The fact that any has both a Free Choice and a Polarity Sensitive profile has been the source of many controversies.In this paper, we have proposed that the different uses of any are manifestations of the general constraint NI. All the cases we have reviewed concern the wayin which any links individuation and eventualities. As noted in [11], the French item le moindre, whose scalar origin is clear, has a very similar distribution.Future work will have to say whether scalarity plays a central role for any, as advocated in [5], and, more generally, for items which have both a PS and a FCsensitivity

Jayez, Jacques

Tovena, Lucia

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Any and eventualities

The fact that any has both a Free Choice and a Polarity Sensitive profile has been the source of many controversies.<br />In this paper, we have proposed that the different uses of any are manifestations of the general constraint NI. All the cases we have reviewed concern the way<br />in which any links individuation and eventualities. As noted in [11], the French item le moindre, whose scalar origin is clear, has a very similar distribution.<br />Future work will have to say whether scalarity plays a central role for any, as advocated in [5], and, more generally, for items which have both a PS and a FC<br />sensitivity

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Any and eventualitiesJacques Jayez, Lucia TovenaTo cite this version:Jacques Jayez, Lucia Tovena. Any and eventualities. Dekker, Paul;Van Rooy, Robert;. 14thAmsterdam Colloquium, 2003, Amsterdam, Netherlands. ILLC (Univ. of Amsterdam), pp.151-156, 2003. <halshs-00157208>HAL Id: halshs-00157208https://halshs.archives-ouvertes.fr/halshs-00157208Submitted on 29 Jun 2007HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Any and EventualitiesJacques Jayez∗and Lucia Tovena†1 IntroductionProceedings of the 14th Amsterdam Colloquium, December 19-21, 2003Paul Dekker and Robert van Rooy (eds.)The fact that any has both a Free Choice (FC) and a Polarity Sensitive(PS) profile has been the source of many controversies (see [4],[5] for recentinventories). If one assumes, following in particular [1], [3], [6], [9], that FCitems in general avoid reference to particular individuals involved in episodicpredications, the examples in (1) are problematic, since all these sentences areepisodic and refer to particular individuals (books, students, girls). One mightdispute the relevance of (1a) by insisting that PS any is different. However(1b,c) are traditionally considered as FC uses. Must we create a third non–PSand non–FC any for such cases? In this paper, by postulating different modes offree choiceness, we show that the different behaviors of any represent differentgrammaticalized ‘answers’ (i.e. constraints) to the same problem.(1) a. Mary didn’t read any book of the listb. Any student ∗(who had cheated) was suspendedc. Mary performed better than any other girl in her class2 Intuitive descriptionWe propose a unified analysis of any as an ‘arbitrary’ item and account forboth its PS and FC properties. Arbitrariness (Fine) means that all individualdifferences can be neglected. More precisely, if we evaluate a sentence of theform [any ] [P ] [Q], every P–individual which satisfies Q in some situation s canbe replaced by every other P–individual in s, or, equivalently, all individualsare on a par. This is called Non Individuation (NI) in [6]. NI can be satisfied indifferent ways, which represent as many versions of any. This accounts for thepersistent conflicting impressions that any is one (its uses are not unrelated)and multiform (its uses cannot be derived from a common semantic core).∗ ENS-LSH, Lyon and CNRS , e-mail: jjayez@ens-lsh.fr† Universite´ de Lille III and CNRS, e-mail: tovena@univ-lille3.fr151Ê The clearest manifestation of NI is known as variation in the literature on FCitems (see e.g. [2], [3], [10]). Variation works well when we have several possibleworlds, as, for instance, in the Vendlerian imperative Pick any apple!. We canimagine than any apple picked in a continuation could be replaced by anotherapple of the initial set of apples. So, the individual properties of the apples donot determine in advance which apple is to be picked or not to be picked.