Apposing intensional quantifiers. Few, almost… Francis Corblin Université Paris-Sorbonne & IJN ABSTRACT Anscombre and Ducrot (1983) argues that the oddness of examples like (1): (1) ?Peu d’automobilistes dépassent le 120, presque 20%. Few drivers go over 80 m.p.h, almost 20%. can only be explained by positing “argumentative opposite orientations” for the quantifiers presque (almost) and peu (few). This paper introduces, against the author’s view, a classical solution to the puzzle dispensing of any recourse to argumentative consideration. The proposal is based on a deeper inspection of the crucial components of the puzzle, namely the relation between quantifiers illustrated by (1), described as a specifying apposition, and the semantics of intensional quantifiers. The paper analyzes intensional quantifiers as comparison with implicit subjective norms; it introduces a new analysis of the quantifier presque (almost) as an intensional quantifier expressing the judgment that the actual quantity is superior to an implicit norm and gives empirical independent arguments supporting this claim. The proposal establishes then, that given the otherwise plausible generalization that the instantiation of intensional variables must be persistent , especially in specifying constructions, the oddness of (1) is directly explained as an “intensional contradiction”, (1) asserting that the actual quantity is all at once under (few) and above (almost) the very same norm.

This paper takes as a starting point a well-known puzzle introduced by Anscombre and Ducrot (1983: 20): (1) ?Peu d’automobilistes dépassent le 120, presque 20%. Few drivers go over 80 m.p.h, almost 20%. The authors note that (1) is, for most French speakers, awkward or ill-formed. Anscombre and Ducrot argue that to explain why such sentences are ill-formed, it is necessary to postulate a separate layer of meaning (unrelated to the denotational meaning of the quantifiers peu and presque) based on the “argumentative orientation” of these two quantifiers. In brief, they argue that peu and presque have opposite argumentative forces that prevent one of the quantifiers from being used to “support” the other in (1). To my knowledge, although the example is well-known and occasionally used, there have been no attempts at providing an explanation of (1) that challenges Anscombre and Ducrot’s view that to solve the puzzle we need “argumentative forces”. The only proposal I am aware of is that of Jayez and Tovena (2008), but as I will show in detail, these authors accept the main part of the argumentative approach of Anscombre and Ducrot. The initial objective of this paper is to provide a solution to the puzzle that is formulated in a classical and parsimonious semantic framework deprived of any argumentative considerations. To provide this solution, I will take a radically different view of (1) and analyze the question as a case of apposition involving two intensional quantifiers. To elaborate on this proposal, two issues will have to be considered. First, the semantics of apposition involving quantifiers, an issue that has received less attention than have other appositive structures, perhaps because the paradigmatic quantifiers (e.g., no and every) cannot be used in appositive structures (see

a.o. Potts 2007). However, once one accepts an expanded notion of quantifier, one must concede that quantifiers appear in structures comparable with (1) that have all of the appearance of appositions. The basic part of the proposal is the semantics of apposition between quantifiers in relation to specification, a view rather common in the literature. I will confirm that this semantics gives the expected results for pairs of extensional quantifiers that are used in structures similar to (1). The second ingredient of the proposal concerns the semantics of intensional quantifiers or, more modestly, the crucial role their semantics plays in such appositive structures. The semantics of intensional quantifiers is a difficult challenge for formal semantics, a point made repeatedly by many influential studies (Keean & Stavi 1986, Partee1988, Lappin2000). In this paper, I will try to make the minimal assumption needed for the solution of puzzles such as (1). This assumption amounts to analyzing intensional determiners as a comparison between the actual cardinality or proportion and what I will call a subjective norm. The minimal assumption regarding norms is that they are the estimated value of the considered quantity in a given world, freely chosen by the speaker as a standard of comparison. By combining the semantic constraints on apposition and the semantics of intensional determiners, the proposal predicts well-formed appositive structures that include quantifiers, and it explains why (1) is ill-formed.

1 Anscombre and Ducrot’s observations and arguments Anscombre and Ducrot observe that the structure exemplified by (1) categorizes the quantifiers into two sets. Some quantifiers, such as presque, are acceptable in (1) if they are introduced by mais (but) but are unacceptable in (1) without mais: plus de (more than), au moins (at least) pattern in this respect with presque (almost). Some quantifiers are acceptable in (1): moins de (less than), au plus (at most), etc. The adjunction of mais with these quantifiers makes the sentence awkward. Anscombre and Ducrot note that the quantity expressed in (1), “20%”, is not a relevant parameter of the problem and that almost any other proportion yields the same judgments with regard to whether the sentence is well formed.1 To account for the observed distribution, the authors adopt the following analysis of (1): Structures such as (1) are acceptable if the detached element (presque 20%) can be interpreted as an argument supporting the choice of the initial quantifier (peu). In order for a quantifier to be used as an argument in support of another one, both quantifiers must have the same “argumentative orientation”. Sentence (1) is atypical because peu has a negative argumentative orientation and presque has a positive one. Because of space considerations, I cannot go into the details of Anscombre and Ducrot’s argumentative theory, which is not the focus of this paper. My objective is to contest the claim that argumentative theory is needed to address the facts exemplified in (1), and thus I will only briefly mention some consequences of their approach.

1

Of course, the larger the proportion, the less acceptable it is as an apposition to few. (i)? Few drivers, 99%, go over 80 m.p.h. However, there is a large range of proportions that would be acceptably represented by few depending on the properties referred to in the sentence, and Anscombre and Ducrot insist that for any value accepted in (i) as a bare numeral, the adjunction of presque or plus de will make the sentence unacceptable.

They insist that the argumentative orientation of lexical items is not related to their denotational semantics and must be added to their definition within a separate layer of meaning. The first obvious drawback to this is that is makes the semantics more complex by introducing “argumentative orientation” as a new primitive in the definition of lexical items. They even suggest that the components of this meaning layer enter into a compositional process when combined: they claim that the adjunction of mais (but) “reverses” the argumentative orientation of the quantifiers involved in examples such as (1) and this is how they explain that the adjunction of mais makes acceptable sentences unacceptable in the absence of mais. One may think that this is a high price to pay for solving a puzzle, and a natural question is the following: Is it possible to derive the observed facts without accepting Anscombre and Ducrot’s argumentative theory, in a more classical and parsimonious approach?

2 Revisiting the data Anscombre and Ducrot’s implicit analysis of (1) is that (1) is a short version of a twosentence discourse such that the second sentence must support the first one: (2) S1: Peu d’automobilistes dépassent le 120. Few drivers go over 120. S2: Presque 20% (d’automobilistes dépassent le 120). Almost 20% (of drivers go over 120). I think that this is the only hypothesis compatible with their view that the separated element (presque 20%) must “argue for” or “support” its host sentence (Peu d’automobilistes dépassent le 120). It is not possible to claim that B supports A without assuming that A and B are propositions. Discourse theories such as Rethorical Structure Theory (Mann &Thompson 1988) define a specific discourse relation, JUSTIFY, and recent work such as that of Biran and Rambow (2011) provides a good sample of sentences intuitively interpreted as justifications. Although Anscombre and Ducrot’s work is anterior and formulated in different terms, it is likely that discourse-oriented studies would translate Anscombre and Ducrot’s view in terms of justification.2 Here is one example of justification from Biran and Rambow: (3) Justification: Our first heading is quite long, and against our MOS, it contains most of the title of the article. Claim: I suggest we shorten it to “Topics”. Here is a short invented example: (4) Claim: I cannot work with him. Justification: He is too stupid However, even if one accepts viewing at structure (1) with a discourse-oriented eye, it does not look like a justification, and it is easy to establish this with a small test. In (1), it is possible to add the expression to be (more) precise without any change regarding acceptability or meaning: (5) Peu d’automobilistes dépassent le 120, presque 20% pour être précis. Few drivers go over 120, almost 20% to be precise. It is impossible, however, to add this expression and to preserve a justification interpretation: 2

This is precisely what is done in Jayez and Tovena (2008).

