Czech binominal each and collective set predicates Mojmír Dočekal & Radek Šimík SinFonIJA 11, 13-10-2018 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 1 / 49 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 2 / 49 Intro data: binominal each vs. distributive each diagnosis of the distributive reading: lack of the cumulative reading (1) Two boys bought three books. (2) a. Each of the two boys bought three books. determiner b. Two boys bought [three beers each]. binominal (2-a): determiner each, two boys restriction, VP nuclear scope (2-b): binominal each, two boys key, three books share syntactic structure: Safir and Stowell (1988) Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 3 / 49 PCDRT Dotlačil (2012), Dotlačil (2012), Brasoveanu (2008) (3) Prediction: expected difference between binominal and determiner each. Both supply distributivity but binominal distributes non-locally. Technical implementation: percolation of distributivity. main point: illustrate the prediction (Czech data) byproduct: semantic and syntactic description of Slavic binominal each and interaction of determiner/binominal each with collectives Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 4 / 49 Cumulative readings in PCDRT (4) Two boys bought three books. essentials: PCDRT works with sets of assignments Info state J u1 u2 j1 boy1 book1 j2 boy1 book2 j3 boy2 book3 columns: values of discourse referents, rows: assignments to drefs cumulative reading fully compositional Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 5 / 49 E(existential) C(losure): shifts predicates into arguments S DPrt,t D ECu1 NPrt two boys VPrt V buy DPrt,t D ECu2 NPrt three books (5) [u1, u2|#(u1) = 2 ∧ boys{u1} ∧ #(u2) = 3 ∧ books{u2} ∧ buy{u1, u2}] Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 6 / 49 Determiner and binominal each in PCDRT (6) a. det-každýun = λPrtλQrt.δun (P(un)) ∧ Q(un) b. binom-každýum = λvr λPrtλQrt.[um |] ∧ δv (P(um)) ∧ Q(um) distributivity operator δ in both but binominal each introduces discourse referents binominal: semantic percolation of distributivity determiner: in-situ application of distributivity main difference: binominal each – EC of the object determiner each: EC of its argument (subject) Types in PCDRT: r . . . drefs, t . . . truth value Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 7 / 49 (7) Each of the two boys bought three books. Info state J u1 u2 j1 boy1 book1 j2 boy1 book2 j3 boy1 book3 j4 boy2 book4 j5 boy2 book5 j6 boy2 book6 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 8 / 49 Determiner each S DPu1 δu1 NP VP V DP NP EC existential closure of the subject (predicative semantics: r, t ) distributes over the atomic drefs (8) [u1|#(u1) = 2 ∧ boys{u1} ∧ δu1([u2] ∧ [|#(u2) = 3 ∧ books{u2}] ∧ [|buy{u1, u2}])] Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicates SinFonIJA 11, 13-10-2018 9 / 49 Binominal each (9) Two boys bought three books each. Info state J u1 u2 j1 boy1 book1 j2 boy1 book2 j3 boy1 book3 j4 boy2 book4 j5 boy2 book5 j6 boy2 book6 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 10 / 49 S DPu1 EC NP VP V DP NP δu1 the same verification info state different computation existential closure of the object distributes over the subject argument ( r, t , t ) Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 11 / 49 (10) [u1|#(u1) = 2 ∧ boys{u1} ∧ [u2|δu1 ([#(u2) = 3 ∧ books{u2} ∧ buy{u1, u2}])]] distributivity percolates through the semantic computation the same truth conditions but: 1 determiner each: distributivity in-situ with predicative meaning of the subject ( r, t ) 2 binominal each: distributivity over u1 at a distance, with referential meaning of the subject (type r ) predicted difference: local vs. distance distributivity Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 12 / 49 Main data puzzle pseudoCzech: binominal each and collective numerals (11) a. Each from twosome athletes won three medals. coll+distr ok b. *Twosome from athletes won each three medals. col+bin-each (12) Two from athletes won three medals each. num+bin ok Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 13 / 49 Collectives predicates like gather, be a good team, be a group (of NP) usually enforce collective reading (13) The group