Ë With episodic sentences, the situation is as follows. Assertions like (1d) areout because the books that are read are determined in the current situation.(1) d. Mary read ∗any book on the listHowever, why is (1a) normal? Since Mary did not read any book on the list, thebooks that are not read are determined (they are all the books on the list). Wedistinguish between two scenarios of NI. The first is uniformity: all individualsmust be able to satisfy or not satisfy the same properties, as illustrated bythe case of variation (Ê). The second involves reference: even when uniformityis respected, FC items avoid reference to particular individuals. E.g. (1d) isexcluded although it may be interpreted as ‘Mary read every book on the list’because it entails that particular books were read. Referential properties dependon different factors, among which the nature of eventualities. Any ‘considers’objects participating in a particular, spatio–temporally situated, eventualityas individuated. PS environments do not refer to positive eventualities: thereis no proper positive event of Mary ‘not reading’ a book because there is nospatio–temporal location at which the event would develop.1 Similarly, in aquestion like Did Mary read any book?, there is no mention of a reading event. PSenvironments simply do not give rise to the kind of individuation that any candetect, namely one which is grounded in positive eventualities. The exclusionof positive eventualities accounts immediately for the fact that sentences thatentail (1a) are anomalous if they mention genuine positive eventualities (1e).(1) e. Mary successively ∗refused to read any book on the listThe idea that any forbids positive events raises the following problem. Supposethat a certain apple cannot be picked in any follow–up to a Vendlerian impera-tive Pick any apple!.2 If the speaker is aware of that and wants to include thisapple in the set of possible choices, any is infelicitous. Yet, not picking the appledoes not count as a positive event and does not individuate the fruit. But, tobe excluded in advance, the fruit has to be characterized by properties whichdistinguish a subset of the set of apples. This configuration is incompatible withNI, which prescribes uniformity.1. Of course, the fact that not reading a book does not count as an event spatio-temporallydoes not prevent it from counting as an event in other respects. The literature on so–called‘negative events’ often mentions examples of the form And what happened? Mary did not readmy novel!, see [8].2. The apple might be rotten, for instance.152Ì Since (1b,c) refer to particular events, they should sound strange. (1b) illus-trates subtrigging ([7]), that is, the fact that an otherwise anomalous any–sentence is redeemed by adjoining an appropriate modifier, here a relativeclause. Clearly, there is a conditional relation between the VP content andthat of the modified noun in such cases. This makes the identity of the stu-dents irrelevant (arbitrariness): students are suspended qua cheaters and notqua particular students.Í As for (1c), the crucial observation is that we cannot refer explicitly to a setof particular events (2).(2) On Monday, Mary beat ∗any other girl in the classThis indicates that (1c) refers to such events only indirectly. As in the caseof subtrigging, individuation by events is possible. Suppose that the girls inMary’s class were engaged in a chess tournament. The fact that Mary beatSally certainly depends on their respective individual strategies. But (1c) ac-tually means that Mary reached the highest performance level when comparedto the other girls. The exact way in which this is achieved, that is the orderand content of the particular confrontation events, is irrelevant. Let {ei : i ∈ I}be the set of particular confrontation events. Mary’s performance correspondsto the set of results {rM (ei)}. The fact that this set is ‘superior’, with respectto some measure operator µ to another set (that is, µ({rM (ei)}) > µ({rx(ei)})for every other girl x) is not related to any particular ei in {ei : i ∈ I}. Thesame configuration obtains if the competition is not a set of confrontations buta comparison of individual performances (for example a competition betweenathletes). If Mary jumps higher than Sally, there is (at least) two ways of ap-plying an event–based ontology. First, we can say that there is an event ofMary jumping higher than Sally, which takes place at some particular spatio–temporal location. Second we can focus on the relation (comparison) betweenthe events of Mary jumping and Sally jumping. The possibility of (1c) suggeststhat any does not pick up particular events in which Mary and the other girlswould participate, but a more abstract relation between events or sets of events.