2 How any got a reputation for being scalar

The question of polarity sensitivity is profiled against the background of the notion of scales (Horn Reference Horn1972; Gazdar Reference Gazdar1979). This notion emerges from Grice's well-known conversational maxims and Ducrot's analogous laws of discourse. Both the Gricean maxim of quantity and Ducrot's law of exhaustivity stipulate that a speaker will convey all the information at his disposal that is necessary for the purposes of the conversational exchange. Thus if a speaker says that Jane is a good researcher, it is reasonable to infer that she is not a bad one, and equally reasonable to believe that she is not an excellent one, since if that were the case the speaker would have been expected to say so. These inferences are reversed by negation: if Jane is said to not be a good researcher, she will normally be understood not only to not be excellent, but to be downright bad. Negation thus affects the positive and negative terms of a pair of antonyms asymmetrically: if Jane is claimed to not be a bad researcher, she may be implied to be a good one, but one might also infer that she is only so-so, i.e. neither good nor bad. Negation of the positive term normally implies assertion of the negative one; negation of the negative term, on the other hand, yields an equivocal value ranging from an intermediate value to the positive pole of the opposition (Horn Reference Horn1989; Levinson Reference Levinson2000: 127–9).

Scales of ordered sets of values interact in a meaningful way with negation, and negative polarity items seem to generally involve such scalar models. Scalarity is a salient feature of the superlative expressions shown by Fauconnier (Reference Fauconnier1975, Reference Fauconnier, Guenthner and Schmidt1978) to give rise to striking pragmatic inferences based on scalar reasoning. Thus in some affirmative contexts, a minimum-value expression such as the faintest noise can convey a universal quantification, as in Jim can hear the faintest noise, while a total negation can be suggested in a negative context, as in Jim can't put up with the faintest noise. Similar contextual variation is found with maximum-value expressions, ranging from Jim can put up with the loudest noise (universal quantification) to Jim can't hear the loudest noise (total negation). While various situations may be involved having to do with factors such as the subject's hearing capacity or the surrounding noise level, the interpretations in both types of context concern an extreme position on a scale, as indicated by the possibility of modifying the superlative by even. The application of negation to such a scalar position is used as a means of negating all lower values on the scale.

Similar interpretative distinctions are observed with any, as in (4) and (5) below, which have led to the assumption that it too is amenable to a scalar analysis:

1. (4) Jim can put up with any noise.

2. (5) Jim can't hear any noise.

The hypothesis that polarity-sensitive expressions occupy extreme positions on a scale was further developed by Michael Israel in his 1998 thesis. Israel discerned an additional condition for negative polarity status besides that of evoking an end-point on a scale: the notion of emphasis. The fact that only emphatic minimal scalar expressions such as the least are able to cover the whole of a scale accounts for their being licensed in negative polarity contexts. Understating minimal scalar expressions such as some, which assert less than one might have expected, do not allow the sort of inferences required in such contexts. These inferences can be carried by any, however, which is therefore claimed to belong to the category of emphatic scalar expressions.

The view that any is a scalar item has been put forward notably by Laurence Horn, who from the 1990s on, in collaboration with Young-Suk Lee in 1995 in the first publication, has proposed a full-fledged development of the analysis of any first sketched in his 1972 thesis (see Lee and Horn Reference Lee and Horn1995; Horn Reference Horn, Horn and Kato2000a, Reference Horn, Carlson and Pelletier2005). The Gricean model developed by Horn uses scales to analyse items which give rise to implicatures, such as the determiner some, the modal auxiliary can and the adjective warm. In their use in neutral assertive contexts, such items often communicate a backgrounded rejection of another proposition. Thus I like some of Pasolini's films implies that the speaker does not like all of them; You can visit the Guggenheim means that the suggested museum outing is not obligatory; The verveine is warm implies that it is not hot. The opposition between one position on a scale and other possible positions would explain these background negations.

Scales are proposed by Lee and Horn to account for the meaning of any, which is treated as an indefinite and compared to the indefinite article. Thus the existential reading of the article is paralleled by the negative polarity use of any:

1. (6) There wasn't a tree in sight.

2. (7) There wasn't any tree in sight.

