Don't scope your universal quantifier over negation! Mojmír Dočekal & Hana Strachoňová Masaryk university, CZ FASL 22 May 4, 2013 Problem • Two logical operators in one natural language sentence usually lead to an ambiguity. (1) John hasn't seen two Jarmusch movies. 2 > -i / -i > 2 • But negation and universal quantifier (all) differ: observed by Jackendoff (1972), Buring 1997, Kadmon 2001. (2) John hasn't seen all Jarmusch movies, -i > V/ ???V > -■ 2/24 Corpus research • SYN2010: representative corpus of contemporary Czech • cca 1000 negated sentences with universal quantifier (lemma všechen) 9 three factors: linearization, bare/modified status of NP, interpretation • 2 linearizations: (1) subject (V) neg-V (-.) (2) neg-V (-.) subject (V) Int. 1: V > -i Int. 1: V > -i Int. 2: -. > V Int. 2: -. > V Lin. Bare NP Modified NP Bare NP Modified NP S neg-V Type 1: 22% Type 2: 87% Type 5: 78% Type 6: 13% neg-V S Type 3: 0 Type 4: 100 % Type 7: 100% Type 8: 0 Examples from Corpus 9 Type 5: bare NP, lin. všichni neg-V, interpretation -i > V (3) Všichni pacienti si ale protilátky nevytvářejí. All patiens REFL though antidotes not-create 'All patiens don't create antidotes though.' • Type 2: mod. NP, lin. všichni neg-V, interpretation V > -i (4) Všichni ti muži nesouhlasili se Šengovou politikou -All the men not-agree with Seng's policy někteří otevřeně, jiní opatrně, some openly others cautiosly 'All the men din't agree with Seng's policy - some of them openly, the others cautiously. 4/24 Examples from Corpus • Type 7: bare NP, lin. neg-V všichni, interpretation -i > V (5) Zatím tu ještě nejsou všichni, ale zbývající hosti so_far here yet not-are all but other guests jistě dorazí co nevidět, certainly arrive-they soon 'All are not here yet but the other guests will certainly arrive soon.' • Type 4: mod. NP, lin. neg-V všichni, interpretation V > -i ) A mě před nimi nedokáží uchránit ani všechny And me before them cannot save not all špatné anglické zákony dohromady, bad English laws together 'And all the bad English laws together cannot save me from them.' 5/24 • the linearization (information structure) isn't the decisive factor: both S neg-V and neg-V S linear order show nearly the same percentage of relative scope 9 the correlation is between the interpretation and bare / modified status of NP Figure 5: interpretation of modified NPs Figure 2: interpretation of bare NPs Contributions • Hypothesis: despite Type 1, Type 2 and Type 4 we claim that the relative scope of V and -i is always fixed: (7) Universal quantifier (of the all type) in natural language is always interpreted under the scope of negation (-i > V). • This holds irrespectively of the information structure (contra proposals of Jackendoff 1972, Buring 1997, Kadmon 2001). 9 Ingredients: (1) competition in grammar (2) illusion of scope • The scope V > -i is never realized by všechno ... r?e-V, as there is more economical way to materialize that meaning -by the negative word žádný (no). Generally it's a result of th competition in the grammar: see Horn (1989), Hoeksema (1998), Percus (2006), Reinhart (2006). (8) Všichni pacienti si ale protilátky nevytvářejí. All patiens REFL though antidotes not-create 'All patiens don't create antidotes though.' a. *Vx[paŕ/er?ŕ(x) —>> ^create-antidotes(x)] b. -Nx[patient(x) —± create_antidotes(x)] (9) Žádní pacienti si ale protilátky nevytvářejí. No patiens REFL though antidotes not-create 'No patiens don't create antidotes though.' a. \/x[patient(x) ^create_antidotes(x)] b. *-Nx[patient(x) —)► create_antidotes(x)] Two big problems • formalization: Horn scales for negated verb n-words and universal NPs form a scale and asserting the logically weaker implicates negation of the logically stronger (1) universal NPs, negative words Two problems (1) Type 1 (22% out of 100%): bare NP linearized S neg-V and interpreted V > -i (2) Type 2 (87% out of 100%): modified NP linearized S neg-V with the interpretation V > -i Problem one • 22 % of sentences with bare NPs interpreted with V > -i scope (Type 1) • half of the sentences contain verbs which are negated only apparently, so universal NPs and n-words are not on the Horn scale (the problem of relevance) (10) pokračoval tak tichounce, že všichni ani continuecLhe so quietly that all not_even nedutali whisperecLthey 'He continued so quietly that all of them keep silent.' (11) Všechny dominantní ženy nesnáší ostatní all dominant women neg-stand other dominantní ženy dominant women 'All dominant women hate all other dominant women.' 10/24 Problem one • in other cases the subject isn't directly competing with n-words (partitive? nikdo z nás 'nobody from us') 2) "Ale všichni/*nikdo se přece mýlit but all/*no_one REFL surely mislead-to nemůžeme." "Samozřejmě že můžete." cannot-we oLcourse that can-you-pl" 'But we all cannot be mislead.' 