(6)

Claim: I cannot work with him. Justification: He is too stupid, # to be precise. Discourse theorists would likely consider the hypothetical discourse (2) as illustrating an elaboration, with P2 making more precise the assertion P1. A second point worth revisiting is precisely the underlying assumption that (1) should be analyzed as hypothetical discourse (2). After all, (1) is a sentence, and most grammarians would say that it is a case of apposition. The tremendous amount of literature on this topic thus becomes a resource for exploring and possibly incrementing using new observations based on (1) because the topic of apposition between quantifiers is not among the best documented in the literature. This might lead as well to a different view regarding the role of mais. For Anscombre and Ducrot, mais is a rescuer for otherwise unacceptable combinations because it reverses the argumentative orientation of the quantifier it introduces. Considering that versions without mais are appositions, and versions with mais are coordinations, leaves open the possibility that acceptability differences arise solely from the difference between coordination and apposition. Furthermore, there is an independent way to establish this point. If it is true that a structure such as (1) is governed by semantic constraints inherited by the fact that it is an apposition (and not a coordination), the very same semantic constraints should apply for any type of quantifiers, even for those that are purely denotational and have at face value nothing to do with argumentative values or subjective judgments. I will test this below. However, the crucial quantifiers of (1), few and almost, are intensional quantifiers. The constraints observed by the authors should be related to what we otherwise have to say about intensional quantifiers and, if possible, used to shed light on their properties. A last point, unnoticed by Anscombre and Ducrot, is that there is at least one quantity, namely ø, that violates the empirical generalization stating that the argument n of presque n has no effect on the acceptability of the structure (1): zero or equivalent negative quantifiers such as aucun (no one), in contrast to any other number or proportion, are ideal with presque but unconventional with mais. (7) Peu d’automobilistes, presque aucun, ne dépassent le 120. Few drivers, almost none, go over 120. (8) ?Peu d’automobilistes, mais presque aucun, ne dépassent le 120. Few drivers, but almost none, go over 120. This appears to be a puzzle within the puzzle that requires an explanation.

3 Apposition vs. coordination The construction illustrated by (1), with a bare detached quantifier, would be considered by most grammarians an apposition, although such examples are not among the most studied cases of the phenomenon: the initial quantifier phrase plays the role of an anchor (ANCH) and the detached constituent plays the role of an apposition (APP). Cases in which both ANCH and APP are quantifiers have not received much attention in the literature. It is well known that the quantifiers every and no cannot be ANCH, but many expressions considered as quantifiers in most semantic approaches (generalized quantifier theory and DRT as well) behave as ANCH in appositive constructions. (9) La plupart des personnes présentes, des étudiants, ont protesté

Most persons present, some students, have protested. (10) Trente pour cent des étudiants, les plus faibles, ont choisi ce sujet. Thirty percent of the students, the weakest, have chosen this subject. Moreover, many quantifiers occur as APP in appositive constructions; this is well known for indefinites, but it is also true for other quantifiers: (11) Beaucoup d’étudiants, plus de 40% d’entre eux, n’ont pas pu être incrits. Many students, more than 40% of them, could not be enrolled. Many authors (del Gobo 2003, De Vries 2002 after Koster1995, 2000) claim that appositive nominals specify the DP that precedes them, the second DP providing further information about the first one. This view is clearly expressed in Del Gobo (2003) as follows: “De Vries (2002) maintains that appositive nominals specify the DP that precedes them; that is, the second DP provides further information about the first DP. He proposes to analyze the apposition and the DP it modifies as two coordinated constituents. The type of coordination involved is specifying coordination (Koster 1995, 2000), in which the apposition denotes a logical subset of the referents denoted by the DP it modifies.” Although I do not think it appropriate to consider apposition a type of coordination (as we will see, there are strong differences that this terminological choice would blur), the general semantic analysis of apposition by these scholars seems to be accurate, and I will apply it to the special case of apposed quantifiers illustrated by (1). Huddleston and Pullum (2002) proposed a distinction between specifying and ascriptive appositions, the use of epistemic expressions such as to be more precise being a test for recognizing specifying appositions. As was already noted, the case illustrated by (1) is also a case that licenses the adjunction of this epistemic expression. We can thus consider that (1) is a case of specifying apposition and rely on the analyses provided for this construction in the literature. These analyses are based on the claim that apposition between two DPs is licensed in general if the denotation of APP is a logical subset of the denotation of ANCH. What is required for analyzing examples such as (1) as appositions is to determine how this general principle can be applied to the special case of apposed quantifiers. The case exemplified by (1) is special because it involves two quantifiers and because APP is reduced to a bare quantifier: (12) QUANT1 A B QUANT2 Few drivers go over 120 Almost 20% ANCHOR APPOSITION The semantic counterpart of the reduction of APP to a bare quantifier is that APP is interpreted as a quantifier over A, the restrictor of the ANCH (compare (1), with a bare quantifier, and (9), in which APP has its own restrictor). The mechanism by which a detached APP quantifier can be interpreted as a specification of ANCH-quantified DP can be conceived as follows: A quantified ANCH Q-A interpreted in its host sentence Q-A-B associates the property Q with the intersection of the two sets A and B (henceforth, REFSET). The sentence “Few students were present” states of the present students, that there were few. To be interpreted as an APP, a quantifier must specify the information given by ANCH; it must be more precise than ANCH: it must denote a property of REFSET that is a subset of the property denoted by few. A comparison might be useful for clarifying the underlying analysis: (13) Few students were present, four to be precise. (14) The present students were few; they were four, to be precise. What apposition does in (13) is exactly what the second sentence does in (14). Just as it is

impossible to reverse the order of ANCH and APP, it is impossible to reverse the order of the two clauses of (14): (15) *Four students were present, few to be precise. (16) *The present students were four; they were few, to be precise. If (15) is ill-formed, it is likely because the relation of specification cannot be established from few to four. We will return to this central issue. In other words, we assume that the quantifier of ANCH in its host sentence is a predicate of REFSET and that the quantifier of APP must be interpreted as such but more precise, i.e., denoting a subset of the of ANCH denotation. This strongly connects apposition and the use of plural pronouns, as the comparison of (13) with (14) shows: APP can be considered a predicate of the discourse referent made accessible by ANCH in its host sentence. This connection has been often made in the literature (see, for instance, Demirdache 1991). There is a sharp contrast between apposition as just defined and coordination using explicit conjunctions such as mais and et, and this contrast reflects the fact that coordination is free from the specification requirement that holds for apposition. (17) Few boys, but many girls, came. coordination well-formed (18) Few boys came, * many girls. *apposition ill-formed The “subset semantic constraint”, which is the realization for quantifiers of the specifying requirement, is responsible for the unacceptability of (18) because no quantifier on girls can denote a subset of a quantifier on boys. However, this relation has no effect on the coordination exemplified in (17): in short, in (17), a conjunction adds the information that another entity satisfies the predicate, and a conjunction can do that for any other entity; in (18), an apposition requires that the detached quantifier denote a subset of the first and apply to the same REFSET, making the assertion more precise, which is impossible. We will now attempt to derive the semantics of quantifiers in apposition and the conditions under which they can be combined by relating more precisely the “subset semantic constraint” and the semantics of individual quantifiers. The first step will be to sketch a typology of quantifiers based on the properties relevant to the problem under consideration.