Both uses concern quantity, i.e. individuals. The generic reading of the indefinite article and the free-choice use of any, on the other hand, are claimed to refer to kinds rather than individuals:

1. (8) A five-year-old knows that wrestling is fake.

2. (9) Any five-year-old knows that wrestling is fake.

Horn's analysis converges with that of Kadmon and Landman, who in their 1993 paper propose an analysis of any along the two dimension of strengthening and widening. Strengthening is the property by which any N entails a N; widening extends the reference of N even to atypical members of the category denoted by the noun. Thus asserting that one does not have any matches is claimed to evoke a reference even to atypical exemplars, such as wet matches, an impression that would not be created by the assertion that one does not have a match, reference with any being intuitively broader than with the simple indefinite.

The intuition of a widening effect is captured by Lee and Horn through the postulate that the notion of indefiniteness in the meaning of any is associated with an underlying even: it is the notion that even the least likely exemplar is included in the predication that extends the set to include atypical members. The presence of the notion of even in the meaning of any also implies the presence of a scale. Free-choice any evokes the lowest point on a scale of kinds and can be paraphrased by even + superlative,Footnote ² as in:

1. (10) Any puppy is cute.

   ‘Even the ugliest puppy is cute.’

NPI any denotes the lowest point on a scale of quantities and can be paraphrased by even a single (for count nouns) and even a bit/even the least bit (for mass nouns), as in:

1. (11) There isn't any person available now.

   ‘There isn't even a single person available now.’

2. (12) There isn't any food in the refrigerator.

   ‘There isn't even the least bit of food in the refrigerator.’

The presence of scalarity with any would be supported by the parallel behaviour of its paraphrases with respect to modification by whatsoever and at all for all usagesFootnote ³ and by absolutely and almost for free choice. This would evidence a scalarity absent from the indefinite article, which does not support these modifications. The hypothesis that scalarity percolates from an underlying even also finds comfort in the observation that this particle is a common morphological component of the equivalents of any in various languages (Haspelmath Reference Haspelmath1997: 157), Hindi being a well-documented case (cf. Lahiri Reference Lahiri1998, Reference Lahiri2001).

The unitary nature of any is accounted for in this approach by the fact that the combination of indefiniteness and the evocation of the lowest point on a scale underlie all of the uses of this determiner, with the NPI/FC distinction being explained by the application of the scalar notion to the domain of ‘quantity’ versus ‘kind’. In later work, Horn has focused on an additional semantic property of any, described by the term ‘indiscriminacy’ (Reference Horn, Carlson and Pelletier2005: 185). This aspect of any's semantics is claimed to be reinforced by the adverb just in usage such as (13):

1. (13) This isn't just any sport utility vehicle.

Here just any is used to convey the proposition, which is then denied, that the predicate holds for an arbitrarily chosen value on the scale of sport utility vehicles, including one at the scalar end-point (Horn Reference Horn, Horn and Kato2000a: 175).

The notion of scalarity is thus a central component of the meaning of any in the analyses proposed by Lee, Horn, Israel and Fauconnier, and is implied by the Kadmon and Landman treatment. These analyses are inspired by a new understanding of Gricean principles, a comparison between any and other polarized items such as superlatives, as well as by paraphrases using other polarity expressions. The centrality of scalarity is re-examined in the next section.

3 Down-scaling any

Is any inherently scalar? This question meets with a highly relevant observation in a comprehensive study of indefinite pronouns by Haspelmath (Reference Haspelmath1997: 121), who points out that interrogatives with scalar end-point indefinites are ‘somewhat odd’, so that a question such as Did you hear the slightest noise? ‘could hardly be meant as an information question, because it is very unlikely that the speaker should be interested about an extreme value’. This difficulty is also acknowledged by Krifka in his 1995 study, in which he concludes that information questions with NPIs are about ‘maintain[ing] an equilibrium between the informational value of the positive and negative answer’ (Reference Krifka1995: 254). This would suggest that the NPI itself does not denote an extreme value on a scale in this type of use, as this would lead to a rhetorical question in which ‘the speaker minimizes the a priori possibility for a positive answer’ (see also Gutiérrez-Rexach Reference Gutiérrez-Rexach1998; van Rooy Reference van Rooy2003): a question such as Did you hear the slightest noise? would only make sense with stress on slightest and in a situation where the speaker wishes to ascertain with certainty that the person being interrogated, who has already denied hearing any noise, really did not hear even the slightest noise. Guerzoni (Reference Guerzoni2004: 320–5; see also Heim Reference Heim1984) notes also that whereas questions with any can be used as neutral requests for information, questions with minimizers such as Does Sue have the slightest idea how hard I am working? are biased towards a negative answer.