of two authors wrote three books. a. *distributive: 2-6 b. *cumulative: 2-3 c. collective: 2(together)-3 usually collectives and distributivity markers clash: (14) *The group of two authors wrote three books each. Dowty (1987), Brisson (2003), Winter (2002), Dočekal (2012) Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 14 / 49 Collectives collective Czech numerals like dvojice ‘twosome’ (parallel data in other Slavic langauges: Polish, Russian, . . . ) enforce the collective reading (15) a. Dva two sportovci athletes vyhráli won.pl 2 2 medaile, medals první first zlato gold a & stříbro, silver druhý second stříbro silver a & bronz. bronze ‘Two athletes won 2 medals, the first one G & S, the second one S & B.’ b. Dvojice sportovců vyhrála 2 medaile, # první zlato a stříbro, druhý stříbro. . . Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 15 / 49 Basic properties of Czech binominal each I For seminal discussion (of English binominal each), see Safir and Stowell (1988), recently Dotlačil (2012), Zimmermann (2002), a.o. Both pre- and post-position wrt share NP (jednu čepici) possible: (16) Chlapci boys.nom.pl si refl koupili bought.pl každý each.nom.sg jednu one čepici. cap.acc ‘The boys bought each one cap.’ (17) Chlapci boys.nom.pl si refl koupili bought.pl jednu one čepici cap.acc každý. each.nom.sg ‘The boys bought one cap each.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 16 / 49 Underlying structure of Czech binominal each I Idea: Czech binominal each contains a covert singular definite description referring back to / bound by a plural antecedent. Example with discourse anaphora: (18) Přišli came nějací some mužii . men.pl Každý each / Jeden one ( ten the muži ) man.sg měl had.sg zbraň. weapon ‘Some men came. (Each) one of them (lit. each/one the man) had a weapon.’ Hypothesized structure of binominal each, where is obligatorily deleted under (partial) identity with its antecedent; cf. Sauerland (1998), Fox (2003), Johnson (2012), a.o., for a similar treatment of traces Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 17 / 49 (19) Ti the mužii men.pl měli had.pl každý each < ten the muži > man.sg jednu zbraň. ‘The men had one weapon each.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 18 / 49 Proposed constituent structure S DP key the men.nom.pli VP V had.pl DP Det each.nom.sg DP DP share one weapon.acc Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 19 / 49 Argument: Movement Binominal each vs. floating all: Binominal each forms a constituent together with the share. (20) [ Každý each.sg.masc /* Všichni all.pl.masc 3 3 medaile] medals jsme be.1pl vyhráli won.pl jen only my. we (Intended:) ‘We were the only ones to win three medals each.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 20 / 49 Each can “float” in both cases, even in a position that apparently points to a binominal each. Note two differences though: NP (being obligatorily plural) triggers plural verb agreement vs. PP antecedent does not trigger agreement → agreement with the postverbal sg každý. (21) [NP Ti the chlapci] boys.nom.pl vyhráli won.pl { každý} each.nom jednu one cenu prize.acc { každý}. each.nom ‘The boys won one prize each.’ (22) [PP Z from těch the chlapců] boys.gen.pl vyhrál won.sg { každý} each.nom jednu one cenu prize.acc { každý}. each.nom ‘Each of the boys won one prize.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 21 / 49 Two arguments that PP antecedents cannot antecede binominal each, despite the initial appearance: Agreement with the each-phrase rather than with the antecedent (see above). No constituent: (23) *[ Každý each.nom jednu one cenu] prize.acc vyhrál(i) won.sg(pl) jenom only [PP z from těch the chlapců]. boys.gen.pl Intended: Only the boys were such that each of them won one prize.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 22 / 49 NP ellipsis of the each-restrictor not obligatory: (24) [PP Z from těch the chlapců] boys.gen.pl vyhrál won.sg [NP každý each chlapec] boy.nom.sg jednu one cenu. prize.acc ‘From the (group of) boys, each boy won one prize.