, D. (2007). Negative indefinites (Unpublished PhD diss.). University of Tübingen.Find this resource:
This is a study of German n-words (such as k-ein) and their scopal properties. The main thesis is that they involve an indefinite component and negation, and there is also typological discussion.
De Swart, H. (2010). Expression and interpretation of negation: An OT typology. Dordrecht: Springer.Find this resource:
This is an analysis of negative concord and negation within the framework of optimality theory. There is also discussion on the acquisition of negation.
de.Swart, H. (2000). Scope ambiguities with negative quantifiers. In K. von Heusinger & U. Egli (Eds.), Reference and anaphoric relations (pp. 109–132). Dordrecht: Kluwer.Find this resource:
Here a pragmatic explanation is attempted for the scope interaction of Germanic negative quantifiers, negation, and modal verbs.
Any: Free Choice or Existential?
Carlson, G. N. (1980). Polarity ‘any’ is existential. Linguistic Inquiry, 11(4), 799–804.Find this resource:
Here Carlson proposes a separation of NPI and FCI any, with NPI-any being existential.
Davison, A. (1981). Any as universal or existential. In J. van der Auwera (Ed.), The semantics of determiners (pp. 11–34). London: Croom Helm.Find this resource:
This work is cited often as the source of some of the core diagnostics for free choice any, for example almost/absolutely modification.
Expletive Negation as a Polarity Item
Espinal, M.-T. (2000). Expletive negation, negative concord, and feature checking. Catalan Working Papers in Linguistics, 8, 47–69.Find this resource:
This is the first formulation of the idea that there is a correlation between expletive negation and nonveridicality/antiveridicality.
Espinal, M.-T. (2007). Licensing expletive negation and negative concord in Catalan and Spanish. In Floricic (Ed.), (pp. 49–74).Find this resource:
Espinal continues to study Catalan and Spanish expletive negation. The approach is mainly syntactic.
Yoon, S. (2012). NOT in the mood: The syntax and semantics of evaluative negation (Unpublished PhD diss.). University of Chicago.Find this resource:
This is an analysis of Korean expletive negation as a mood (subjunctive marker) licensed by nonveridicality.
Aloni, M. (2007). Free choice, modals and imperatives. Natural Language Semantics, 15, 65–94.Find this resource:
Alonso-Ovalle, L., & Menendez-Benito, P. (2010). Modal indefinites. Natural Language Semantics, 18(1), 1–31.Find this resource:
Arregui, A. (2008). Some remarks on domain widening. In Natasha Abner and Jason Bishop (Eds.), Proceedings of the 27th West Coast Conference on Formal Linguistics (pp. 45–53). Somerville, MA: Cascadilla Proceedings Project.Find this resource:
Atlas, J. D. (1993). The importance of being only: Testing the neo-Gricean versus neo-entailment paradigms. Journal of Semantics, 10, 301–318.Find this resource:
Atlas, J. D. (1996). Only noun phrases, pseudo-negative quantifiers, negative polarity items, and monotonicity. Journal of Semantics, 13, 265–328.Find this resource:
Baker, C. L. (1970). Double negatives. Linguistic Inquiry, 1, 169–186.Find this resource:
Bernardi, R. (2002). Reasoning with polarity in categorial type logic (Unpublished PhD diss.). University of Utrecht.Find this resource:
Beaver, D., & Clark, B. (2003). Always and only: Why not all focus sensitive operators are alike. Natural Language Semantics, 11, 323–362.Find this resource:
Borkin, A. (1971). Polarity items in questions. Proceedings of the Annual Meeting of the Chicago Linguistics Society (= CLS) 7 (pp. 53–62). Chicago: Chicago Linguistics Society.Find this resource:
Carlson, G. (1977). Reference to kinds in English (Unpublished PhD diss.). University of Massachusetts, Amherst.Find this resource:
Chatzopoulou, A. (2012). Negation and nonveridicality in the diachrony of Greek (Unpublished PhD diss.). University of Chicago.Find this resource:
Chatzikonstantinou, A. (2016). Greek NPIs: Their semantic and prosodic processing (Unpublished PhD diss.). University of Chicago.Find this resource:
Chatzikontantinou, A., Giannakidou, A., & Manouilidou, C. (2015). Gradient strength of NPI-licensers in Greek. Paper presented at the 12th International Conference on Greek Linguistics. University of Potsdam.Find this resource:
Cheng, L. L.-S., & Giannakidou, A. (2013). The non-uniformity of wh-indeterminates with polarity and free choice in Chinese. Strategies of Quantification, 44, 123.Find this resource:
Chierchia, G. (2006). Broaden your views: Implicatures of domain widening and the “logicality” of language. Linguistic Inquiry, 37, 535–590.Find this resource:
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The bias is typically attributed to an implicit even which can actually be overt—Did he even say a word?—and which is independent of the minimizer: Is this even a real question? See Giannakidou (2007) for more details.