Î Finally, note that we do not want to rephrase any as a garden–variety in-definite (like a) combined with the NI requirement. For instance, (3a) and (3b)are not equivalent, since only (3a) gives one the right to consult an unlimitednumber of files. This is why we represent any as an existential quantifier on setsrather than on individuals in (4.1) below.(3) a. You may consult any fileb. You may consult a file, any file3 Calibrating anyÊ E+ denotes the set of positive eventualities. We adopt a Davidsonian notation153for eventualities.(4) A sentence with a tripartite structure M([any ] [P ] [Q]), where M is a(possibly null) modal operator,1. asserts M(∃X(X ⊆ [[P]] & X ⊆ [[Q]])),2. implies that there is no a ∈ [[P]] such that either:a. ∃e,∃e′ ∈ E+(P (a, e) & Q(a, e′)) if M is null, orb. 2∃e, e′(P (a, e) & Q(a, e′)) or2¬∃e, e′(P (a, e) & Q(a, e′)).(4.2) distinguishes two cases. For simple assertions, no positive eventu-alities must be involved. For modal sentences, no individual in the restrictionP can be imposed or excluded as a satisfier of the scope Q. Clearly, (4.2a) istoo strong because it predicts that subtrigging is impossible. In (1b), there arepositive events of suspension.Ë We replace (4.2a) by (4.2a’).(4) 2a’. ∃e,∃e′ ∈ E+(P (a, e) & Q(a, e′)) if M is nullunless 2[∀x∀e(P (x, e) ⇒ ∃e′ ∈ E+(Q(x, e′))] holds.(4.2a’) suspends the prohibition on positive eventualities whenever there is anecessary implication between being a P–object and being a Q–object. In thiscase, the positive eventualities can be interpreted as the manifestations of a gen-eral constraint, which does not take into account the identity of the individualsinvolved (arbitrariness).Ì For comparatives, the intuition is that there is no genuine positive eventuality.However, as for subtrigging, condition (4.2a) is too strong and so is condition(4.2a’). The problem comes from the fact that we cannot deny the status ofeventuality to did–better–than(Mary, x). So (1c) can be translated as:∀x((in–Mary’s–class(x) & x 6= Mary) ⇒ ∃e did–better–than(Mary, x, e)).Since the sentence presupposes that there are girls in Mary’s class, it impliesthat there are positive eventualities of Mary doing better than other girls. Wesaw in section 2.Í that, in such cases, any selects the relations between events.So we rephrase (4.2a’) as (4.2a”).(4) 2a”. ∃e,∃e′ ∈ E+(P (a, e) & Q(a, e′)) if M is null, unless(i) 2[∀x∀e(P (x, e) ⇒ ∃e′ ∈ E+(Q(x, e′))] holds, or(ii) for every e′ ∈ E+ such that ∃e(P (a, e) & Q(a, e′)), Q(a, e′) is equiv-alent to φ(a) for some non–Davidsonian (possibly complex) expressionφ(4.2a”) adds the idea that there is a non–Davidsonian property φ whichreplaces the Davidsonian Q. Suppose that (1c) refers to a chess tournament inwhich each girl must play against each other girl, and that the players are rankedby number of victories. Let v(x, n) mean that x won n times. (1c) implies:154∃x, e, e′(in–Mary’s–class(x, e) & x 6= Mary & did–better–than(Mary, x, e′)).This form violates (4.2a”). The following form does not.(5) ∃x, e(in–Mary’s–class(x, e) & x 6= Mary & ∃n, n′(v(Mary, n) & v(x, n′)& n > n′)).4 Remaining issuesSummarizing, we connect the PS uses of any with a sensitivity to positiveeventualities, the apparent exceptions (subtrigging and comparatives) with thefact that regularities or relations are fore–grounded, leaving eventualities in thebackground, and the modal uses with the variation requirement (uniformity).Several problems remain.