Towards a Multidominant Theory of Movement Lecture One: Introduction Kyle Johnson University College London University of Massachusetts at Amherst 20 June 2016

Movement has been used to model a variety of syntactic relations that, frankly, A. Diference in Semantic Displacement ofentimes look quite diferent. Here are some examples. a. Total Reconstruction: (1) a. ...að Mary kaupir ekki skó? (Icelandic) Mary kaupir ekki skó. ≡ ¬ Mary kaupir skó ...that Mary buys not shoes Head Movement b. Variable Binding: ! Which book Mary had read ≡ b. I asked which book Mary had read AMovement Tesetofpropositionssuchthat∃x Mary had read x, x a book. ! A guard stands before every bank ≡ c. A child seems to have lef.AMovement∀ ! x if x is a bank then a guard stands before x d. every bank adiferent guard stood before every bank. An argument that the semantic relationship between a moved verb and its under- ! lying position is diferent than a moved phrase and its underlying position can Quantifer Raising be made from their diferent behavior in ellipsis contexts. VP Ellipsis can leave behind an object DP or a verb in contexts where that DP or verb has moved out Why are we tempted to see each of these cases as special instances of the same of the VP. In English this is possible with a DP, in what goes by the name “pseu- relation? Perhaps because they (sort of) share these three properties. dogapping.” emantic isplacement (2)S D (5)Iknowwhatkindofriceshewilleatbutnotwhatkindofstarch she should. Some part of the meaning of the moved expression is applied to aposition diferent from where it is spoken. Te position vacated by the moved object must be semantically equivalent to the (3)Terseness matching position in the antecedent VP for the ellipsis to be licensed. Tat posi- Temoveditemsemanticallyoccupiestwopositions,butisspoken in only tion must be occupied by a variable. one of them. (6)Whatkindofrice she will [VP eat x ]butnot ! (4)Locality what kind of starch she should [VP eat x ] Tetwopositionsthatamoveditemisrelatedtoaresubjecttoalocality ! condition. Because [VP eat x]and[VP eat x]aresemanticallyequivalentforthepurposesof Tese properties don’t manifest themselves in exactly the same way across these ellipsis resolution, VPE is possible. Tesameisnotthecase,however, for (some) various kinds of movement, though, and so that’s a challenge to seeing these as situations in which a verb has moved out of a VP that elides. SeeGoldberg(2005). shared properties. Tefollowingareherexamples,inspiredbyDoron(1999). Kyle Johnson Towards a Multidominant Theory of Movement 20 June 2016

(7)Q:Ha’imMiryam hevi’a et Dvora la-xanut? C. Diferences in how Terseness is violated Q Miryam bring ACC Dvora to.the-store (9) ng¯On¯U `n w`a n¯a `n kaIJ ng´OnUIJ IJa (Vata) ‘Did Miryam bring-past Gvora to the store?’ sleep you want NA you FUT-A sleep Q Ai: Ken, hi hevi’a. ‘Do you want to sleep?’ yes, she bring-past (Koopman 1984,(2a): 154) ‘Yes, she brought.’ Aii: * Ken, hi lakxa. Here “ngOnU” (‘sleep’) has been clefed and is pronounced in both the clef po- yes, she take-past sition and the position inside its VP. Tis is probably movement since locality ‘Yes, she took.’ conditions are satisfed. Tis is derived if the movement in these cases doesn’t leave a variable, but is in- (10)*t¯ak¯a `n w`a f`otIJo` m¯UmU`IJ `n takIJ aIJ áIJO `ab`a stead, semantically vacuous. show you like picture ITIT you showed REL Aba ‘It’s show that you like the picture you showed Aba.’ (8)Q:Ha’imMiryamhevi’a[VP hevi’a Dvora la-xanut ] ! (Koopman 1984,(15): 159)

A: Ken, hi lakxa [VP lakxa Dvora la-xanut] When a verb clefs in Vata, both copies must be pronounced. (9)isungrammati- ! cal if either verb isn’t pronounced. When nominal material clefs, by contrast, only the higher copy may be pronounced. (11)illustrates. Because the VPs in these examples aren’t semantically equivalent, VPE isn’t al- lowed. (But see Hartman (2011)forevidencethatsuggeststhatverb movement (11) ng´On´Ul`i m´i `n w`a `a does leave variables.) sleep-NOM IT you want Q ‘Is it sleeping you want?’ (Koopman 1984,(2b): 154) B. Diferences in Locality a. Head Movement Constraint: What we have in these examples is a kind of Amovementofaverb.Whenverbs, or predicates, move, we sometimes get violations of Terseness that involve two *HaveMaryshould read a book. ! pronunciations of the moved predicate, and that’s what Vata illustrates. b. Ross’s Islands Idon’tknowofanythingsimilar,though,whenaDPhasAmoved.Inthose cases, violations of Terseness take a diferent shape. Tey produce resumptive Which book has Mary shown [CP would change your life]? ! pronouns. For instance, in Lebanese Arabic there are resumptive pronouns that show Semantic Displacement efects when islands aren’t violated. (See Sichel *WhichbookhasMaryshown[DP the proof [CP that would change ! forthcoming and references therein.) your life]]? c. Tensed S Condition *Achildseems[CP (that) has lef]. !