4 Intensional vs. extensional quantifiers Keenan and Stavi (1986) set intensional quantifiers such as few and many apart from quantifiers accessible to the theory of generalized quantifiers because the truth of sentences using these quantifiers cannot be determined even if one has access to a perfect quantitative knowledge of the model. This provides a test for splitting quantifiers into two categories: (19) A test for intensionality If two speakers can agree on the extension of the REFSET denoted by a quantifier and can disagree on whether the quantifier applies, the determiner is intensional. A quantifier is extensional otherwise. According to this test, few, many, and almost a are intensional, and six, more than six, exactly six, and about six are extensional. 4.1 Apposing extensional quantifiers The schematic semantic pattern of appositive structures exemplified by (1) is the following: Host sentence Apposition α satisfies Q α satisfies Q’ α stands for the cardinality of REFSET or the proportion of the cardinality of REFSET over the cardinality of Q’s restrictor. The general specifying semantic constraint on apposition requires that the apposition be able to be interpreted as a specification of the host sentence. Considering that quantifiers denote cardinalities or proportions, their denotations can be defined as disjunctions over numbers or proportions. More simply, the cardinality of a given set is a natural number, i.e., 1, 2, 3, etc. The anchor quantifier Q in the host sentence gives information about the cardinality of REFSET, which means eliminating some alternatives of this disjunction. What Q’ must do to be interpreted as giving more information about this quantity is denote a subset of those alternatives, thus eliminating some of the alternatives covered by Q. The following example illustrates this view: (20) More than fifty students, 54 to be precise, passed the exam. The ANCH quantifier Q eliminates for the cardinality of α all of the values inferior to 51. More than fifty makes only the alternatives above 50 acceptable options. To be interpreted as an apposition, the APP quantifier Q’ must denote a subset of these alternatives and hence be interpreted as giving more precise information about α. From these general constraints, it is possible to make a number of predictions and to test whether they are borne out, especially for extensional quantifiers because there is no doubt about their denotation: 1. Only quantifiers that allow for alternatives can be used as ANCH. This explains why quantifiers such as exactly a cannot. 2. Only ANCH/APP pairs in which APP denotes a subset of ANCH are licensed. Assuming that bare detached quantifiers can only be interpreted as apposition (a rough simplification, as we will see later), the above predictions explain a large set of nontrivial data involving extensional quantifiers very well: (21) ? More than five students passed, less than ten. (22) More than five students passed, more than ten. Although more than five and less than ten are compatible and can be conjoined for characterizing the cardinality of a set, they cannot combine in apposition because less than ten is not a subset of more than five. On the contrary, the prediction is that (22) should be

acceptable, more than ten being a proper subset of more than five, a prediction that is borne out. The proposal predicts, as a consequence, that no pair of differently oriented comparatives (more than/less than) can form a valid apposition. Another prediction of the proposal is that quantifiers of approximation (around a, between a and b) will always be acceptable as APPs of comparative ANCH if the domain of variation of APP is a subset of ANCH: (23) More than fifty students, about sixty, passed. If the ANCH/APP relationship is reversed, as in (24), the sentence becomes awkward: (24) ? About sixty students, more than fifty, passed. This is a prediction of the proposal because more than fifty is not a subset of about sixty. Some speakers accept (24) but it is very likely that when doing so, they interpret the sentence as: (25) About sixty students, so (therefore) more than fifty, passed. In other words, they interpret the sentence as a type of implicit coordination, not as an apposition. The problem is that we assume that a bare detached quantifier is, by default, interpreted as an apposition, which does not exclude that it can be interpreted as an implicit conjunction. This blurs the data regarding acceptability because an impossible apposition can be resolved as an implicit conjunction. Nevertheless, some tests can be used for establishing that when speakers find (24) acceptable, they do not interpret it as an apposition. For instance, the adjunction of therefore is incompatible with an apposition because apposition must add new precision about the quantity α. However, therefore can be inserted in (24) without altering acceptability or meaning. Compare, in contrast, what the adjunction of therefore makes of (23), i.e., an unacceptable (or false?) sentence: (26) ? More than fifty students, therefore about sixty, passed. 4.2 Intensional quantifiers Thus far, we have only defined intensional quantifiers negatively, by contrasting them to extensional quantifiers. A positive semantic analysis is needed to attempt to understand the interaction with the constraints on appositions. (27) Intensional quantifier–a tentative definition: An intensional quantifier Q, in Q-A-B, expresses a comparison between α, the actual cardinality |A∩B| or the proportion |A∩B|/|A| and a subjective constant n, a norm. A norm is the estimated value of α in some possible world considered by the speaker as the relevant standard of comparison. A norm can be: what α should be, α might have been, α is in most words, α is with regard to other contextual parameters, etc. This definition derives the distinctive property of intensional quantifiers: two speakers can agree on the exact value of α but disagree that an intensional quantifier holds for α; this is because the choice of the norm is a subjective matter, and speakers can disagree about what is the relevant norm to be chosen as a standard of comparison. The definition derives as well the possibility of combining intensional quantifiers with typical adjuncts such as for x, compared with, etc. It relates them to implicit comparatives such as tall or expensive (Kennedy 2001) and to predicates of personal taste (Lasersohn 2005). I will not discuss these issues, instead focusing on using this definition to characterize the semantics of the quantifiers brought into focus by the initial puzzle (1).

(28) The semantics of few as an intensional quantifier Peu Few

d’automobilistes dépassent le 120 presque 20% drivers go over 120 almost 20% α80|/|D| n is a subjective value chosen by the speaker. All we know is that n is greater than α. For simplicity, we represent only the proportional reading of peu in (28). In line with the above approach to quantifiers as disjunctions over numbers, we can see the denotation of peu as a disjunction (ø∨1∨2 ∨… ∨n), n being the value chosen by the speaker as its subjective norm. In what follows, we will retain this very underspecified analysis and we will say very little about the difference between cardinal and proportional readings of few/many (Partee 1988) and about the choice of n. 4.3 Extensional appositions to the intensional quantifier peu Many extensional quantifiers can be APPs for the intensional quantifier peu: (29) Peu d’étudiants, 45 en tout, ont réussi l’examen. Few students, 45 in all, passed the exam. Again, this is a prediction of the proposal on apposition considering the semantics of peu that was just introduced: n being implicit and subjective, the choice by the same speaker of a definite value in an appositive structure is interpreted as being more precise, i.e., as denoting a subset of the alternatives made available by the ANCH quantifier peu. Apposition is licit because there is nothing in the very unspecified disjunction denoted by few that makes it impossible to take the definite value 45 as a subset of it; as a consequence, the subjective value n, the norm of the speaker, becomes less private: asking to interpret 45 as an apposition to peu commits the speaker to disclose that the norm she chose is more than 45. The prediction is that any precise quantifier (such as 45) is a licit apposition and is interpreted as being inferior to the norm chosen by the speaker. Only pragmatic considerations can limit the choice of the precise quantifier: the sentence might become unconventional if the choice of this precise quantity reveals that the speaker is using a norm that is too far from what the hearer is prepared to accept. Some extensional quantifiers cannot be APPs for the quantifier peu. A prediction of the current proposal is that any comparative of superiority will be ruled out. To understand why this is so, consider the terms of the problem: Disjunction covered by peu: α < n |||||||||||||||||||||||||||||||-------------> n Disjunction covered by more than a: α > a

---------||||||||||||||||||||||||||||||||||||||||> a The only n value that makes APP a subset of ANCH is, for proportions, n = 100%, a very trivial and unlikely choice for a norm. One can thus conclude that the proposal predicts that comparatives of superiority cannot be APPs for the ANCH peu.

In contrast, any comparative of inferiority α < a is expected to be acceptable with the associate commitment that the speaker’s norm n is superior to a. Both predictions are borne out. The only restriction on the acceptability of the full range of numbers or proportions for a comparative of inferiority comes from the domain of variation one accepts for peu. If one considers that peu is restricted to a domain of small numbers, one accepts only for APP a disjunction bound to the same range. This is not, however, an argument against the proposal. On the contrary, it is a confirmation: the apposition is licit if APP can be interpreted as a subset of ANCH. We have chosen here to work with maximally underspecified semantics for few, considering that it can vary over the full range of proportions or numbers except for the maximal value (i.e., 100%). To sum up, let us consider a close variant of (1): Few

drivers

go over 80 α ø 20% |//////////////////////////////|---------------------------------> ø n

It is possible to accommodate values for n such that “less than 20%” is a specification. The sentence is thus acceptable under accommodation, which makes the speaker’s norm less private: her norm is higher than 20%. The proposal predicts that the only extensional quantifiers that can fail to satisfy the associated semantic constraints of few are unbound comparative determiners: approximation quantifiers (about 100, between 50 and 80) and precise quantifiers (exactly 34) will be accepted because there can be successful accommodations for them. This prediction is verified at least for extensional determiners, and all predictions are based on logical properties of determiners, without any need to use argumentative values.