Ê How does all this interact with NI? Uniformity and subtrigging clearly put allindividuals on a par. Comparatives and downward entailing sentences constrainthe reference to events. Comparatives do not forbid positive events that involveparticular individuals but they also refer to comparisons between events. Con-sider two girls a and b in Mary’s class. If they each confront Mary, this givesrise to two distinct events. If their performances are compared to that of Mary,it is more difficult to say that we have events ‘of comparison’. One might objectthat the outcomes of the comparisons may be distinct and help to individuatea and b. The point is that, in a sense, the outcomes are reduced to the mini-mal information that Mary did better than a and b.3 So, the relations betweenMary and a and Mary and b cannot be distinguished. The difference with (2)is that, in that case, we may associate a and b with different events ea and eb,whereas, with (1c), a and b participate in the same relation to Mary. Finally,downward entailing sentences do not mention positive eventualities. Therefore,it is impossible to distinguish individuals on the basis of their participationsin eventualities. We conclude that, in spite of their differences, all these casesmake the pairing of individuals with eventualities impossible or irrelevant.Ë Uniformity, subtrigging and compatibility with comparatives can be observedwith FC items in French and in Greek (see [6] for n’importe quel and tout, and [3]for opjosdhipote). Since there is no morphological relation between these itemsand any, it is unlikely that the sensitivity of any to eventualities is parochial.Rather, eventualities constitute an important resource for individuation, andforbidding these resources or making them inefficient is a standard strategy forensuring NI. PS behavior is not observed with the items mentioned above. Lackof space precludes a discussion of the possible accounts one can propose for thisdifference.Ì It is well–known that any oscillates between an existential and a universalinterpretation. It has been proposed that FC items tend to be indefinites and3. Note that, in (5), the outcomes n and n′ are bound by ∃ and thus convey no specificinformation.155that their universal interpretation comes from the interchangeability of indi-viduals across worlds (uniformity), see [3] in particular. How this derives the ∀behavior observed in subtrigged sentences and comparatives is not quite clear,however.5 ConclusionIn this paper, we have proposed that the different uses of any are manifestationsof the general constraint NI. All the cases we have reviewed concern the wayin which any links individuation and eventualities. As noted in [11], the Frenchitem le moindre, whose scalar origin is clear, has a very similar distribution.Future work will have to say whether scalarity plays a central role for any, asadvocated in [5], and, more generally, for items which have both a PS and a FCsensitivity.References[1] Veneeta Dayal. ANY as inherently modal. Linguistics and Philosophy,21:433–476, 1998.[2] Anastasia Giannakidou. Polarity Sensitivity as (Non)Veridical Depen-dency. Benjamins, Amsterdam, 1998.[3] Anastasia Giannakidou. The meaning of free choice. Linguistics and Phi-losophy, 24:659–735, 2001.[4] Laurence R. Horn. Pick a theory, not just any theory. In L.R. Horn andY. Kato, editors, Negation and Polarity. Syntactic and Semantic Perspec-tives, pages 147–192. Oxford University Press, Oxford, 2000.[5] Laurence R. Horn. Any and (-)ever : Free choice and free relatives. IATL,15 (Proceedings of the 15th Annual Conference of the Israeli Associationfor Theoretical Linguistics):71–111, 2001.[6] Jacques Jayez and Lucia Tovena. Free choiceness and non–individuation.Linguistics and Philosophy, to appear.[7] Jean Ehrenkranz LeGrand. Or and Any: The Semantics and Syntax ofTwo Logical Operators. PhD thesis, University of Chicago, 1975.[8] Adam Przepio´rkowski. On negative eventualities, negative concord, andnegative yes/no questions. In Proceedings of SALT IX, 1999.[9] Kjell J. Sæbø. The semantics of Scandinavian free choice items. Linguisticsand Philosophy, 24:737–787, 2001.[10] Lucia M. Tovena and Jacques Jayez. Any as a finian quantifier. In Pro-ceedings of the 11th Amsterdam Colloquium, pages 295–300, 1997.[11] Lucia M. Tovena and Jacques Jayez. Any : from scalarity to arbitrariness. InEmpirical Issues in Formal Syntax and Semantics 2, pages 39–57. Thesus,The Hague, 1999.156

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