The Case of Free Choice Ability

Semantics & Pragmatics Volume 11, Article 4, 2018 https://doi.org/10.3765/sp.11.4

This is an early access version of

Nouwen, Rick. 2018. Free choice and distribution over disjunction: the case of free choice ability. Semantics and Pragmatics 11(4). https://doi.org/10. 3765/sp.11.4.

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Free choice and distribution over disjunction: the case of free choice ability*

Rick Nouwen Utrecht University

Abstract This squib discusses the semantics of ability modals in relation to the law of distribution over disjunction and free choice eﬀects. Most current analyses of free choice need distribution over disjunction as a theorem for modals in order to correctly derive free choice inferences. Famously, however, ability modals have been argued to fail to meet distribution over disjunction (Kenny 1976). The squib explores to what extent free choice abilities are dependent on the distribution property.

Keywords: free choice, disjunction, ability, homogeneity

1 Free choice disjunction

The classical puzzle of free choice permission is that while (1) is not valid in any classical deontic logic, it seems valid for the corresponding natural language sentences, as in (2) (Kamp 1973).

(1) ^[p ∨ q] ⇒ ^p ∧ ^q (2) You may pick an apple or a pear a. ⇒ You may pick an apple b. ⇒ You may pick a pear.

The effect turns out to be independent of modal flavour (for instance, Zimmermann 2000) and, in fact, has even been argued to be independent from modality (for instance, Klinedinst 2007, Fox 2007). The generality of the phenomenon is one reason why large parts of the literature seek an explanation of the free choice effect in the interaction of existential quantificational force and disjunction. In this squib, I explore the generality of the phenomenon by turning to a particular constraint on free choice inferences that is left implicit in a dominant approach.