* every bank adiferent guard showed [CP that the road stood before every bank]. !

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(12)t@lmiiz-a lk@sleen ma baddna nXabbi [wala mQallme] P@nno (15)Wenglaubst du, dass sie getrofen hat und dass sie liebt? student-her the-bad NEG want.1P tell.1P [no teacher] that who think you that she met has and that she loves huwwe zaQbar b-l-faès ‘Who do you think that she met and that she loves?’ he cheated.3SM in-the-exam˙ (Felser 2004,(37a): 560) ‘her bad student, we don’t want to tell any teacher that he cheatedon By contrast, a parallel across-the-board movement but with the wh-phrase pro- the exam.’ nounced in the lower positions as well – (16)isanexample–seems to assume (13)*t@lmiiz-a lk@sleen ma badkun tXabbro [wala mQallme] Qan that the answer will provide the identity of individuals thatmeetthedescriptions student-her the-bad NEG want.2P tell.2P [no teacher] about provided in each of the clauses separately. l-b@nt yalli huwwe zaQbar maQ-a b-l-faès the-girl that he cheated.3sm with-her in-the-exam˙ (16)Wenglaubst du, wen sie getrofen hat und wen sie liebt? (Her bad student, you don’t want to tell any teacher about the girlwith who think you who she met has and who she loves whom he cheated on the exam.) ‘Who do you think that she met and that she loves?’ (Felser 2004,(37b): 560) (Aoun, Choueiri, and Hornstein 2001,(25b) & (29b): 381–2) T I think, then, that there is a diference in how Terseness is violated depending on is diference in meaning suggests that there is a separate quantifcation, one for each of the lower wh phrases, in the copy construction that is absent in the the category of the thing being moved. Tere is a potential problem for this be- non-copy construction version. If that is correct, it will require that the copy con- lief in the wh-copying construction that colloquial German (and other languages) display. struction include more quantifcational expressions than are found in the simpler, single pronunciation, movement structure. (See Dayal 1994.) (14)German I’ll assume that there is a diference between moved DPs and moved other a. Wen glaubt John wen Mary getrofen hat? things that is responsible for how Terseness is relaxed in them. who thinks John who Mary met has Whatwewant,then,isatheoryofmovementthatexplainsthesethreeproper- ‘Who does John think Mary has met?’ ties: Semantic Displacement, Terseness and Locality. But that theory should also be fexible enough that it gives us a handle on why these three properties manifest b. * Wieviel Geld meint sie wieviel Geld das kostet? themselves diferently depending on the particulars of the movement operation. how-much money thinks she how-much money that costs I’m going to take a few, very small, steps in that direction, building on an idea ‘How much does she think that costs?’ about what movement is that was in an early unpublished manuscript by Stan- (Rett 2006,(1b): 355,(6): 358) ley Peters and Robert Richie, carried forward by Engdahl (1980)andhasnow ä It’s hard to say in these situations whether the intermediatecopyisaresumptive found many proponents, including G rtner (1997), Starke (2001), Nunes (2001), T pronoun or a copy. But there are certain properties of the copyconstructionwhich Frampton (2004), Citko (2005), Kobele (2006)anddeVries(2007). at idea is suggest that it is diferent from a “normal” movement construction with just a sim- that movement gives an expression two positions by re-merging it. ple violation of Terseness. Tere are interesting semantic diferences between the (17) merge(α,β)=def. γ ,wherethelinearorderofα and β is two constructions. A striking one is described in Felser (2004). She notes that in not determined. ö cases where a phrase has moved in across-the-board fashion outoftwoco rdi- α β nated clauses, as in (15), the question seems to assume that the answer will provide individuals that meet the descriptions provided by both of the clauses.

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Aderivationthatinvolvesremerge: tions. Tat is going to be the focus of most of the seminar, I suspect, butwewon’t start that process until Wednesday. (18) (She asked) which book he knows. It’snotobviousthattheserepresentationsprovideanynew handle on the ques- tion why movement is subject to locality conditions. I’ve taken a very vague stab a. VP b. TP at trying to make that connection in a paper that was deliveredinthe2009 meet- ing of the Chicago Linguistics Society. Teideainthatpaperusesaconstraint V DP TVP on derivations that Chomsky proposed which, I think, he calledthe“extension condition.” knows which book V DP (19)ExtensionCondition merge knows which book ’s arguments must be root nodes. c. TP Te Extension Condition is one attempt at deriving the fact that moved items al- ways go “up” in a phrase marker. It would block the derivation in (18), and there DP TP is no way of getting to the representation at the end of that derivation without violating the Extension Condition. So if the Extension Condition is correct, then he T VP the closest we can come to (18)iswithsomethinglike(20). a. VP b. TP V DP (20) XP XP