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 23 / 49 Repeating the pattern pseudoCzech: binominal each and collective numerals (25) a. Each from twosome athletes won three medals. coll+distr ok b. *Twosome from athletes won each three medals. col+bin-each (26) Two from athletes won three medals each. num+bin ok Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 24 / 49 The collective sentence (27) Dvojice twosome sportovců athletes.gen vyhrála won.sg.fem 3 3 medaile. medals. *distributive S DP1 ECu1 two-ice athletes VP1 V won DP2 ECu2 3 medals Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 25 / 49 (28) a. S = [u1, u2|#(u1) = 2 ∧ athletes{u1} ∧ #(u2) = 3 ∧ medals{u2} ∧ win{ u1, u2}] b. DP1 = λQrt.[u1|#(u1) = 2 ∧ athletes{u1}] ∧ Q( u1) c. VP1 = λvr [u2|#(u2) = 2 ∧ medals{u2} ∧ win{v, u2}] d. DP2 = λQrt.[u2|#(u2) = 3 ∧ medals{u2}] ∧ Q(u2) our addition to PCDRT: treatment of numeral collectives as imposing the collectivity on its argument technically (28-b) Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 26 / 49 (29) [u1, u2|#(u1) = 2 ∧ athletes{u1} ∧ #(u2) = 3 ∧ medals{u2} ∧ win{ u1, u2}] one verifying info state: collective on the subject all the athletes won together the three medals (technically win{ u1, u2}) Info state J u1 u2 j1 athlete1 medal1 j2 athlete2 medal2 j3 athlete1 medal3 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 27 / 49 The determiner distributive sentence (30) Každý each z of dvojice twosome.gen sportovců athletes.gen vyhrál won.sg.masc 3 3 medaile. medals distributive Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 28 / 49 verifying info state: Info state J u1 u2 j1 athlete1 medal1 j2 athlete1 medal2 j3 athlete1 medal3 j4 athlete2 medal4 j5 athlete2 medal5 j6 athlete2 medal6 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 29 / 49 needed ingredients: (31) a. det-každýun = λPrtλQrt.δun (P(un)) ∧ Q(un) b. z ‘from/of’ predicates of groups → predicates of their parts – λPrtλvr .[|v ⊆ P] c. predicative meaning of CN: λwr [|#(w) = 2 ∧ athletes{ w}] d. whole subject: λQrt.[v|δv ([|λvr .[v ⊆ λwr [|#(w) = 2 ∧ athletes{ w}]]]) ∧ Q(v) determiner each quantifies over parts (partitioning z ‘from’) of the group denotation predicative meaning results in: (32) [v, u2|athlete{v} ∧ δv ([|λvr .[v ⊆ λwr [|#(w) = 2∧athletes{ w}]]])∧#(u2) = 3∧medals{u2}∧win{v, u2}])] Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 30 / 49 The cardinal numerals plus binominal each sentence (33) Dva two sportovci athletes vyhráli won.pl.masc každý each.sg.masc 3 3 medaile. medals distributive Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 31 / 49 the same info state as for (30) Info state J u1 u2 j1 athlete1 medal1 j2 athlete1 medal2 j3 athlete1 medal3 j4 athlete2 medal4 j5 athlete2 medal5 j6 athlete2 medal6 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 32 / 49 S DP1 key.pl VP1 V won.pl DP2 Det each.sg NP3 u1 the athlete.sg NP2 share Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 33 / 49 Clash of CN with binominal each (34) *Z dvojice twosome sportovců athletes.gen vyhrál won.sg.masc každý each.sg.masc 3 3 medaile. medals star for the binominal each can be floated each but not the binominal each the problem is that the percolated distributivity cannot be applied to the subject’s argument meaning plus argument subject imposes collectivity ↔ clash: (35) a. DP1 of (34) = λQrt.[u1|#(u1) = 2 ∧ athletes{u1}] ∧ Q( u1) b. VP1 of (34) = λvr [u2|δu1 ([#(u2) = 3 ∧ medals{u2}]) ∧ win{v, u2}] Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 34 / 49 Thanks! Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 35 / 49 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 36 / 49 Appendix Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 37 / 49 Derived collective numerals Czech: group nouns/numerals derived from cardinal numerals with the suffix -ice: tr-oj-ice námořníků properties: 1 both singular and plural: s troj-icíINST.SG námořníků, s troj-ice-miINST.PL námořníků 2 incompatible with the singular universal quantifier všechno ‘all’: *všechna troj-ice námořníků (not mass) 3 obligatorily non-cumulative: troj-ice + troj-ice = 2 troj-ice 4 obligatorily non-divisive: parts of troj-ice are not troj-ice Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 38 / 49 5 can be counted with cardinal numerals: dvě troj-ice námořníků 6 usualy enforce the collective interpretation: Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 39 / 49 Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 40 / 49 Bare (non-determined) share NP not allowed; cf. VP-related each (36-c): (36) ??Chlapci boys.nom.pl si refl koupili bought.pl každý each.nom.sg čepici. cap.acc Intended: ‘The boys bought each one cap.’ (37) ??Chlapci boys.nom.pl si refl koupili bought.pl čepici cap.acc každý. each.nom.sg Intended: ‘The boys bought one cap each.’ (38) Chlapci boys.nom.pl si refl každý each.nom.sg koupili bought.pl čepici. cap.acc ‘The boys each bought a cap.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 41 / 49 Clause-mate restriction (39) *Chlapci boys.pl říkali, said že that Marie Marie koupila bought každý each.sg.m jednu one čepici. cap.acc Intended: ‘Each of the boys said that Mary bought one cap.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 42 / 49 Key can be any argument, not just subject. (40) Marie Marie přinesla brought chlapcům boys.dat.pl každému each.dat.sg jednu one čepici. cap.acc ‘Marie bought each of the boys one cap.’ (41) Marie Marie přinesla brought ty the čepice caps.acc.pl každou each.acc.sg jednomu one chlapci. boy.dat ‘Marie brought each of caps to one boy.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 43 / 49 Share can be nominative (subject?) (42) Těm the chlapcům boys.dat.pl se refl líbila liked každému each.dat.sg jedna one dívka. girl.nom ‘The boys liked one girl each.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 44 / 49 Possibility to combine binominal each with distributive po: (43) Ty the slepice hens.nom.pl snesly layed po po třech three vajíčkách. eggs.loc ‘The hens layed three eggs each.’ (44) Ty the slepice hens.nom.pl snesly layed každá each.nom tři three vajíčka. eggs.acc ‘The hens layed three eggs each.’ (45) Ty the slepice hens.nom.pl snesly layed každá each.nom.sg po po třech three vajíčkách. eggs.loc ‘The hens layed three eggs each.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 45 / 49 Comparison with prepositional restrictors The following two have identical truth-conditions in Czech → the singular nominative NP ten chlapec can have the same use as a prepositional PP containing a (partitive?) plural genitive těch chlapců. (46) Každý each.nom [NP ten the chlapec] boy.nom.sg vyhrál won.sg jednu one cenu. prize.acc ‘Each of the boys won one prize.’ (47) Každý each.nom [PP z from těch the chlapců] boys.gen.pl vyhrál won.sg jednu one cenu. prize.acc ‘Each of the boys won one prize.’ Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 46 / 49 každý v vs. každý z the distinction seems to be between non-distinguishing každý z vs. plurality non-accepting každý v partially based on ČNK: case distinction: LOC vs. GEN (48) Každý z a. pronouns: nich, nás, . . . b. plural count: manželů, partnerů, účastníků c. -ice: trojice d. numerals (indefinite?): pěti, . . . e. collective nouns: týmu, rodiny Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 47 / 49 (49) Každý v a. collective nouns: týmu, říši, rodině, nemocnici b. entity denoting: Praze, ČR, c. *plural count: # každý v účastnících, #každý v manželích, . . . d. *pronouns: # [každý v nich], . . . e. *numerals: # [každý v pěti], . . . f. -ice: každý ve dvojici (dostane do ruky . . . ) Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 48 / 49 References Brasoveanu, Adrian. 2008. “Donkey Pluralities: Plural Information States Versus Non-Atomic Individuals.” Linguistics and Philosophy 31 (2). 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Johnson, Kyle. 2012. “Towards Deriving Differences in How Wh-Movement and QR Are Pronounced.” Lingua 122 (6): 529–53. https://doi.org/10.1016/j.lingua.2010.11.010. Safir, Ken, and Tim Stowell. 1988. “Binominal Each.” In Proceedings of Nels, 18:426–50. Sauerland, Uli. 1998. “The Meaning of Chains.” PhD thesis, Cambridge, MA: MIT. Winter, Yoad. 2002. Flexibility Principles in Boolean Semantics: The Interpretation of Coordination, Plurality, and Scope in Natural Language. Vol. 37. MIT press. Zimmermann, Malte. 2002. Boys Buying Two Sausages Each: On the Syntax and Semantics of Distance-Distributivity. Netherlands Graduate School of Linguistics. Mojmír Dočekal & Radek Šimík Czech binominal each and collective set predicatesSinFonIJA 11, 13-10-2018 49 / 49