* The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement no. 313502, which I hereby gratefully acknowledge. For discussion and comments, I would like to thank Bart Geurts, John Horty, Nathan Klinedinst, Matthew Mandelkern, Daniel Rothschild, the editor in charge, Paul Elbourne and the anonymous reviewers. early access errmynwrao bu h pae’ netos h i h pae s a use speaker the did why intentions: speaker’s the about reason now may hearer A ii hstp fraoigcnbe can reasoning of type this (iii) hr r ruhy w id fapoce ofe hie nteoehn,there hand, one the On choice. free to approaches of kinds two (roughly) are There Cirhae al. et Chierchia instance, (for of part is it interpretation of level which and volves nta,ti qi ocrstelresrn fltrtr httet rechoice free treats that literature of strand approaches. large these about the say concerns to nothing squib have this will (Aloni I Instead, operator 2011). existential Barker the 2005, of Simons or 2003, 2005) Geurts e 2000, choice (Zimmermann free disjunction the think that approaches are disjunction over Distribution 2 ihrbt ijnt r emte rbt r o permitted: not statements: are choice both free or for permitted reading strange are pretty disjuncts a both predict either we’d here, things left we If (4) ¬ it, from that draw would concludes we hearer inference why the reasons or possible false, two is now are there that So, particular, hearer false. 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She then reasons that i 3 p q q ] ∧ q ^ are possibilities. To be clear: these intentional p ) 1 ∨ [ . 1 erent status in Geurts’ theory than alternative i airs. These di q ) p ^ ff [ q is permitted. This is known as ff ^ ^ ^ ∧ ¬ q ∧ erently, but follows a reasoning pattern that is quite q To illustrate, let me go through what the same mecha- are permitted. And, so, the free choice inference is alternatives erent setup. The account of free choice implicatures p ff ^ or ∧ ¬ 2 ff q ^ p p ^ ∧ ¬ ^ p both ∨ ¬ ^ p ( ¬ ^ ∨ individual disjuncts ) ⇒ q ] -world and no accessible q ^ p ∨ ∧ that, traditionally, receives this label in the literature). Yet, from a purely . That is, here the p p , which I will abbreviate as DOD: q [ ^ ^ ^ ∧ ¬ -world. While the Kratzer-Shimoyama style reasoning leads to ,(5) it is only q Given DOD, the hearer may dismiss As I said, Kratzer and Shimoyama’s idea has been implemented in strongly This final crucial step is what I want to focus on in the following. I assumed here p ∨ ^ p The above description of theused mechanism theory is of quite(2007),Fox closely who implementedimplicature. implements in It the the straightforwardly free prominent inherits choice and the recipe widely For prediction in the a that initiated, grammatical free technically, mechanism choice without for wouldleading DOD not to the arise the alternatives without implicature DOD. alternatives logical point of view, they playchoice inference. a similar role in getting to the end-result of a free also be disregarded, because if the speaker had been in one of these states she would ¬ alternative (classes of) states of a possibilities have an altogether di utterances or grammatical structures in our discussion above, (which are the kind of nism looks like in ain quiteGeurts(2011) di is framed di similar to that of aboutKratzer the & intentional(2002). Shimoyama state The ofentertain the idea one speaker. of is For four that a possibilities: hearers sentence ( reason (6) through the DOD theorem in (6)to that the the free combination choice of inference (3) and (5) is strengthened opposing theoretical corners. disjunction In standard modal logics, distributionin over a disjunction possible is world a semantics theorem.no for For accessible modals, instance, (6) follows from its semantics: if there is However, since the assertion in (3) itsays follows that from at (5) least oneaccounted that of for. the disjuncts is permitted, that (3) entails that either Free choice and distribution over disjunction (5)( with the speaker’s assertion that whether or not the 2 For this reason, I am tempted to call this status quo the 1 early access aosyage,dsrbto vrdsucinis disjunction over distribution argued, famously (1976) Kenny As as interpreted was ,sneteeaeas rmwrsta eyon rely that frameworks also are these since (2010), Rooij van and 2011) (2009, hsi eas eko htdsucinraiytkssoewdrta surface than wider scope takes readily disjunction that know we because is This eigbtenteeitnil(oa)qatfiraddsucinta irp the for disrupt holds DOD that While disjunction DOD. and of quantifier validity (modal) existential the between vening utiaieawrdi hc nyoeohrwrdi cesbe hl rmthat from while accessible, is world other one only which in world a imagine Just (7) statement modal the make would it invalid, DOD Were space. Franke logical in a arises up issue dividing similar a Quite (5). implicature the to leading dismiss thus to excluded, able being be hearer must the speaker on the that conclusion the state at in conveyed arrives simply hearer the that way, something This respectively. namely shorter, something said have aeteaiiyt ikacr n rdc t oo.Wehrtecr o iki red is pick you card the won’t Whether simply color. chance. you its on conjuror, predict completely skilled and relies a that card black are that a or you from pick follow unless to should ability But it to the true. holds, ability have is DOD the (10) have if However, or obviously You pick true. (9) to black. is