V DP TVP knows which book X X d. CP e. CP knows which book V DP

C TP CP knows which book c. TP d. CP DP TP C TP XP XP

DP TP C TP he T VP DP TP X X

he T VP DP TP V DP he T VP

V DP he T VP knows which book V DP

knows which book V DP knows which book

You can s ee how (18e) provides a way of capturing Semantic Displacement. Te knows which book moved term — here which book — is syntactically in two positions and so its deno- tation has two positions where it can be applied. Tediferences in how Semantic Displacement arise are going to come about, I will claim, from the particular ways in which the expressions that are “moved” get broken up into two diferent posi-

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e. CP (22) (She asked) which book he knows. a. VP b. TP CP XP V DP TVP C TP X knows which book V DP DP TP knows which book he T VP c. TP d. CP

V DP DP TP C TP

knows which book he T VP DP TP We might imagine that (20e) is close enough to (18e) that we canmakebasically the same theories around them. Of course, we should identify “X.” V DP he T VP Te frst step in (20)iswhatCitko(2005)calls“parallelmerge.”For it to arise without a violation of the Extension Condition, we’d have to understand Merge knows which book V DP to be able to apply at the same time to two pairs of root nodes. Soderivations would have to be understood not as sequences of single applications of Merge, knows which book ′ but as sequences of any number of applications of Merge. (Make me do this on e. CP DP the board.) ′ ′ Suppose islands are those phrases at which a phonological or semantic evalu- C TP which book ation must take place. Tis might be what “phases” are. If islands are phases that arise at the point in a derivation where there remain two roots, as in any but the last DP TP of the steps in (20), then arguably a semantic and phonological evaluation will not be possible, as our semantics and phonology are (perhaps) defned only for rep- he T VP resentations with a single root. Tis, at any rate, is one way of thinking about how to seek an answer to the question of why islands emerge uniquely with movement V DP on an account that uses multidominant representations. I’ll have nothing more to say about islands in these classes. I’ll focus on the remaining two properties: knows which book terseness and semantic displacement. We’ll start by tackling how multidominant representations derive Terseness. I’ll adapt a popular explanation for Terseness due to Jairo Nunes. Nunes worked with a (possibly) diferent account of movement: the “copy” theory of movement. Tis theory does not countenance multidominant representations, like that in (18e), but instead involves a “copy” operation. (21) copy(α)=α′, an exact syntactic and semantic replica of α. Tis gives us derivations like (22).

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f. CP merge CP

′ ′ DP CP DP CP

′ ′ ′ ′ which book C TP which story C TP ′ ′ about her DP TP should DP TP

he T VP none of T VP the women V DP V DP

knows which book forget which story Tis theory too is able to account for Semantic Displacement, and it does so in a about her way rather like that of the remerge account. So, for instance, it gives an account of Tere is a copy of her spoken in a place diferent from where it is (apparently) “reconstruction,” a special case of Semantic Displacement that (23)illustrates. interpreted. (23)Whichstoryabouthershouldnoneofthewomenforget? Tese representations allow Terseness to arise from an operation that “deletes” ′ one of the two phrases in the copy relation. What Terseness amounts to, then, is CP copy CP DP the observation that (with the exceptions noted) this deletion process is obliga-

′ ′ tory.I’llsketchthewaythisisdoneinNunes(2004,chapter1), which is a reworked C TP C TP which story ′ ′ version of his 1999 University of Connecticut dissertation, and an improved ver- about her sion of Nunes (1995), and then I’ll modify it so it works with multidominant should DP TP should DP TP phrase markers. Te leading idea is that a representation with undeleted copies will not be able to be linearized. none of T VP none of T VP To see this, we’ll need to spell out what those constraints areandwhatlin- the women the women earizations are. I will assume that syntactic representations are converted into V DP V DP phonological representations (PFs) by matching vocabulary items to terminals in the syntactic representations and linearizing those vocabulary items. I shall adopt forget which story forget which story the formalism, made popular by Kayne (1994), of expressing a linearization as a about her about her set of ordered pairs. A linearization results from an algorithm which evaluates a syntactic structure and computes from the information in that structure how each vocabulary item in the structure is ordered relative to every other vocabulary item in the structure. So, for instance, the structure in (24)wouldmapontotheordered pairs in (25).

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(24) TP He then builds a linearization algorithm that has a variety ofinterestingconse- quences for the shapes that phrase markers may have. DP TP Simplifying somewhat, Kayne’s procedure forms the ordered pairs in a lin- earization with (28)  Mary T VP (28) a < b is in the linearization if a,oraphrasecontaininga,c-commandsb.