5 Intensional appositions to the quantifier few The original example (1) is based on the impossibility of using presque n (almost n) as an APP to the ANCH few. 5.1 The classical semantics of presque There is a great deal of literature on the semantics of almost and presque. To keep the initial problem in focus, I will discuss only the properties of presque a that are needed to explain the original example (1) and attempt to stay theory-independent to the extent that I can. Presque a has a denotational meaning component on which there cannot be any disagreement among speakers. Briefly, presque a asserts (or implies) that the actual quantity or proportion ∝ is ranked on a scale strictly under the position occupied by a:3 a ------------------------------------------|||||--------------------------------> presque a Note that the natural order of numbers is not always the one that must be considered, which makes it impossible to say merely that presque a implies less than a. 3

This is the analysis of Hitzeman (1992) and Penka (2005, 2006) for almost and the analysis of Del Prete and Amaral (2010) for the Italian quasi.

Consider, for instance, plugging in a new refrigerator. Normally, it would be expected that the temperature will gradually decrease to the desired one4. Consider the interpretation of (30) in this context: (30) The temperature inside the refrigerator is almost 4° now. The sentencte (30) implies, at least in the preferred reading, that the temperature is above 4°, and this implication does not hold for the corresponding sentence with less than: (31) The temperature of the fridge is less than 4° now. Sentence (31) implies that the temperature is under 4°. This scalar interpretation of presque and the fact that it is highly sensitive to contextual scales and progressions is relevant for explaining why almost nothing has a standard literal meaning denoting a small quantity, although less than nothing is only a stylistic device for emphasizing “nothing”; we will return to this. As in most cases, however, and by default, the scale used by presque is the natural order of numbers; in the context of the present discussion, it will be assumed that almost a implies less than a. Presque has also an intensional meaning component associated with the proximity to the point of reference. Briefly, presque a “means close to a”, and “close” is an intensional predicate that can be formulated as a comparison with a subjective norm: A is close to B if the distance between A and B is under some standard of smallness on which speakers can disagree. Both components have been extensively discussed in the literature, but they cannot, as far as I know, offer an explanation for what happens with presque in (1). On the contrary, the denotational property leads one to expect that presque should be acceptable in (1) because it embodies a comparative of inferiority (presque a = less than a). Anscombre and Ducrot argue from this that the denotational properties of presque cannot predict what is observed. Meanwhile, the property related to the closeness to the point of reference does not change anything and predicts that presque it should be as good as “slightly less than”, which is wrong, as shown by (32), a perfectly acceptable sentence: (32) Peu d’automobilistes dépassent le 80, un tout petit peu moins de 20%. Few drivers go over 80, slightly less than 20%. Note that this “slightly” adjunction makes any extensional comparative (of superiority or inferiority) acceptable as an apposition to few, which is also a prediction of the proposal because, so to speak, it eliminates the part of the disjunction that prevents establishing a subset relation from APP to ANCH. In sum, the properties most often associated with presque in the literature, even if taken separately, lead to the expectation that presque should be acceptable in (1), which is, unfortunately, not the case. Additionally, this again appears to be a confirmation of Anscombre and Ducrot’s view because it seems that something must be added that is not derivable from the basic meaning of presque to explain its behavior in (1). We, however, will argue that what is needed is not an argumentative orientation but an additional intensional feature.

4

This has been noted by Sadock (1981), who observes that “It is almost 0°C” can apply to situations in which the temperature is higher or lower than 0°C depending on the progressive falling or rising of the temperature in context.

5.2 An enriched analysis of presque There is, I think, a property of presque a that is not clearly captured by the current analyses. Roughly speaking, presque a conveys, in addition to the two features discussed above, the intensional judgment that α is above a norm n. I will give now independent evidence supporting this view. A basic fact is that if someone tells you that her income is “presque a”, you are invited to infer that she is happy about that income, that she thinks “it is not that bad”. This cannot derive from the “less than + close to” analysis. Consider the very hypothetical dialogue (33): (33) A - You just said your salary is now 1950 €. So I can write in my paper: “X, a worker making now almost 2000 €…” B - I would not say that myself. You know, what I make is nothing compared with what is needed for living in Paris. The matter of disagreement is neither inferiority nor closeness but the way the amount of money is evaluated when compared with a contextual norm. B is insisting that for saying himself “presque a”, the amount of money should have been above a contextual norm. In essence, the underlying assumption is that presque a contains a meaning component of the same type as peu, namely, that presque compares α to a subjective norm n, but in contrast with peu asserts that α is above a subjective norm. Some examples come immediately to mind that show that this assumption appears to be accurate. Consider the following contrast: (34) A: Ton père est petit? Your father is small? B: Oui. Il mesure presque 1,50m. Yes. He is almost 1,50m (35) A: Ton père est grand? Your father is tall? B: Oui. Il mesure presque 1,50m. Yes. He is almost 1,50m. Although 1,50m is not considered tall for men, (35) is highly preferred by the speakers I asked about to (34), which was considered unusual. Adjectives such as small and tall are generally considered to express the judgment that a size is above some standard. It is atypical to confirm that someone is small by saying one’s size is almost a, whatever a is. This looks understandable if almost a expresses the judgment that a quantity is above a standard. Before going on to other confirmations, it is important to discuss briefly the status of this intensional meaning component when presque is combined not with quantifiers, but with predicates (avoir presque fini, être presque mort, to have almost finished, to be almost dead).5 When modifying a predicate, the interpretation of presque is that the predicate is verified up to a degree very close to the maximal degree consisting of the full accomplishment of the predicate.6 However, if the degree of achievement is very close to 100%, this degree is above any norm one can conceive of as a standard of comparison. The idea, then, would be that the 5

This paper focuses on the interpretation of presque a in which a is a quantifier. It does not address the full range of combinations of presque with other syntactic categories (see, for instance, Morzycki 2001 for a study addressing the cross-categorial nature of almost). The following paragraph merely briefly considers whether the new feature introduced for the analysis of almost a could be part of the meaning of almost in all of its uses.

6

This analysis was introduced for the Italian quasi by Del Prete and Amaral (2010). They state that it is the accomplishment of the event denoted by the VP that provides the relevant scale and the “limit point” required by the semantics of quasi.

superiority with relation to a standard of comparison is trivially satisfied by the fact that the argument of presque is the maximal degree of achievement. Consider, in contrast, an arbitrary degree on a scale, for example, presque 5°. Because this degree is not the maximal one, if presque means that α is above a subjective norm, this interpretation will appear to be distinct from the information “very close to five”. Once it is admitted that in all of its uses presque asserts that what is evaluated, a quantity or a degree of accomplishment, is ranked on a scale under a value provided by its argument and close to it, there is no need to assume for presque a component of meaning expressing the negation of the argument (presque a/“not a”, presque mort/“not dead”). This negative content is just an inference, but not a is no more related to the meaning of presque a than it is to the meaning of more than a or to the meaning of less than a, or to be extreme, to the meaning of any b. Because of space considerations, and because this paper is centered on presque a, I will not further discuss the semantics of presque. Other independent confirmations that presque a implies that α is above a norm are based on constructions involving causality. Suppose one believes that there is a correlation between two progressions: the depth of the economic crisis and the reduction of employment. In other words, one believes that the deeper the crisis, the fewer the jobs. Consider the interpretation of (36) in this belief context: (36) ?A cause de la crise, l’entreprise propose presque une centaine d’emplois. Because of the crisis, the firm is offering almost 100 jobs. The fact is that (36) is unconventional whatever one guesses about the size of the firm. A causal relation between A and B leads one to expect, if there is a correlation (A↑B↓), that the measure of B will be inferior to what it would be if A were not satisfied. In other words, in the context “because of the crisis…”, we expect a number of jobs inferior to the norm. A possibility that I will not discuss in detail is that in the context of the causality adjunct, a contextual norm is imposed: the number of jobs that would have been offered otherwise. Even if the details of the mechanism are not fully outlined, the phenomenon itself can be interpreted as follows: in (36), if the sentence is atypical, it is because presque a implies that α is superior to a norm. This can be confirmed by the substitution of quantifiers that do not have this semantic content, as in (37), which is ideal: (37) A cause de la crise, l’entreprise propose un peu moins de 100 emplois. Because of the crisis, the firm is offering slightly less than 100 jobs. A concessive relationship (in spite of…) when there is a known correlation implies, on the contrary, that the actual quantity will be above the standards, and presque is again ideal: (38) Malgré la crise, l’entreprise offre presque une centaine d’emplois, In spite of the crisis, the firm is offering almost 100 jobs. To sum up, there is independent evidence for arguing that the semantics of presque a in addition to the “less than and very close to” components implies that for the speaker, the actual quantity ∝ is above a contextual norm. Because of the “very close to” feature, there is not a great extensional difference between “∝ is above a contextual norm” and “a is above a contextual norm”. There are, however, two reasons for preferring the former formulation: 1) the formulation “n < a” would license the option “∝ n

lower ranking closeness higher than a subjective norm

ext. int. int.