These observations have significant import for the analysis of uses of any in interrogative contexts such as (14):

1. (14) Did you hear any noise?

Contrary to questions with end-point scalars, such sentences usually do have the force of neutral information-seeking questions. Since information questions do not normally bear on scalar end-points, a scalar analysis of any is highly problematic in this environment. By itself, this use of any would be sufficient to call into question the scalar account. However it is not an isolated case. Other commonplace instances of NPI and free-choice readings also appear to be incompatible with a scalar interpretation. Examples from both domains are given below.

4 Finean arbitrariness and scalarity

The paraphrase just given for (20) is reminiscent of the notion of arbitrariness proposed by Tovena and Jayez (Reference Tovena, Jayez, Corblin, Dobrovie-Sorin and Marandin1999) as the key to understanding the unity underlying the free-choice and polarity uses of any. As elaborated by Fine (Reference Fine1985), arbitrariness concerns the irrelevance for the truth of a given proposition of individual variants. According to Tovena and Jayez, free-choice any applies arbitrariness to individuals, which become ‘arbitrary objects’ in Fine's sense of having their individuality treated as irrelevant in favour of some generic property which they satisfy wholly and exclusively. Applied to (21) below, this means that it is only because it is on the reading list that a given book b is read, and not because of its intrinsic interest or clarity:

1. (21) Mary read any book on the reading list.

In the polarity-sensitive use of any, arbitrariness is applied to events or propositions rather than to individuals: a proposition I is arbitrary with respect to a proposition J if J entails I and any individual variant of I. Arbitrariness is here fundamentally equivalent to the logical notion of dependency: an object is arbitrary if its choice is solely dependent on a certain property and not because of other properties it might have, so one object with the desired property can be chosen arbitrarily just as well as any other. This is connected, according to Tovena and Jayez, to the unprovability of a negative statement such as (22):

1. (22) Mary did not read any book.

There are infinitely many possible events of reading book b which are excluded by a judgement such as Mary did not read b, thus making this judgement unverifiable by direct observation. All of the possible events negated by a sentence such as (22) are treated by means of any as individual variants of the event-type ‘read a book’; these individual events are therefore irrelevant to the truth of the proposition, any one of them being replaceable by any other with the same properties. In this view, modification by whatsoever and absolutely extends the number of relevant entities of choice, and modification by almost restricts it, without there being any need to refer to scales.

Scalarity may, however, be accounted for by arbitrariness. If a given book is said to be read by virtue of the fact that it is on the reading list, then it has not been read in virtue of its intrinsic interest, clarity or any other property it might have. These properties may be unevenly distributed among the books in question, which can then be more or less likely to be read by Mary. This may yield a ranking of books according to the likelihood of their being read by Mary, which produces an interpretation akin to a scalar effect. While scalarity cannot be a necessary consequence of arbitrariness, in view of the existence of non-scalar uses of any in both polarity (15–17) and free-choice (18–20) contexts, arbitrariness could explain scalarity. The arbitrariness hypothesis thus seems to provide a broader account of the uses of any than does the scalar view. What is more, it offers the potential to explain scalarity effects. These effects can be favoured by various linguistic factors in the utterance, three of which are considered in the following section.

5 Conditions for scalarity

The story so far is that, contrary to what is suggested by paraphrases containing superlatives and minimizers, any does not always evoke an extreme position on a scale of values. An information question such as (23):

1. (23) Would anyone like a coffee?

simply indicates that each person within earshot is treated equally as a possible candidate for wanting more coffee. Scalar effects can however be produced under certain conditions.