V′ T V DP Tis has a number of interesting consequences for phrase markers, which is the focus of Kayne’s work. It also has two other consequences that are of interest to kaup′ ir kaup skó us: ⎧   ⎪ Mary < T T

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(32) TP is built into Kayne’s linearization scheme. We don’t need to choose among them, though, and it will be convenient (and harmless) to avoid engaging the details. In DP TP what follows, therefore, I will leave open how the choice fromthepossibilitiesal- lowed by the constraints to the one appropriate for English is made. I will call that this sentence T VP portion of the linearization procedure that makes the language particular choice, the “language particular component.” erseness V DP Nunes’s method of deriving T hinges on the proposal that Anti- symmetry, and the other constraints on a linearization, cannot distinguish a copy illustrates agreement from the thing it is copied from. Moreover, the way Nunes executes his idea re- lies on Kayne’s requirement that the linearization algorithm necessarily applies to (33) a. this sentence T illustrates agreement every vocabulary item in the structure being linearized. When these are coupled b. sentence this T illustrates agreement with the copy theory of movement, they will produce unlinearizable results. c. this sentence illustrates agreement T Consider, for instance, what the linearization procedure and the language par- d. sentence this illustrates agreement T ticular component will together produce for a phrase marker created by move- ment. e. this sentence T agreement illustrates f. this sentence agreement illustrates T (34) CP g. sentence this T agreement illustrates DP′ CP h. sentence this agreement illustrates T i. T illustrates agreement this sentence who′ C TP j. T illustrates agreement sentence this k. illustrates agreement T this sentence did DP TP l. illustrates agreement T sentence this m. T agreement illustrates this sentence she T VP n. T agreement illustrates sentence this V DP o. agreement illustrates T this sentence p. agreement illustrates T sentence this visit who T eill-formedlinearizationsin(33)are,manyofthem,wellformed in other lan- Telinearizationof(34)thatsatisfes the language particular component as well guages. For instance, (33f) corresponds roughly to how Germanwouldlinearize as Totality, Contiguity, and Transitivity is (35). this structure, and (33i) corresponds roughly to how Nuiean would. While not all of these outcomes are ones that we might want to permit cross-linguistically,1 I will nonetheless treat them all as language-particular possibilities. Testepfrom this range of linearizations to the one that is correct for English, then, engages that component of the theory which models word order variation. Tere are a variety of proposals in the literature on how to model word order variation. One of those

1 (33n,o) are vanishingly rare according to Dryer (1996).

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(35)=who′ did she visit who Tis is how Terseness is derived. T ′ < < < < < is method provides an interesting account for those examples of Head ⎪⎧ who did did she she TTvisit visit who ⎪⎫ ⎪ ′ ⎪ Movement where Terseness seems to be relaxed. For instance, Vata predicate clef ⎪ who < she did < Tshe< visit T < who ⎪ ⎪ ′ ⎪ constructions involve a structure like (38), in which the verbal root has moved ⎨ who < Tdid< visit she < who ⎬ ⎪ ′ ⎪ and joined with a functional head that encodes focus. ⎪ who < visit did < who ⎪ ⎪ ′ ⎪ ⎩⎪ who < who ⎭⎪ (38) l¯ı IJO d¯a sak´aIJ l¯ı Tis linearization has pairs like who′ < visit and visit < who in it, and under Nunes’s eat she/he perf rice eat proposal, these will be violations of Antisymmetry: who′ and who are indistin- ‘she/he has eaten rice.’ guishable for Antisymmetry, and these pairs amount to saying, then, that who (39) FocP both precedes and follows visit. To produce the correct outputs, Nunes’s deletion operation, which he calls Foc TP “chain reduction,” applies. l¯ı Foc DP TP (36)ChainReduction Delete α, α a syntactic constituent that has been put into the Copy rela- IJO T VP tion. Chain Reduction should be seen as an operation that is part of PF, the component d¯a DP V of the grammar that converts syntactic representations to phonological ones. We want Chain Reduction to remove material from the phonological representation sIJaká l¯ı of the sentence, but leave unafected how that material is semantically interpreted. ′ Because the result of clefing a verb in Vata makes it merely a part of the vocabu- In the case of (34), it could remove DP or DP and thereby produce representations  from which the linearization algorithm produces the stringsin(37). lary item that is Foc ,Antisymmetryisabletobesatisfed without invoking Chain Reduction. If constraints like Antisymmetry make referencetovocabularyitems, (37) a. = who did she visit and not the terminals from which those vocabulary items are composed, then ′ ⎪⎧ who