either were or (8) you red so If be card, colours. either a the would pick concealing cards it down, playing cards, face regular these are of of cards deck one The a you. is if there front Say follows. in as goes argument The modals. disjunction over distribution and Ability 3 lexical to turn to need force. therefore universal we and choice existential free of of combinations DOD-dependency see the did test we to order If taking. form scope surface the on of constraint sentence any a to for immune choice free seems it fact, In scope. choice. free blocks disjunction and quantification existential between intervening neither but true, a access may we world latter rely to inferences holds. choice disjunction free over distribution of not occurrence or the no expect whether would on on simply we are is then reasoning there track, Kratzer-Shimoyama modals, right the follow the existential that for approaches semantics the standard If discussion. the of theorem a valid. is been had DOD if than cells partition more with consistent notntl,w antts ietywehra prtrwt nvra force universal with operator an whether directly test cannot we Unfortunately, inter- operators at look to be would route One prediction? this test we do How it Because literature. choice free the in modals for assumed tacitly is DOD i 1 ^ h tt hr h recoc neec od.Ti eutcuilyrelies crucially result This holds. inference choice free the where state the , [ p ∨ ^ q ] ^ ; p > nor ^ ∨ p > ^ ∨ p q ^ o hc recoc olw tagtowrl.In straightforwardly. follows choice free which for , ∧¬ . q q ol n a and world i 4 fDDde o od only hold, not does DOD If . ^ 4 [ p ∨ q ^ q tde o odfor hold not does it ] ∧¬ > p > ol.Ti makes This world. ∨ tcudsml eta it that be simply could it invalid i 2 ^ and [ ^ ^ p o ability for i p 3 ∨ Nouwen a be can [ or q p ]: ∨ ^ q q ] , early access q ). w ( A : m , which has this ∈ w ∀ ): w ( N ∈ means that there is some action good possibility m p ∃ true, this does not entail that there is an q 5 With such a view of ability, DOD no longer ∨ 4 p if and only if that maps worlds to propositions (the available the semantics of w N in can about or that there is an action that reliably brings A being true. p p and a function W For now, however, I would like to focus on the how the theoretical 3 has the ability to α I can bring it aboutblack that card. either I am picking a red card or I am picking a (Kenny 1976, p. 215) In part due to Kenny’s observations there have been many proposals that give a does not have the abilityAs of two choosing reviewers which rightly colour point helinked out, picks to such (i.e. the a when agent. view she’s That only not is, works a the when conjuror). actions the in available question actions havegloss are to over somehow be such actions important controlled details. by the agent. Because Portner(2009) suggests that within aassigning Kratzerian ability framework modals there like is thesame option structure of of a combination of existentialAs and an universal anonymous force. reviewer rightly observes, for instance, that intuitions for a minimal variation on about. For instance, (1988)Brown uses aset semantics of that worlds has modelsactions made in up that of world). a Ability is now interpreted as(11) follows: among many others Horty &many Belnap of, 1995 theseThomason is2005.) the Thethat intuition following: will someone behind reliably is result able in to holds. If some action reliablyaction makes that reliably brings see below, Kenny’s observations regarding (8) statements. are not representative of alldevelopments ability triggered by Kenny’s observations tieliterature. in with the recent free choice semantics of ability that does not yield distribution over disjunction (for instance, (9) (10) I can bring it aboutI that can I bring pick it a about black that card. I pick a red card. over disjunction to hold. Given my current focus on freethe choice disjunction inferences, of however, (9) and follow(10) does either. not Kenny’s follow example from (8),free(8), in choice their in other conjunction tandem does words, with not shows an absence an of absence distribution of over disjunction. ability As we will Kenny’s argument targets analyses that characteriseof the simple concept quantification of ability over in worlds: terms Such analyses wrongly predict distribution Free choice and distribution over disjunction (8) (8) are not so clear: “I can pick a red or a black card from the stack” is pretty odd when the speaker what is important to the present paper is mainly the quantificational structure of ability modals, I we can take the argument one step further. Given the fact that Kenny observes that 4 3 early access midbe oa nnmu eiwrfrugn et ehn h icsinbelow. discussion the rethink to me urging for reviewer anonymous an 6 to indebted am I 5 ehv sue that assumed have We that (13) from infer easily We inference: choice free a has (13) doubt, a Without Clearly, hnDDi nai.S h rdcini htteewl en recoc ability. choice free no be will there that is prediction the So combination, invalid. a such is involves DOD indeed ability then Assuming force. universal and existential (12) recoc neecs i ouini nsm asprle owa ilnwdsusfrability for discuss now will I no what be to to parallel there ways predicts some proposal in his is that modals. observe solution does His he inferences. universal DOD, choice and discuss e free existential not choice combines does free