The assumed semantics for presque is obtained as a conjunction of these tree components. My proposal for explaining (1) will rely on the idea that any use of presque a expresses this conjunction and does not assume any special mechanism for downgrading or back-grounding one of these components. This contrasts with many theories that assume that one of the components, “∝ n intensional This association is very rare and contrasts strongly with a general tendency to associate intensional implicatures that are co-oriented with extensional comparatives: for instance, less than 2.000 € is an extensional comparative of inferiority and can be used without any implicature in formal discourse (descriptive analysis, law, etc.). The sentence in (41), for instance, is merely a quantification of an amount of money with no subjective judgment: (41) For people making less than 2.000 €, the tax rate is 35%. In conversation, however, if someone says her salary is less than 2.000 €, you will immediately infer that she is not pleased with this amount and intends to convey the judgment that what she makes is under her subjective norm. This can be expressed by the empirical generalization (42): (42) Extensional comparatives and their intensional implicatures: Extensional comparatives trigger a co-oriented intensional implicature: ∝ > a triggers ∝ > n and ∝ < a triggers ∝ < n, n being a subjective norm chosen by the speaker. The specificity of the lexical item presque is that it combines a denotational comparative of inferiority (∝ < a) and an intensional semantic component expressing a comparison oriented in the opposite direction (∝ >n). Note that French, for instance, offers at least three ways to express the same denotational content and that presque is the only one that conveys superiority to a norm judgment:

Un peu moins de a à peine a presque a A little less than a barely a almost a Intensional ? ∝n This might explain that in general this intensional component of presque cannot be backgrounded. We also see no case in which the “close to a” component should be back-grounded, and, as does the ∝ > n component, it behaves as a strong, indefeasible part of the lexical item. The “less than a” component, meanwhile, seems to be a part of most uses, and I do not find convincing any proposal that assumes that a and presque a are indistinguishable. It seems to me that no commitment to presque a can be extended to a commitment to a. What remains to be explained, then, is why some sort of back-grounding appears to be necessary for treating cases such as (42) for which replacing presque a with the conjunction of the three components of its meaning does not produce, at first glance, the intended interpretation: (42) Je suis heureux qu’il fasse presque 20°. I am happy that the temperature is almost 20°. (43) Je suis heureux (que la temperature soit inférieure à 20%; que la temperature soit proche de 20%; que la temperature soit plus élevée qu’elle aurait pu être.) I am happy (that the temperature is less than 20%; that the temperature is close to 20%; that the temperature is higher than it could have been.) First, the main predicate (to be happy that…), in contrast to what happens most often, does not guarantee that from a conjunction as argument it can be inferred that any member satisfies the predicate. Consider (44): (44) I am happy that Mary came and Peter left. For many speakers, it is not true that (44) implies that I am happy that Mary came: (44) can be true if I am happy that Peter left but not happy that Mary came. This is different from what happens for a predicate such as believe or know: (45) I know that Mary came and Peter left. If (45) is true, it can be inferred that I know that Mary came and that I know that Peter left. Once it is admitted that some member of a satisfying conjunction can fail to satisfy the predicate to be happy, it is less surprising that with presque, some member of the conjunction of meanings fails to staisfy the predicate. A suggested explanation that it is the meaning component “less than all” that does not satisfy the predicate “to be happy” might be that there is a strong common-ground belief that a person would be happy if all of her friends came to her party and less happy if they did not. Even though these remarks cannot count as a complete explanation of examples similar to (41), they suggest that it would be perhaps more efficient to address the special features of special cases than to postulate that the denotational meaning component of presque has a special status (back-grounded or conventional implicature). In what follows, the meaning of presque will be considered merely the conjunction of three meaning components, and the backgrounding of the “less than component” will not play any role in the solution I propose for puzzle (1).7 5.3 A solution for the initial puzzle Part of the problem is that examples such as (1) combine, within an appositive syntactic 7

This is an important difference, as we will see later with a previous proposal by Jayez and Tovena (2008).

construction, two intensional determiners: peu and presque (few and almost). In our terms, this indicates two quantifiers involving a comparison of the very same quantity α with a subjective norm n. In general, it seems sound to allow each occurrence of an intensional quantifier in a sentence or in a discourse to freely select the subjective norm it takes as a standard of comparison, even for characterizing the same quantity. One is free to say things such as (46) or (47): (46) A. Have you many students in your course? B. Well, compared with the number last year, they are few, but considering the number of essays I will have to read, I would say they are many. (47) Dix étudiants inscrits; c’est à la fois peu et beaucoup. Ten students enrolled; this is at the same time few and many. In other words, in general, implicit standards of comparisons can be as different as explicit ones can be. (48) Dix étudiants inscrits; c’est beaucoup pour l’enseignant, mais au regard des normes de cette université, c’est très bas. Ten students enrolled; this is many for the teacher in charge, but compared with the norms of this university, it is very low. Consider now simple discourses such as (49) and (50): (49) ?J’ai peu d’argent. J’ai presque 200 €. I have little money. I have almost 200 €. (50) J’ai peu d’argent, mais j’ai presque 200 €. I have little money, but I have almost 200 €. The discourse relation most speakers would want to associate with (49) is elaboration, and many would find that this discourse is not well formed. The example in (50) is well-formed and would be analyzed by discourse theorists as a contrast. Thus, in general, it is possible to combine with discourse relations intensional determiners that differently evaluate the same quantity. It is possible for the same speaker to combine a sentence stating that α is superior to a norm n and a sentence stating that α is inferior to another norm n’. However, elaboration imposes specific constraints, as the data in (51) show: (51) J’ai peu d’argent. J’ai à peu près 10 €. I have little money. I have about 10 €. moins de 10 € less than 10 € * plus de 10 € *more than 10 € * presque 10 € almost 10 € As already noted, elaboration rests on the same semantic relation as apposition, i.e., a specifying relation: the disjunction covered by the second quantifier must be a subset of the disjunction covered by the initial one. The impossibility of *plus de 10 €can be explained by a purely logical constraint (see above): “more than 10” is unbound and covers alternatives that cannot be a subset of the alternatives covered by peu, which have a definite (but implicit) value that cannot be the top of the scale. The same constraint predicts that moins de 10 € is acceptable and reveals that the subjective norm of the speaker is more than ten; it predicts also that à peu près 10 € is acceptable. However, the impossibility of *presque 10 € cannot be explained via its extensional content. The following schema illustrates what should be obtained from the semantic extensional content of presque: ---------||||--------|--------------------> 10 n This works perfectly for the extensional equivalent “un tout petit peu moins de 10 euros”, which is acceptable and leads to the same inferences. •

Thus, the problem is located in the interaction between the semantic relation specification and the intensional layer of the quantifier presque that we proposed to add in the enriched semantics for this quantifier. The basic feature of the configuration created by an attempt at interpreting (49) as an elaboration is that an intensional quantifier (peu = “α < n”) should be made more precise by a quantifier, presque, including as a component of its meaning the judgment that α is above a subjective norm. We can be sure that this is the root of the problem because an otherwise equivalent quantifier deprived of this component, for example, “slightly less than”, can accomplish the task with no problem. If we maintain the general rule that any occurrence of an intensional quantifier can rest on the free choice of the norm taken as a standard of comparison, there is still no solution. Suppose for instance that peu means “α < n”, and presque means “α > n’”, the relationship between n and n’ being unknown. Considering what we assumed otherwise, the discourse (49) should be appropriate and should accept being connected by an elaboration relation: Peu Presque a

|||||||||||||||||||--------------------> n -----|-----|||||||----------> n’ a

There is no logical difficulty in interpreting presque a as a subset of peu, which gives the following result: -----|-----|||||||----|------> n’ a n In other words, “α is inferior to the norm I chose when using peu, or, to be more precise, α is slightly less than a and superior to another norm n’ that I chose when using presque.” What may look strange is the idea that one can interpret something as being more precise, i.e., by eliminating some of the options made available by the first quantifier if this something uses a quantifier that makes a comparison with another subjective norm. The basis of my proposal for deriving these facts is that for apposition and elaboration, the subjective constants, if present in both quantifiers, must be unified. The implementation of the claim is very simple: (52) In order for A to be interpreted as a specification of B, the intensional variables of both A and B, if any, must be unified. First, I will show that this claim correctly derives the data involving intensional quantifiers in appositive and elaboration structures, and then I will attempt to argue that this claim is not counterintuitive.