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(24) TP

DP TP

Mary T VP

V′ T V DP

kaup′ ir kaup skó   ⎪⎧ Mary < T T

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Hartman, Jeremy. 2011. Te semantic uniformity of traces: Evidence from ellipsis References parallelism. Linguistic Inquiry 42:367–388. Kayne, Richard S. 1994. Teantisymmetryofsyntax. Cambridge, Massachusetts: MIT Press. Aoun, Joseph, Lina Choueiri, and Norbert Hornstein. 2001.Resumption, move- Kobele, Gregory Michael. 2006.Generatingcopies:Aninvestigation into struc- ment, and derivational economy. Linguistic Inquiry 32:371–403. tural identity in language and grammar. Doctoral Dissertation, University of Citko, Barbara. 2005.Onthenatureofmerge:Externalmerge,internal merge, California, Los Angeles, Los Angeles, CA. and parallel merge. Linguistic Inquiry 36:475–496. Koopman, Hilda. 1984. Tesyntaxofverbs. Dordrecht, TeNetherlands:Foris Dayal, Veneeta Srivastav. 1994.Scopemarkingasindirectwh-dependency. Nat- Publications. ural Language Semantics 2:137–170. Nunes, Jairo. 1995. Tecopytheoryofmovementandlinearizationofchainsin Doron, Edit. 1999. V-movement and VP ellipsis. In Studies in ellipsis and gapping, the Minimalist Program. Doctoral Dissertation, UniversityofMaryland. ed. Shalom Lappin and Elabbas Benmamoun, 124–140. New York, New York: Nunes, Jairo. 2001.Sidewardmovement.Linguistic Inquiry 32:303–344. Oxford University Press. Nunes, Jairo. 2004. Linearization of chains and sideward movement. Linguistic Dryer, Matthew S. 1996.Wordordertypology.InHandbook on syntax, ed. J. Ja- Inquiry Monographs. Cambridge, Massachusetts: MIT Press. cobs, volume 2, 1050–1065.WalterdeGruyter. Engdahl, Elisabet. 1980. Te syntax and semantics of questions in Swedish. Doc- Rett, Jessica. 2006.Pronominalvs.determinerwh-words: evidence from the copy toral Dissertation, University of Massachusetts, Amherst, Massachusetts. construction. In Empirical issues in syntax and semantics 6,ed.OlivierBonami and P. Cabredo Hofherr, 355–374.CNRS. Felser, Claudia. 2004.Wh-copying,phases,andsuccessivecyclicity. Lingua 114:543–574. Sichel, Ivy. forthcoming. Resumptive pronouns and competition. Linguistic In- Frampton, John. 2004. Copies, traces, occurrences, and all that: Evidence from quiry . Bulgarian multiple wh-phenomena. Unpublished manuscript, Northeastern Starke, Michal. 2001.Movedissolvesintomerge:Atheoryoflocality. Doctoral University. Dissertation, University of Geneva. Gärtner, Hans-Martin. 1997.Generalizedtransformationsandbeyond. Doctoral de Vries, Mark. 2007.Internalandexternalremerge:Onmovement, multidom- Dissertation, University of Franfurt/Main. inance, and the linearization of syntactic objects. Unpublished manuscript, Goldberg, Lotus Madelyn. 2005. Verb-stranding VP ellipsis: A cross-linguistic University of Groningen. study. Doctoral Dissertation, McGill University, Montreal.

11 Towards a Multidominant Theory of Movement Lecture Two: Linearization and Terseness Kyle Johnson University College London University of Massachusetts at Amherst 21 June 2016

We lef last time looking at how Nunes derives Terseness. His method uses the of vocabulary items that satisfes Totality, Antisymmetry, Contiguity and the lan- linearization scheme in (1). guage particular setting. Consider how that will work in a case of wh-movement, whose parse, on our theory, will be (3). (1) a. If a and b are vocabulary items in P, then put either a < b or b < a in the linearization for P. (3) CP b. Totality All vocabulary items in the phrase marker p must be in the lineariza- CP XP tion of p. c. Antisymmetry C TP X For all vocabulary items, a and b in p,thelinearizationofp cannot include both a < b and b < a. Q DP TP d. Contiguity Let α be a word dominated by A and β be a word dominated by A’s she T VP sister. i. ∀α, β, α < β,or should V DP ii. ∀α, β, β < α. like D NP Tis, recall, is that portion of a linearization algorithm that is common to all lan- guages. Tis won’t produce a linearization for a particular sentence in a particular which N language. Instead, it will produce a set of linearizations foranyparticularsentence. Te language will pick from this set the one(s) that ftthelanguage particular set- paper tings for a linearization. To (1), Nunes adds (2). Because the wh-phrase has two positions, we can imagine that the way the ordered (2) a. If a and a′ are copies, then Antisymmetry and Totality cannot distin- pairs are collected up into a linearization permits two positions for the wh-phrase: guish them. the position in the string assigned by English to Specifer of CP and the position in the string assigned by English to complement of V. Let’s consider, then, the three b. Chain Reduction ′ linearizations that satisfy Totality in (4). If a and a are copies, then one of them can lef out of the linearization. (2a) follows from a multidominant theory of movement. So to the degree that Nunes’s program is successful, it can be read as evidence for multidominance. But this requires that we do away with Chain Reduction and change the linearization procedure. As a frst step, I suggest that we jettison Chain Reduction and (1a). (1a) is just Totality. Let’s let the linearization for a sentence be any set of ordered pairs a < b Kyle Johnson Towards a Multidominant Theory of Movement 21 June 2016