also he of statements analysis Although such an force. for develops semantics who Nickel’s (2010), statements. Nickel generic by for inspired know is below we However, discussion The so. reliably not some just that rod, option fishing the makes nose balancing open reliably a leaves his that in This on way result nose. no balance John’s may is rod on actions there upright fishing that stand the means rod makes (14) fishing reliably that the say that would act account to an John Such for way a is that say Let’s force. eye. bull’s the hit nose. can’t his John on rod fishing a balance can’t John (15) (14) turn (15). in and this (14) show, Compare statements. will ability I DOD negated As abilities these sense. for make that really means not does give succeeding not accidentally does about the something the on bringing person based at that was success modals accidental ability someone’s for that DOD fact of validity the against argument Kenny’s success accidental and Homogeneity 4 argument. the this in muddling show subtleties several will are I there As ability. squib, choice this free of be remainder have cannot now We there instance. that for prediction chin, problematic Kratzer her on that rod chin. argument fishing her a an on balancing or of nose capable her is on Betty rod fishing a balance can Betty (2011). Geurts from (13) (13), by demonstrated is as out, prediction this borne (8), not for is observation Kenny’s to contrast in and however, Unfortunately, What w.r.t. p o oa base modal a For odpossibility good ∨ q a eago osblt vni neither if even possibility good a be can h F ability , g i fadol if only and if _ obigti bu.Frsm blte,hwvr h daof idea the however, abilities, some For about. this bring to can [ sigrdi aacn nJh’ nose John’s on balancing is rod fishing A / hrswt rw’ cinsmnisi hti combines it that is semantics action Brown’s with shares hmym-tl prahst recoc aethe make choice free to approaches Shimoyama-style novssm obnto feitniladuniversal and existential of combination some involves F n nodrn source ordering an and ∃ w is ∈ ai.Tebs a oseti st consider to is this see to way best The valid. F 6 ∀ w 0 [ w > g 5 , w 6 0 p → g nor : p p ( w q sago possibility good a is 0 sago possibility. good a is )]. ] tnsfor stands Nouwen there ff ects . early access ] is q q ∨ since p ] [ _ q ∨ _ accidental nor p [ p , and thus we According to 7 _ _ is true in all these (17b) , homogeneity says q q to and can only be true in every p (17a) q ∨ p is true, but neither ] q ∨ p [ 7 : for any action, if it is the right one it will ) ) q q _ ¬ _ . If we now consider cases in which is true in all these worlds or ] q p ∧ ¬ ¬ ∧ p p ¬ ∨ homogeneous _ q ¬ ( ( [ ]. ∨ ∨ q ) ) ] homogeneous ability ∨ q q ϕ erent for (15), however. Imagine this sentence is about John’s p p p and ¬ [ ff ] ¬ _ _ p _ ∧ ∧ ∨ _ ¬ ¬ p p ϕ are reliably false after any action, and, consequently, free choice follows. q ∨ [ _ _ p b. : it holds for some cases, but definitely not for all. When homogeneity does and [ p In sum, homogeneity for ability is tied with the absence or presence of Things are di (18)( (19)( subsequently accessible world if true is simply ruled out, due to homogeneity. Clearly the second disjunct isboth incompatible with the statement that homogeneity, as in (16), makes DODthat valid. Considering is true, we see that, from some accessible world, Homogeneity also predicts the presencethe of Kratzer-Shimoyama free recipe we choice get inferences. interpreted the inference as in (18) for an ability statement success hold, it looks like (16).end This up will concluding allow us from to (14) strengthen that any action will(16) reliably cause the rod to fall(17) down. a. precisely aim a dart atif a he darts tried. board. This Then means hemay that may hit this still the kind hit bull’s of the eye ability bull’s isthat eye is inconsequential he by not to cannot accident homogeneous. his reliably The ability. hit fact The the that only bull’s he thing eye. He that therefore matters lacks is the relevant ability. that balancing-abilities are reliably result in a balancingdown. rod; if it is not, it will reliably result inabilities the of rod playing falling darts. Imagine that (15) is true and that John lacks the ability to Free choice and distribution over disjunction that if you lack thefall ability down. to Fishing balance rods the don’t rod, accidentally gravity stay will upright. make This sure is that another way the of rod saying will This result will not come as a surprise as soon as we realise that the assumption of According to (16) this will be strengthened to: worlds (or both). A situation in which 7 Again, see (2010)Nickel for a parallel argument for generic statements. early access hnst naoyosrvee o rigm oselti u somewhat. out this spell to me urging for reviewer 9 anonymous an to Thanks 8 ihu cietlsces eodpsil aecudb hthmgniyis homogeneity that be could take possible second A success. accidental without ooeet antb assumed. be cannot homogeneity (15), in as On abilities, valid. other DOD for make hand, do other they the homogeneity, through of and force however, quantificational homogeneous, the are attribute that analyses the of follow prerequisite _ a we is If DOD (ii) of choice. validity free the choice, free to approach Shimoyama-inspired Ocrcnwl rtl.*FC Betty can “How like discussion under question (teleological) a guests?”