(53) A proposal for (1): Few

drivers

go over 80 α n

“intensional” contradiction In other words, to make the initial quantification more precise, the speaker is committed to the judgment that the very same amount is both lower and higher than a given value, which is incoherent. The proposal derives many intensional appositions, for instance, (54): (54) Many drivers go over 80, almost 20%. Many

drivers

go over 80 α> n

almost 20% α < 20% α ≈ 20% α >n

It also derives (55): (55) Beaucoup d’automobilistes dépassent le 120, énormément. Many drivers goes over 120, lots of them. If beaucoup implies that α is higher than n, and énormément implies that α is much higher than n, then the two judgments are compatible and there is no problem interpreting énormément as eliminating some of the alternatives covered by beaucoup. Is the requirement that intensional variables be unified in apposition and elaboration counterintuitive? The first thing worth noting is that allowing a completely free choice for intensional variables used to evaluate a given quantity α within a small discourse span is too liberal. There are obvious pragmatic constraints that make a commitment to some norm to evaluate a quantity, something that stays valid by default and can only be retracted explicitly. This can happen, for instance, in dialogue, as in (56): (56)

A. Il y avait peu d’étudiants à mon cours. There were few students in my course. B. Tu plaisantes. Personne n’en a eu autant. You are joking. Nobody had that many. A. Oui. Tu as raison. C’est un effectif correct, après tout. Yes. You are right. It is a correct audience, after all.

However, in a monologue, and in the absence of any explicit indication, it is almost impossible to switch from one norm to another one: (57) Je gagne peu d’argent. ? Comme je suis bien payé, je ne me plains pas. I earn little money. Because I am well paid, I do not complain. Explicit introduction of different standards of comparison is required, as in (57’): (57’) Je gagne peu d’argent. Il est vrai que je suis bien payé pour ce que je fais. I earn little money. It is true that I am well paid for what I am doing. (58) Je gagne peu. Il est vrai que je suis bien payé, pour un débutant. I earn little. It is true that I am well paid for a beginner. Moreover, typically such a switch requires (or strongly prefers) an explicit conjunction involving a contrast such as but, on the other hand, etc. Conversely, it is a general rule that contrast allows the norm to be changed, as illustrated by French expressions such as (59): (59) C’est peu mais c’est beaucoup. It is little, but it is a lot. Returning to Anscombre and Ducrot’s observation that mais is a rescuer in (1) (see above), we can be now more precise. What we said before is that mais, and more generally conjunctions, is free from the specification requirement for apposition. This is how we explained examples (17) and (18) recalled under (60) and (61): (60) Few boys, but many girls, came . coordination well-formed (61) Few boys came, * many girls. *apposition ill-formed This is only a way of saying that what is valid for apposition is not necessarily valid for coordination. The observation that mais has the specific property of allowing the speaker to switch the norm being used to evaluate a given quantity is a positive specification of mais and might be used to explain the licensing of but +bare quantifier as a detached element. Because the detailed analysis of the mais version of (1) is not within my scope in this paper, I will make only few comments. No quantifier is licensed as a detached element introduced by mais: (62) ?Peu d’étudiants étaient présents, mais trois. Few students were present, but three. As for precise extensional quantifiers introduced by mais (mais trois, mais quatre, etc.), it can be observed that there is no way to make them acceptable by changing the initial quantifier. (63) ? Plus de 25 étudiants sont venus, mais trente. More than 25 students came, but thirty. (64) ?Quelques étudiants sont venus, mais trente.8 Some students came, but thirty. This leads to the thought that mais can only introduce intensional quantifiers or quantifiers that generate an intensional implicature (see above for intensional applicatures associated with extensional comparatives). For instance, an extensional comparative such as less than 10 generates the co-oriented intensional implicature that the actual quantity is, for the speaker, below the norm. Additionally it is observed that but less than ten can be used, as in (65) and (66): (65) Quelques étudiants sont venus, mais moins de 10. 8

Rectification sentences such as “I did not see 20 students, but 30” should be kept apart.

Some students came, but less than ten. (66) Plus de 50 étudiants sont venus, mais moins de soixante. More than fifty students came, but less than sixty. The sentence is also well formed if the initial quantifier and the detached quantifier introduced by mais do not contain co-oriented implicatures; compare the following sentences and the associated judgments. (67) ? Plus de 50 étudiants, mais plus de 30, sont venus. More than 50 students but fewer than 30 came. (68) ?Peu d’étudiants, mais moins de 30, sont venus.9 Few students, but less than 30, came. (69) Peu d’étudiants, mais plus de 30, sont venus. Few students, but more than 30, came. If we are correct, peu d’étudiants means that the actual number is estimated to be under the standard of comparison, and plus de 30 generates the implicature that the actual number is above a norm. First, considered as a mere empirical generalization, the fact that mais + bare quantifier is acceptable if the bare quantifier introduces an intensional comparison with a different orientation from that of its anchor is indirect proof that the analysis of presque introduced in this paper is correct. Because peu mais presque a is appropriate, presque should introduce an intensional comparison oriented in the opposite direction (this is the new component I propose to introduce in the semantics of presque). Second, the lexical marking of norm switching by items such as but or on the other hand signals that norm switching is a marked option and that without explicit indication of the contrary, the norm chosen by a speaker is supposed to be persistent. In semantic contexts interpreted as further specification (apposition and elaboration), a fortiori, the assumption that the norm must remain the same seems more than natural.

6 A comparison with a previous proposal, Jayez and Tovena (2008) The attempt by Jayez and Tovena (2008) is the only one I know of that proposes a solution to the puzzle (1). Their proposal rests on the assumption inherited from Anscombre and Ducrot that the considered construction is argumentative in nature, and they attempt to explain that the “argumentative properties” of presque prevent this item from playing the role devoted to the apposed constituent in the construction illustrated by (1). A very interesting claim of the paper is that argumentative properties can be derived from “comparative meanings” and that plus (more) for instance has the same “argumentative properties as presque”, but they do not implement any explicit derivation from “comparative meanings” to “argumentative meanings”. For instance, they do not give any proof establishing why superiority comparatives such as plus de are not acceptable in the construction and why inferiority comparatives such as moins de are. This is in contrast with the present proposal, which gives a motivated explanation for the behavior of extensional comparatives in the context of (1). Their analysis of Anscombre and Ducrot’s original example (1) is based on the explicit claim that the construction rests on a discourse relation of justification that cannot be satisfied by 9

Some speakers say that this sentence is acceptable, but all agree that it is considerably less natural than the more than version.