(4) a. which paper Q she should like ⎪⎧ which < paper paper < Q Q < she she < should should < like ⎫ ⎪ ⎪ ⎪ which < Q paper < she Q < should she < like ⎪ ⎪ ⎪ ⎨ which < she paper < should Q < like ⎬ ⎪ ⎪ ⎪ which < should paper < like ⎪ ⎪ ⎪ ⎩⎪ which < like ⎭⎪ b. Q she should like which paper ⎧ Q < she she < should should < like like < which which < paper ⎫ ⎪ ⎪ ⎪ Q < should she < like should < which like < paper ⎪ ⎪ ⎪ ⎨ Q < like she < which should < paper ⎬ ⎪ ⎪ ⎪ Q < which she < paper ⎪ ⎪ ⎪ ⎩⎪ Q < paper ⎭⎪ c. which paper Q she should like which paper ⎧ which < paper paper < Q Q < she she < should should < like like < which which < paper ⎫ ⎪ ⎪ ⎪ which < Q paper < she Q < should she < like should < which like < paper ⎪ ⎪ ⎪ ⎪ which < she paper < should Q < like she < which should < paper ⎪ ⎨ ⎬ which < should paper < like Q < which she < paper ⎪ ⎪ ⎪ which < like paper < which Q < paper ⎪ ⎪ ⎪ ⎩⎪ which < which paper < paper ⎭⎪ Of these, only (4b) satisfes all the constraints. (4c) is a violation of Terseness, and it’s clear how Antisymmetry blocks it. TelinearizationsthatobeyTotalityand Antisymmetry are (4a) and (4b), and these are the two that we want to make cross- linguistically available. Terseness emerges from a linearization of multidominant structures if we let the linearizations be any collection of ordered pairs that satisfy Totality and Antisymmetry. We don’t need a deletion rule likeChainReduction. TecorrectoutcomeinEnglish,ofcourse,is(4a) – so we must fnd awayof making Contiguity permit (4a) as well as (4b). But we don’t want to give Conti- guity up. Not only is it obeyed in parses that don’t have movement, it’s also mostly obeyed in parses that do have movement. For instance, we should block giving (3) the linearization in (5). (5)paperQsheshouldlikewhich ⎧ paper < Q Q < she she < should should < like like < which ⎫ ⎪ ⎪ ⎪ paper < she Q < should she < like should < which ⎪ ⎪ ⎪ ⎨ paper < should Q < like she < which ⎬ ⎪ ⎪ ⎪ paper < like Q < which ⎪ ⎪ ⎪ ⎩⎪ paper < which ⎭⎪

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Tis linearization satisfes Totality and Antisymmetry as well, but I don’t think we c. C(p) (“contiguous path”) is a path in which, for every P ∈ p that has should admit it into the class of possible linearizations. It violates Contiguity in a adaughterα ∉ p, the linearization contains orderings such that: way that (4a) doesn’t. It makes the phrase that is in two positions non-contiguous. i. ∀x, y ∶ x < y for x ∈ d(P) − d(α) and y ∈ d(α),or In general, we want Contiguity to weed out random linearizations. We want it to ii. ∀x, y ∶ y < x for x ∈ d(P) − d(α) and y ∈ d(α). preserve an image of the hierarchical structure of a sentence. Contiguity presently enforces a relationship between substrings and phrases. d. Totality It requires of a phrase A that dominates a phrase B that the words in B will be a For every X in P, Π(P) must contain a p(X). substring of the words in A. It says that you can recover the dominance relations e. Antisymmetry among the phrases of a sentence by looking at how strings are nested. I want to AlinearizationcannothavebothX < Y and Y < X. replace that idea with a very similar one. I want Contiguity to enforce a relation- f. Contiguity ship between “paths” and substrings. A path is not just one phrase that dominates Every p(X) in Π must be C(p(X)). some set of words, but a set of phrases that dominate that set ofwords.Whatour Te language particular component – the information that languages contribute new Contiguity will do is require that every word in a sentencebepartofapath tothelinearization–isinthechoicebetween (6c-i) and (6c-ii), and how the p(X) which is contiguous. A path is contiguous if all of the its members – that is all of is chosen for words that have more than one path. Tis system is defned for mul- the phrases in the set making up that path – are contiguous. Te way the strings tidominant trees that use the parallel merge derivation – notremerge. of a sentence are nested will now be an image of the paths in a sentence. Let’s run through how (6) works. We’ll start with a vanilla example with no Multidominant phrase markers will give to some item more thanonepath.In multidominance. those scenarios, Antisymmetry is violated if both paths are used in forming the linearization. Contiguity and Antisymmetry must together work to force all of (7) TP† the material in a phrase that has two paths to be linearized according to the same path. So the linearization procedure I will invoke is one thatallowsasentence’s DP† TP structure to be factored into a set of paths. Tose paths will be subject to Totality, Antisymmetry and Contiguity, and this will result in a set of possible lineariza- D† T VP tions. In multidominant phrase markers, there will be more than one choice of paths that will satisfy Totality, and this too will be a vectoralongwhichlanguages she should V DP can vary. So, here is the new defnition of Contiguity, along with its attendant defni- like D NP tions. I’ve also changed Totality, so it makes reference to paths. Te complexity of these defnitions is a result of my attempt to remove “dominance” from them. the N I want the relations that a linearization looks at be entirely defned in terms that refer to paths. fowers (6)LetP and P′ be phrases and X be a node that immediately dominates a TelargestΠ(7)is(8). word. Π(P) is a set of paths, p(X),formedfromXsinP. a. Let i(α)beanodethatimmediatelydominatesα.Apathfromα (8) a. p(D†) = {DP†, TP†} (=p(α))isthesetofnodes,β,suchthatβ=i(α)orβ=i(β). A path must b. p(T) = {TP, TP†} include the root node. c. p(V) = {VP, TP, TP†} b. d(P) is the set of Xs whose p(X) includes P. d(X) is X. d. p(D) = {DP, VP, TP, TP†} e. p(N) = {NP, DP, VP, TP, TP†}