'Of course you all can. Problem two • the generalization holds only as far, as the universal quantifier and n-words really compete • but they are not exchangeable salva veritate in all contexts (13) specific collective/distributive n-words * / vsechno 'all' / / 12/24 Problem two • n-word are extremely unspecific in Czech, they cannot combine with specificity markers as certain - see (14) vs. (15) (14) *Žádný jistý námořník nepřišel. no certain sailor not-came 'No certain sailor came.' (15) Všichni jistí námořníci nepřišli, all certain sailors not-came 'All certain sailors didn't come.' 13/24 Problem two • All examples of Type 2 are marked as specific (Všichni ti muži 'all the men'), so žádný isn't concurrent for them: the specific NPs express the meaning unavailable for the Czech n-words. • That still doesn't explain why the specific Type 2 is interpreted with the scope V > -i, the 50%/50% interpretation would be expected 14/24 Proposal It's an illusion of scope which comes from the homogeneity presupposition illustrated in (16) from Lobner (2000): (16) The cow is not black. 9 (16) in isolation is interpreted only as conveying that the cow is all not black 15/24 Presupposition of homogeneity • other examples of the homogeneity presupposition (from Beck 2001): (17) The women don't know the men. a. Vx[x G WOMEN Vy[y G MEN ^KNOW{x, y)]] b. *^Vx[x G WOMEN Vy[y G MEN KNOW(x,y)]] » even in cases where the negation is uncontroversially scoping over the universal quantifier: (18) It's not the case that the children are asleep. a. Vx[x G CHILDREN ^SLEEP{x)]] b. *^Vx[x G CHILDREN SLEEP(x)]] < □ ► < if? ► < ► < -z ► -E -0 0,0 16/24 usion of Scope • Beck's (2001) formulation of the homogeneity presupposition is in (19). (19) *P(A) = a. 1 iff Vx[x e A -> P(x)] and b. 0 iffVx[xe>\-^-iP(x)] Figure: Presupposition of homogeneity aubuc a b c Figure 8: Presuppositon homogeneity □ S1 usion of Scope 9 Structurally the negation still scopes over V. 9 But due to the homogeneity presupposition we have an illusion of the opposite scope. <* But the presupposition can be explicitly canceled (from Loebner 2000): (20) The cow is not black, it's black and white. • This is also explanation of the 13 % of modified NPs interpreted with the -i > V - Type 6 . (21) Úplně všechno se neztratilo. Všechno ne. totally all REFL neg-lost_it. All not. 'Totally all wasn't lost. All not.' Predictions • V > -i interpretation of vsechno ... neg-V arises only for specific NPs. This supports Kadmon's (1990, 2001) analysis of definite NPs as requiring both maximality (from the semantics of all) and familiarity. • ingredients both from the Russell/Sharvy and Heim's frameworks (scenario with Leif having 10 indistinguishable chairs): (22) a. Leif has a chair. It's not so comfortable, though. b. Leif has four chairs. They are not so comfortable, though. 19/24 Predictions • Examples of the familiarity marking strategies (the most common types of modification in Type 2): (1) demonstrative: (23) Všechny ty škody nemohly mít jiný účel ... The purpose of all the damages was nothing else . .. (2) relative clause: (24) Pokud ovšem všechno, co jste prohlásila, není lež. 'If all, what you told us, isn't a lie.' 20/24 Predictions 2 9 Conjunction a 'and' in Czech act similarly to všechno 'all', as V and A are logically equivalent, see also Szabolcsi & Haddican (2004). • Consequently the conjunction of two specific NPs has the reading: A > -i but the conjunction of two indefinite NPs has both readings A > -i and -i > A 5) Petr nepřečetl Temno a Babičku. Petr neg-read Darkness and Grandmother 'Petr didn't read The Darkness and The Grandmother.' a. -ip A -iqr b. *^(p A q) = -ip V -iqr 21/24 Predictions 2 Petr nepřečetl dvě knížky od Jiráska a tři knížky Petr neg-read two books by Jirásek and three books od Němcové, by Němcová 'Petr didn't read two books by Jirásek and three books by Němcová.' a. -ip A -iqr b. -i(p Aq) = ^pV^q 22/24 Predictions 3 9 Information structure isn't the decisive factor. • According to Jackendoff (1972) (27) has only the V > neg due to the informational structure (focused element has the widest scope). • This cannot be right, as the corpus data show, the real factor is specificity, see also Kadmon (2001) and Kadmon & Roberts (1986), Kučerová (2012). (27) [AII]F the men didn't go. a. V> - b. -. > V 23/24 References Beck, S. 2001. Reciprocals are definites. Natural language semantics 9: 69-138. BLiring, D. 1997. The great scope inversion conspiracy. Linguistics and Philosophy 20: 175-194. Chomsky, N. 1995. The Minimalist Program. Cambridge, MA: MIT Press. Horn, L. 1989. A natural history of negation. Chicago: University of Chicago Press. Jackendoff, R. 1972. Semantic interpretation in generative grammar. Cambridge, Ma: MIT Press. Kadmon, N. 1990. Uniqueness. Linguistics and Philosophy 13: 273-324. Kadmon, N. 2001. Formal pragmatics. Blackwell. Kadmon, N.&C. Roberts. 1986. Prosody and scope: the role of the discourse structure. In CLS 22, Papers from the Parasession on Pragmatics and Grammatical Theory. Chicago: University of Chicago Press. Kučerová, I. 2012. Grammatical marking of givenness. Natural language semantics 20 (l):l-30. Lobner, S. 2000. Polarity in natural language: predication, quantification and negation in particular and characterizing sentences. Linguistics and Philosophy 23: 213-308. Percus, O. 2006. Anti-presuppositions. In Theoretical and empirical studies of reference and anaphora, ed. A. Ueyamada, 52-73. Japan Soc. for the Promotion of Science. Reinhart, T. 2006. Interface strategies. Optimal and costly computations. Cambridge, MA: MIT Press. Szabolcsi, A & B. Haddican. 2004. Conjunction meets negation. Journal of Semantics 21: 219-249. 24/24