presque because this item has no positive relevance (Merin 1999) for the initial few. As detailed above, I disagree with both arguments. I have shown that (1) and its discourse counterpart do not exemplify justification but instead a relation of “specification”, and I argued that the “to be precise” test is a strong argument supporting this view. Moreover, I do not share the interpretation that (1) is unacceptable because the assertion of presque has no relevance for the assertion of peu. I have the strong intuition that (1) is perceived as awkward because it implies some sort of incoherence or contradiction in the speaker’s commitments. Jayez and Tovena’s analysis is that presque a means “superior to a left proximity threshold of a », a’, which they take to be “indiscernible from” a. The notion of “indiscernibility” is argumentative in nature and is explicitly given as inspired by the original analysis of Anscombre and Ducrot, who claim that “presque a” argues in the same direction as a. Leaving aside indiscernability, what is new in this proposal is that presque a means “superior to a’, a’ being inferior to a but very close to a”. This is the part of the meaning of presque that makes it a comparative of superiority and explains that it has properties similar to those of “plus de a” with regard to cases such as (1). Of course, presque a implies “inferior to a”, and it might also be analyzed as a comparative of inferiority. Thus, one might also expect that it should behave as a comparative of inferiority such as “less than a”, which is not the case. Jayez and Tovena eliminate this potential problem by claiming that this part of the meaning of presque is a conventional implicature and is thus, so to speak, “invisible” in argumentative mechanisms. This is a crucial point for maintaining that presque has the same behavior in (1) as that of comparatives of superiority.10 Note that without this assumption, if the semantics of presque is the conjunction “more than a close predecessor of a, a’, and less than a”, the expectation is that presque should have the properties of expressions such as “more than a and less than b” or “between a and b”, which is not the case, as observed earlier in this paper. However, the claim that the less than a component of presque a is a conventional implicature might raise problems in its turn. Thus, a proposal without this commitment is preferable to a proposal endorsing it. The Jayez and Tovena analysis of presque a, disregarding the distinction content/implicature, is not itself uncontroversial. I share the belief that presque implies as part of its meaning a comparative of superiority, but I am not sure the relevant standard of comparison is simply a very close predecessor of a as Jayez and Tovena assume. As shown above, this analysis does not explain why, if a is an arbitrary degree on a scale (presque 1000 €, almost 1000 €), presque a conveys the judgment of the speaker that α is above the subjective norm chosen by the speaker. For standard comparatives (less than a, more than a), we made the hypothesis that extensional comparatives generate a co-oriented intensional comparison: more than a comes with the implicature that the quantity is higher than the norm. In the case of presque, however, the extensional comparison cannot predict this intensional meaning because it is oriented in the opposite direction, presque being an intensional comparative of inferiority. In Jayez and Tovena’s proposal, thus, as in most analysis found in the literature, the intensional layer of the meaning of presque is absent and not derivable from the denotational meaning they associate with presque. A key part of my proposal is the claim that this intensional component of the meaning of presque: 1) is independently needed although it is not derivable from the classical analyses; and 2) is the crucial element for explaining puzzle (1).

10

The notion of “assertoric inertia” (Horn 2002), although different from the recourse to a conventional implicature in Jayez and Tovena, plays a similar role when applied to presque. It provides a means of explaining that a lexical item meaning “less than a” does not have the same behavior as that of other comparatives of inferiority.

7 A note on “almost nothing” The combination of almost with everything and with nothing has been invoked in many linguistic discussions regarding the common semantic nature of the latter expressions but is more rarely considered per se. Generally speaking, presque cannot combine with every quantifier. It combines well with precise quantifiers but less easily with vague ones. Precise quantifiers can be defined as quantifiers that characterize the cardinality of intersection sets as definite cardinals, as illustrated by 20 in (70), and not as disjunctions of cardinals as illustrated by about 20 in (71): (70) Elle a presque 20 ans. She is almost twenty years old. (71) * Elle a presque à peu près 20 ans. She is almost about twenty years old. Considering that everything and nothing denote definite proportions and are not vague, they qualify for being modified by presque. The mere possibility of combination, thus, does not support the view that nothing is universal, as assumed in the early discussion about the nature of N-words such as nothing, but only that both quantifiers denote definite quantities, as does 20, for instance. Two things remain to be explained. 1) How does the meaning of presque combine with these particular quantifiers to derive the attested meaning? 2) Why is almost none acceptable in the (1) schema as an APP to the ANCH few, a fact unnoticed by Anscombre and Ducrot, who claim that the value of a does not change the oddness of presque a in (1)? 1) The combination of almost and nothing/everything First, there is a clear contrast between almost a and the comparative quantifier slightly less than a that prevents considering the latter an implication of the former. In French, un peu moins que rien (slightly less than nothing) is ill-formed for many speakers, and moins que rien (less than nothing) can only be interpreted as a trope. In contrast, presque rien is commonplace and is commonly used for a very small quantity. The following table sums up the data:

(71) Combination of presque with rien (nothing) and tout (everything).

+ rien

+ tout

Colloquial: “slightly more than nothing”

Colloquial: “Slightly less than everything”

Moins que

Trope: “nothing and even less”

Not used

Plus que

Not used.

Trope: “everything and even more”

Presque

These data are expected if moins que/plus que are extensional comparatives: “moins que rien” has no literal meaning and can only be acceptable as a trope; the same is true for “plus que tout”; moins que tout and plus que rien are not used, possibly because they are extensionally equivalent to the meaning of quelque chose (some). The adjunction of “slightly” supports this view: “slightly less than nothing” is ill-formed for most speakers because slightly rules out the interpretation as a trope and because there is no literal interpretation; “slightly less that 100%” is correct because slightly prevents the trivial equation with some. Conversely, the adjunction of slightly makes the combination of more than with the expression of the totality ill-formed (the trope is no longer available) and the combination with the expression of nullity interpretable (“slightly more than 0%”). The very different behaviors of presque a may be interpreted as confirmation that presque is not an extensional comparative (meaning “less than a”) but a scalar item meaning “immediately under the degree a on a scale” (see above). This view explains, without any stipulation, that presque tout (almost everything) is colloquial. Items interpreted as universal quantifiers (all, every, 100%) are naturally interpreted as marking the highest degree on scales. The semantics of presque a defended in this paper defines it as selecting the degrees on the relevant scale that are immediately inferior to the degree identified by a. Note that this does not explain directly why presque can combine with aucun (no one) or rien (nothing). Normally, almost nothing should denote the degrees immediately inferior to nothing (which of course often do not exist) and should be as unacceptable as the expression “slightly less than nothing”. Penka (2006) propose to explain the licensing of almost nothing by the conjunction of two properties: 1) almost (as less than, or at least) is an operator associated with a scale; and 2) the negative operator introduced by nothing reverses the scale otherwise associated with almost. Roughly speaking, although almost everything implies “less than everything” because the associated scale has everything as its top element, almost nothing implies that “nothing” becomes the top element of the relevant (reversed) scale and denotes the portion of the scale immediately inferior to nothing (i.e., above it in the standard scale). Although I think that scale reversal is a correct way to explain why almost nothing means “slightly more than nothing”, I do not think it is sufficient to say as Penka (2006) does, that scales used by scalar operators are reversed under negation. This is a general view that should apply to almost but also to other scalar operators such as at least or less than, which are also

scalar operators in Penka’s approach. Thus, it would be expected that less than nothing, for instance, is grammatical and means “slightly more than nothing”, which is not the case, as shown above. I think that the key to understanding the specific property of presque here is that presque, but not true comparatives such as less than, takes the scales induced from its argument just as a default, whereas true comparatives inherit strictly the scalar properties of their arguments. Consider in this respect the interaction between numerals and the pair almost/less than. A numeral n provides a degree on an increasing scale. For a comparative such as less than, only this increasing scale is accessible, and “less than n” can only mean “inferior to n” on this increasing scale; less than zero and less than nothing behave exactly as though zero and nothing were just ordinary numbers: either they denote a negative number or, if that is impossible, the expression is ill-formed and is only acceptable as a trope. If negation per se were a scale reversal, it would license (and even impose) the interpretation of less than nothing as “more than zero”. The specific property of presque a is that the orientation of the scale on which it denotes degrees inferior to a is only determined by a as a default and remains open to contextual effects. We have already encountered a manifestation of this in the refrigerator example. If the context makes salient a decreasing scale, almost 0°C can be extensionally equivalent to “more than 0°C”. This example is interesting because there are degrees inferior to zero and nevertheless, almost 0°C is, in this context, ambiguous. Thus the correct generalization is that almost is highly dependent upon its context for selecting the orientation of its scale—its argument being that a number induces by default an increasing scale—but the discourse context may induce a decreasing scale, and presque can choose one or the other. Let us return briefly for the sake of illustration to the new refrigerator example. It is expected that the temperature will decrease, and thus any natural number identifying a degree Celsius will be interpreted as a step in a decreasing progression. There are two indices that the relevant scale is decreasing: disjunctions (and “in-between” expressions) are natural when the greater element comes first and presque a means more than a. (72) Ce réfrigérateur devrait être à 5 ou 4°C maintenant. This refrigerator should be at 5 or 4°C now. (73) Ce réfrigérateur devrait être entre 5 et 4°C maintenant. This refrigerator should be between 5 and 4°C now. (74) Ce refrigérateur devrait être à presque 0°C maintenant. This refrigerator should be at almost 0°, now. (= more than 0°C). The pancake eating contest example (thanks to Karl Devries for this example) provides similar situations: (75) Quand il me restera entre 15 et 10 crèpes à finir, je boirai un verre d’eau. When between 15 and 10 pancakes remain, I shall drink a glass of water. (76) Quand j’en serai à presque 10 crèpes de la fin, je boirai. (=more than 10). When I am at almost 10 pancakes, I shall drink. One can observe, nevertheless, that there is a very strong tendency to prefer the default and to consider any natural number to be interpreted on an increasing scale. Only very specific situations can allow the interpretation of a number on a decreasing scale, and this decreasing interpretation is never obligatory: in most cases, subjects maintain the increasing interpretation as a possibility. We can now return to the case of almost nothing without adopting the view that negation per se triggers a scale reversal. Nothing is by default interpreted as the bottom degree on an increasing scale, which means