3 Kyle Johnson Towards a Multidominant Theory of Movement 21 June 2016

From (8)wecancalculatethed relations. (I only look at the d of phrases, since only one position, and another in Vata, which resulted in the pronunciation of the the d of heads is trivial.) head in two positions. Today we are going to look at Hebrew, which has in one language both kinds of Head Movement. As we saw yesterday, Hebrew has verb (9) a. d(DP†) = {D†} movementtoT.Italsohasverbtopicalization,ratherlikeVata. See Landau (2006). b. d(TP†) = {D†, T, V, D, N} Tey combine to form a string in which the verb is pronounced in its topicalized c. d(TP) = {T, V, D, N} position and in the position it gets infected. d. d(VP) = {V, D, N } (11)liknot,hi kanta et ha-praxim. e. d(DP) = {D, N} to-buy, she bought ACC the-fowers f. d(NP) = {N} ‘As for buying, she bought the fowers.’ (Landau 2004,(8b): 37) And this allows us to evaluate Contiguity. Contiguity will besatisfed if the d of every element in every head’s path in Π provides a contiguous mapping onto the Note that the verb in topicalized position is pronounced as aninfnitive, and the linearization. For instance, suppose that the linearization of (7) is (the correct one verb in T position is pronounced with tense morphology. TeVposition which in) (10). holds the root is not pronounced. We can assume, as we did for Icelandic, that ⎧ D† < T T

4 Kyle Johnson Towards a Multidominant Theory of Movement 21 June 2016

TelargestΠ(12)is(13). (15) CP† (13) a. p(Top)={TopP} CP XP b. p(D†) = {DP†, TP†, TopP}  c. p(T )={TP, TP†, TopP} C TP† X d. p(D) = {DP, VP, TP, TP†, TopP} e. p(N) = {NP, DP, VP, TP, TP†, TopP} Q DP† TP

Note that there is no p(V), because V doesn’t immediately dominate a word. From D† T VP (13)wecancalculatethed mappings: (14) a. d(TP†) = {D†, T, D, N} she should V DP b. d(TP) = {T, D, N} like D NP c. d(VP) = {D, N} d. d(DP) = {D, N} which N e. d(NP) = {N} Notice, again, that V is not included. fower Because V is nowhere included, you can see that this is a tree that will get All the nodes dominating words in this sentence have just one path except for linearized in the same way it would if V were absent. Because it’s only V that is those in the DP which fower. TelargestΠ(15)is(16). in a multidominant relationship, this means that the linearization process won’t see the multidominance and things should run as if it weren’t there. Tat’s what (16) a. p(C) = {CP, CP†} we want, of course: that is Nunes’s idea about why these cases end up speaking b. p(D†) = {DP†, TP†, CP, CP†} the multidominated term in more than one position. Tis case, then, collapses to c. p(T) = {TP, TP† CP, CP†} (basically) the one in (7). TeonlylinearizationsthatsatisfyContiguity are also d. p(V) = {VP, TP, TP† CP, CP†} ones that satisfy Antisymmetry, and of those the Hebrew particular choice is (11) Now let’s consider an example of wh-movement. e. p(D) = {DP, VP, TP, TP† CP, CP†} f. p(D) = {DP, XP, CP†} g. p(N) = {NP, DP, VP, TP, TP† CP, CP†} h. p(N) = {NP, DP, XP, CP†} i. p(X) = {XP, CP†} Let’s consider frst a language, like English, which chooses XP