. after the of inference entertain reading choice ability free a a on with available fine is choice free think not German by or masked English sometimes speak is statements ability of for polysemy inferences the choice free of unavailability relative The choice. (20) free both triggering Clearly, without held absent. abilities, which is homogeneous suggested, involve success I (21) accidental line whenever and theoretical present first is the choice dismiss free also that (21) and (20) that Note (21) choice free the lose that example rod fishing inference: Geurts’ talk. on variations or are walk talk. there can Similarly, can Oscar and walk can he which at age the (20) an to of communicating now of is way Oscar straightforward odd son more decidedly my are a that there is hearer but judgments, which his (8) (20), with Take about agree too. intuitions you Kenny’s examples, if occur. there point not Second, in hit does case. case accidentally ability this a might choice in are John free hold if where to even cases homogeneity true clear assume is are cannot it we that So is eye. (15) bull’s for the intuition the all, of First deontic for generally arises it free like so statements. just and generally, epistemic case, arise statements, and the to such were predicted all be this for would If hold choice made. would is disjunction over statement distribution ability then an whenever excluded abilities made. is involve are success that that ascriptions predict ability statements to whenever ability instantiated come those somehow we only then and value, all face in at points occurs these choice take free simply we if First, ie hs a niintopsil hoisbsdo hs assumptions. these on based theories possible two envision can I this, Given & Kratzer the to According (i) following: the know now we stock, Taking hn ecndsistescn fteetere ut aiy o w reasons. two for easily, quite theories these of second the dismiss can we think I oaiiis hn oial blte ontmk O ai.(i)Sm abilities Some (iii) valid. DOD make not do abilities logically then, abilities, to uthrlf ad *FC with potatoes hot four juggle or nose hand. her left on her rod just fishing a balance can Betty 9 can ..b t miut ihrsett oa aor fyuaetl ht“ that told are you If flavour. modal to respect with ambiguity its by i.e. , ,teei la recoc neec natlooia edn of reading teleological a on inference choice free clear a is there ”, 8 can hn h xml is example the think I (21), for Similarly . 8 hti,accidental is, That oncan John can Nouwen do I . early access at Se- the not / can to say: this sp.3.10. / 10.3765 / doi.org // 9 , vol. 114, Konstanz: Universität Konstanz. the absence versus presence of DOD. erences between the example with and those without ff 3(1). 1–38. https: not mantics and Pragmatics A shared idea within the approaches I targeted in this squib is that free choice I think what is crucial to good examples of ability free choice is that they typically In summary, then, the predicted DOD-dependence of free choice ability is Sinn und Bedeutung (SuB) 7 Aloni, Maria. 2003. Free choice in modal contexts. InBarker, Matthias Chris. Weisgerber (ed.), 2011. Free choice permission as resource-sensitive reasoning. disjunction. This is obviously an attractive idea, given that it reducesshown is free that choice the to fringes a testing of ground the for landscape this of way existentialthe of operators test. thinking. is At a first challenging glance, the dominant approaches fail References phenomenon. This is in stark contrastsee toEckardt other, 2007 modelPortner free2010). choiceconstraints Right phenomena that (though now appear I to see govern no it. way of making senseis of triggered the simply by the logical interplay of existential quantificational force and I have identified two challengesdisjunction. First, for the the dominant semantics Kratzer andfree and choice pragmatics Shimoyama-style inferences of approaches come to free about how choice times need to triggers explain such how inferences it withouttheorem. is distribution Secondly, possible there over ability is disjunction an being empirical a challenge. valid Ability free choice is a limited statement and I have no explanation for this observation, but I do have In contrast, (21) contains two distinctSpeculating abilities, somewhat, which free somehow choice prohibits ability freeinferences always choice. that seems concern to the involves a same conjunction general of ability. This is obviously not a very precise phenomenon, but that the limitation seems disconnected from homogeneity involve two variations of the samehere ability, as as (22). in Geurts’ original example, repeated (22) Betty can balance a fishing rod on her nose or on her chin. free choice inferences, it is Free choice and distribution over disjunction attested. Instead, what can be observed is that free choice ability is quite a limited 5 Conclusion very general pragmatic (or, alternatively, grammatical) process. What I hope to have validity of DOD. Whatever accounts for the di early access heci,Gnao an o ejmnSetr 01 h rmaia view grammatical The 2011. Spector. Benjamin & Fox Danny Gennaro, Chierchia, ability. of logic the On 1988. A. Mark Brown, lndnt ahn 2007. Nathan. Klinedinst, In modalities. dynamic and abilities Human 1976. Anthony. Kenny, action, permission. of choice study Free A 1973. Hans. stit: Kamp, deliberative The 1995. Belnap. Nuel & F John Horty, implicatures?!? 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