One such condition is the presence of stress on any, a factor recognised by KrifkaFootnote ⁴ (Reference Krifka1995; see Beaver and Clark Reference Beaver and Clark2008 for a more general treatment of the role of stress for meaning). Whereas an unstressed any in a sentence such as (24) below simply evokes the obligation to remove whatever dirt there might be:

1. (24) Any dirt has to be removed,

placing stress on any would produce the effect of evoking the low end-point of a quantity scale. Stress in English can have two values, ‘contrast’ (Rooth Reference Rooth1992) and ‘intensification’ or ‘emphasis’ (cf. Hirst Reference Hirst and Séguinot1977), as illustrated by (25) and (26) below:

1. (25) I want the BIG one (i.e. not the small one).

2. (26) That was one BIG animal, that moose!

Since any does not denote any particular quantity which could be contrasted with another quantity, we assume that stress is used emphatically when it occurs with this quantifier, placing emphasis on the notion of indiscriminate freedom of choice. Emphasizing this notion, moreover, creates the effect of inducing a pragmatic scale in the following way: if a speaker insists on the fact that no matter what dirt must be removed, this will logically entail the inclusion of even the tiniest speck of dirt. Of course, this amount is also implicitly covered in the unstressed use of any, but without focus on the fullness of the freedom of choice, the end-points of the scale are not given any particular status with respect to the other quantities in the range of reference, all of the latter being placed on the same footing as possible candidates to which the predication applies.

There is no stress on any in the imperative Pick any card, which has been used by Giannakidou (Reference Giannakidou2001) and Horn (Reference Horn2000) as a counterexample to analyses associating free choice with some form of universal quantification (see also Larrivée Reference Larrivée2007b). As expected also, there is no impression of a scale in such a use either, neither a quantitative one (*‘even a single card’) nor a qualitative one (*‘even the card you would be least likely to pick’). The deck is not conceived here as being ranked in any particular hierarchy – all of the cards have the same status as eligible candidates for selection. If stress were to be placed on any, however, a scale could be created. This would correspond to a situation in which the hearer had shown some signs of treating certain cards (perhaps the ones on the top of the deck) as being unselectable. The speaker could then cancel the assumption of selectiveness by emphasizing the complete fullness of freedom of choice.Footnote ⁵ The fact that even the cards the hearer might suppose to be excluded from the possible range of choice are said to lie within it would be associated here with an ordering of the cards in terms of their selectability.

Conditionals and interrogatives follow the same pattern:

1. (27) (a) If you hear anything, wake me up.

2. (b) If you hear ANYTHING, wake me up.

3. (28) (a) Can you see anything?

4. (b) Can you see ANYTHING?

As pointed out by Haspelmath (Reference Haspelmath1997: 125), there is a clear difference in meaning between the utterances with and without stress on any: in the (b) sentences ‘a scale of alternative values is present of which the chosen value is the end-point’; in the (a) sentences ‘no such scale is present’. The (a) sentences involve the applicability of the condition or question equally to all possible candidates which it might concern. Emphasizing the fullness of the freedom of choice as in the (b) sentences, on the other hand, leads to a focus on the extreme fringes of the range: ‘even the slightest noise’, ‘even the fuzziest outline of a thing’. As Guerzoni (Reference Guerzoni2004: 321) points out, in such contexts interrogatives are usually biased towards a negative answer rather than being neutral requests for information. This is because a question about a fringe value implies that the speaker has already received a negative response about core values and is double-checking the situation by inquiring about extreme values.

The use of unstressed any in negative contexts can also be argued to be non-scalar. Haspelmath (Reference Haspelmath1997: 125) observes in this respect that both ‘emphatic’ and ‘non-emphatic’ indefinites are possible in direct negation, but admits ‘it is not clear to me whether one can say that only the second involves a scale’:

1. (29)

   1. (a) I didn't SEE anything.

   2. (b) I didn't see ANYTHING.