that there is no degree under the degree associated with nothing. Less than nothing is illformed (and only acceptable as a trope) because it has no choice but to operate on this scale. Using almost nothing presupposes that there are degrees immediately inferior to nothing, but almost as opposed to less than is not bound to the increasing scale associated with nothing. It is only a default that is ruled out by the nonexistence of degrees inferior to nothing. Note that zero will have the same effect if there are no inferior degrees (77) J’ai fait presque zéro fautes. I made almost zero mistakes. The only way to satisfy the presupposition is to accommodate that the scale used by presque is a decreasing scale having nothing or zero as its top element. The resulting interpretation is that almost nothing denotes degrees immediately inferior to this top element on a decreasing scale. This is not special in the behavior of presque because in many other contexts (see the refrigerator example) it operates on decreasing scales. The only peculiarity of almost nothing is that nothing forces operation on a decreasing scale, whereas in the refrigerator example, it is the context that makes a decreasing scale salient. A prediction of this analysis is that in almost a, no a other than nothing, zero, or 0% can make obligatory an interpretation “slightly more than a”, and this prediction is borne out. For any other quantity, the only accessible interpretation is “slightly less than a”, see for example the contrast between (77) and (78): (78) Presque aucun étudiant n’a de bourse de thèse. (= more than 0) Almost no student has a grant for her dissertation. (79) Presque 1% des étudiants obtiennent une bourse de these. (= less than 1%). Almost 1% of the students have a grant for their dissertation.11 2) The second matter to explain is why almost none, or almost 0%, in contrast to any other almost a, is appropriate in (1). In the present proposal, there are two types of quantifiers admissible as APPs to the ANCH few: extensional quantifiers (e.g., 10%) and intensional quantifiers expressing the judgment that α is inferior to the norm associated with few (e.g., a very small number). I will attempt to show that presque a, when it must be interpreted by association with a decreasing scale, returns the judgment that α is inferior to a norm. Consider the example of plugging in the refrigerator, and someone asserting (80): (80) The refrigerator temperature is almost 0% C now. Any part of the meaning of almost a has to be measured in relation to a decreasing scale: “α lower than a” on a (decreasing) scale means that α is above a on the standard increasing scale used for measures. This is why we interpret (80) as meaning that the temperature is slightly superior to 0%. However, the intensional part must also be converted. In the refrigerator example, a contextual common norm is the ambient temperature at the time the refrigerator is plugged in. The intensional meaning of presque a is “α > n”, which means, in this decreasing context, that α is higher than the ambient temperature on a decreasing scale; that is, α is lower on the increasing scale used to measure temperatures than is the ambient temperature taken as a norm. Thus, any time presque a must be interpreted in relation to a decreasing scale, it conveys the judgment that α is below the norm (on the standard increasing scale). If this is true, presque a is acceptable as an apposition to few because the unification of intensional 11

As has already been discussed, only some very special contexts associated with decreasing progressions, such as in plugging in the refrigerator or in the pancake eating contest, can offer the option “more than a” for interpreting presque a.

variables is possible. Once it is admitted that almost (nothing, zero, 0%) systematically requires the use of a decreasing scale (see above), the prediction is that almost nothing, zero, and 0% are acceptable as appositions to few, and there is an indirect way to confirm this hypothesis. We have shown that only nothing, zero, and 0%,, as opposed to any other quantifiers, impose a decreasing scale. This finding predicts that no other quantifier should be accepted as an APP almost a to the ANCH few, and this prediction is borne out even for very small numbers or proportions12. (81) ? Few drivers goes over 80 mph, almost 1%. Example (81) strictly parallels the observation that only if a =ø does almost a imply “more than a”, although in any other cases, it implies “less than a”. The generalization is finally that almost a is a licit apposition to few if and only if almost a implies more than a, which means that there are some reasons to interpret presque a in relation to a decreasing scale. The particularity of nothing is that it is the only lexical expression that makes it obligatory to interpret almost in relation to a decreasing scale.

8 Conclusion The solution of Anscombre and Ducrot’s initial puzzle (1) provided in this paper rests crucially on a deeper semantic analysis of its parts and avoids any recourse to an argumentative layer of meaning. The key parts of the proposal are an analysis of intensional quantifiers as implying a comparison with a subjective norm, a semantics of presque involving a superiority comparison with a norm, and a view of apposition as a specifying relation imposing the unification of intensional variables if any. It might be useful to make clear, part by part, how this proposal and Anscombre and Ducrot’s approach compare. On the analysis of presque. Anscombre and Ducrot insist that the denotational semantics of presque cannot explain its behavior and that something else must be added to its meaning. I agree with this, and I have proposed to add a new component to the meaning of presque, a superiority comparison with a subjective norm. This might seem similar to the notion of “argumentative force”, but it is different: all of the ingredients (comparison, norm) are required for the semantics of basic lexical items (such as tall, big, etc.), and they do not make the semantic ontology more complex. It seems accurate to think that such judgments comparing with a norm can play a role for argumentation, but it is a different story. What I share with the authors is the view that this intensional meaning component of presque is strongly “disconnected” from the others and not predictable from them. I have noted that although there is a regular process that generates a co-oriented implicature from extensional comparatives, the lexical item presque associates “divergent comparatives”: an extensional comparative of inferiority on a scale and an intensional comparative of superiority (to a norm). In this respect, I think that Anscombre and Ducrot were correct in assuming that the extensional meaning of presque gives no clue for predicting its non-extensional one. Regarding the reasons (1) is atypical, my explanation is rooted in the claim that when an intensional norm is introduced for evaluating a quantity, it is “persistent”, which means that no other norm for evaluating the same quantity can be introduced within the space of a specifying apposition. Sentence (1) is for this reason seen as a semantic intensional 12

The fact that the quantity denoted by a in presque a has no relevance for the acceptability of structure (1) was noted by Anscombre and Ducrot (see above), but they did not discuss the case of nothing.

contradiction (the very same value is assumed to be under and above the same subjective norm). The system of explanation of Anscombre and Ducrot is different because they see (1) as a pragmatic failure, a mistake in an argumentative process. On the nature of the structure illustrated by (1), for Anscombre and Ducrot, structure (1) is conceived as a justification relation (as it is for Jayez and Tovena (2008)). In the analysis I defend, (1) is a case of specification, and the closest discourse relation is elaboration, not justification. The analysis of this puzzle rests on a number of choices regarding general issues that deserve further investigation. I will only list a subset of them as research questions: the nature of apposition as a specifying relation and the relationship between apposition and plural pronouns; the analysis of intensional determiners as implicit comparisons with subjective norms; the scalar nature of presque and its association with increasing and decreasing scales; and the “superiority to a norm” content of presque and the conditions under which it is overt (for arbitrary degrees) or invisible (for top-elements of scales).

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