If however the negation in (29a) is analysed as applying to whichever possibly chosen element one might like to consider within the range of things that could have been seen by the speaker, there is no need to invoke the presence of a scale to explain the production of the effect of total negation. To be sure, the negation of the minimal quantity on the scale of things possibly seen by the speaker (‘not even one thing’) is logically equivalent to (29a). But such an equivalence is situated on the level of the end achieved (the message of a total negation) and not on that of the linguistic means used to achieve this end. The account proposed here has the advantage of showing how usage in negative contexts fits into the overall pattern of the uses of any and its interaction with the feature of stress. The unambiguous impression of a scale observed with the stressed use of any in (29b) can be explained by means of the same principles as those applied to the other types of context discussed above.

To sum up the discussion of the role of stress, one could say that it activates a potential for scalarity in the notion of indiscriminate arbitrariness expressed by any. The notion of a possibility of complete freedom of choice within a range has the potential to give rise to a scalar impression if something causes focus to be brought to bear on the fringe of the range. One factor associated with such a focus is placing emphasis on the fullness of freedom of choice, which can provoke the inference that even the outer fringes of the range are covered.

The production of a scalar impression can also be due to the grammatical number of the noun following any.Footnote ⁶ The role of the noun's grammatical number in a noun phrase introduced by any is to specify whether the possible candidates for selection are to be extracted from the range singly or in groups. This can be seen in the contrast between (30a) and (30b):

1. (30)

   1. (a) She'll marry any blonde with a million dollars.

   2. (b) ?* She'll marry any blondes with a million dollars.

Only the first sentence makes sense in a monogamous culture, as it signifies a free choice ranging over singulars and not plurals. Because of any's meaning, in some cases the end result on the level of the message expressed may be basically the same whether the selectable candidates are extracted singly or multiply, as can be seen from the sentences in (31):

1. (31)

   1. (a) He didn't get any question in Section B right.

   2. (b) He didn't get any questions in Section B right.

Since all of the questions, whether they be considered one by one or in subsets, are covered as cases which, if adverted to, are negated, the resultant message is that of total negation in both of these sentences. This is not to say, however, that the two utterances are exactly equivalent: (31a) produces the impression of a stronger negation, associated with the notion of a quantitative scale (‘not even one’). The second sentence with the plural noun could simply be a factual report on how many questions the student got right in Section B on the exam, in which case there would be no stress on any. In contrast, the first sentence is difficult to imagine without stress on the determiner.

The relevant factor here is the default expectation with respect to a student's performance on a section of an exam, which is that normally at least a few questions should have been answered correctly. This default plurality is negated in (31b), which says that one can pull out whichever subset of questions one likes and the negation applies to it. The singular noun question in (31a), however, represents a departure from normal expectations. This entails that there must be some contrast between the actual situation and the norm which has led the speaker to envisage the possibility of getting questions right on the exam in terms of singular questions rather than in terms of groups of questions. Together with negation, this produces the impression that the person taking the test might have got at least one question in Section B right, but in fact did not. To our knowledge, the influence of the noun's grammatical number has not been taken into account in any study of any to date. The impressions involved are sometimes subtle, but cases such as (31) show that they are nonetheless real. The topic calls for an in-depth examination of usage which, unfortunately, cannot be undertaken here. More detailed research might for instance uncover the basis for Lee and Horn's (Reference Lee and Horn1995) intuition of scalarity in (32):

1. (32) Does Sue have any pen?

The authors cited get the impression here of ‘even a single pen’. This could be due to the noun being in the singular: since usually people have more than one pen, if someone asks a question applicable only to whatever singular pen Sue might have, it could be because something has contradicted the default expectation and led the speaker to question whether Sue has even one pen.

A third factor which can give rise to a scalar interpretation is the presence of a gradable concept in the noun phrase introduced by any. This can be seen in the contrast between (33a) and (33b) below:

1. (33)

   1. (a) Any mechanic will tell you that a Toyota has a better engine than a GM.

   2. (b) Any mechanic with a bit of sense will tell you that a Toyota has a better engine than a GM.

Whereas (33a) simply expresses the idea that you will get the same answer from whatever mechanic you might choose to ask, the presence of the quantitatively gradable notion in (33b) favours a scalar interpretation in which even the mechanic with the least bit of sense is covered by the speaker's assertion. The connection between gradability and scalarity is obvious and requires no further comment.