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(17) { T

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The path for D goes through XP and the path for N goes through VP (31)t@lmiiz-a lk@sleen ma baddna nXabbi [wala mQallme] P@nno student-her the-bad NEG want.1P tell.1P [no teacher] that Consider fnally:   huwwe zaQbar b-l-faès (26) a. p(C) = {CP, CP†} he cheated.3SM in-the-exam˙ b. p(D†) = {DP†, TP†, CP, CP†} ‘her bad student, we don’t want to tell any teacher that he cheatedon c. p(T) = {TP, TP† CP, CP†} the exam.’ d. p(V) = {VP, TP, TP† CP, CP†} (Aoun, Choueiri, and Hornstein 2001,(25b): 381) e. p(D) = {DP, XP, CP†} Tese kinds of examples show up in clefsandrelativeclauses.Iwillsketchaway f. p(N) = {NP, DP, VP, TP, TP† CP, CP†} ofcapturingthemthatassumesthattheyonlyhappenincases that have the syntax g. p(X) = {XP, CP†} of relative clauses. Te frstthingweneedtodoisunderstandwhatapronounis.Pronouns share Tis is the choice of paths necessary to get the kind of linearization in which the certain characteristics with defnite descriptions. For instance, their context of use pieces of the moved phrase are linearized in diferent positions; for instance: is, many times, similar. Tesentencesin(32)areoddinthecontext of this class (27)XwhichQsheshouldlikefower for the same reason. We want to block this possibility. (32) a. Tewomanisbored. Techoiceofpathsin(26)won’tbeabletojointlysatisfyAntisymmetry and b. She is bored. Totality. To see this, consider the following ds. I’m going to assume that there are bored women in my class by thetimeweget (28) a. d(XP) = {X, D} to this point in the handout, so these sentences should both betrue.Butthey’re b. d(CP) = {C, D†, T, V, N} not because the subjects do not refer properly, and this is because there is more c. d(DP) = {D, N} than one woman in my class (unless all but one of them have lef by now). Tis is modeled by making both the woman and it trigger the presupposition that there Consider how C can be satisfed by p(N). C will require VP (which is in p(N)) to is one unique female in the situation being described by the sentence. Tis pre- order V the same way with everything in d(DP). Tis puts in the linearization: supposition comes with the,sowe’llbuilditintothedenotationofthe. (29) { V

7 Kyle Johnson Towards a Multidominant Theory of Movement 21 June 2016

(34) bored(ιx woman(x) = )= (37) bored(ιx female(x) =  ∧ sing(x) = )= IP IP

ιx woman(x) =  λx bored(x)= ιx female(x) =  ∧ sing(x) =  λx bored(x)= DP TP DP TP

the woman T AP the fem sing T AP

is bored is bored !DP" and !IP" are defned just in case there is a unique x in the relevant !DP" and !IP" are defned just in case there is a unique x in the relevant situation which is a woman. situation which is female and singular. To capture the fact that pronouns are similar to defnite descriptions in these Bottom line: a pronoun can be the way a defnite description is pronounced when ways, we can give them a similar composition. Imagine, for instance, that a pro- the combines with ϕ features. noun is just the way English speaks defnite description whose NP part are the Now let’s consider the structure of a relative clause. relevant person, gender and number features. I’ll assume that “third person” is the absence of frst or second person. So the pronoun her on this view might look (38)apictureofherselfthatMaryisselling like (35). (See Elbourne 2005.) Notice that we get semantic displacement here, just as in the Arabic example. (35) DP Terefexive pronoun herself is being semantically interpreted in the position it moved from, not the position it is spoken. Tis shows us that the NP picture of herself has moved from the object position of selling.Supposethatisallthathas D NP moved, the NP that makes within the object of selling not the DP that makes the object of selling.Wepositastructurelike(39).1 the fem sing

Suppose that the denotations for fem and sing are sketched by (36). (Te actual de- notation for number is more complex. See Sauerland (2008)andKratzer (2009).) (36) a. !fem" = λx.x is female b. !sing" = λx.x is an atom Tis gives us (37)for(32b). (32b) She is bored.

1 See Schachter (1973), Vergnaud (1974), Kayne (1994)andBianchi(2000).

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(39) DP (41) DP

D XP D XP

a CP XP the/a CP XP

C TP X C TP X

that DP TP that DP TP

Mary T VP every woman T VP

is V DP is V DP

selling D NP selling D NP

the picture of herself the ϕ NP Our linearization scheme will force the NP in (39)tobelinearized in just one of sing picture of herself its positions, and this is what happens in English relative clauses. If this is the right structure for relatives, it means that English must have a silent defnite determiner Recall that pronouns are just the way that defnite descriptions are pronounced which is used in the lower position, because nothing is spokeninthatpositionin when their NP part just has ϕ features. TeNPthatisthecomplementtothe English. lower the in (41)consistsonlyofϕ features – at least in terms of its string infor- Consider now a language in which ϕ-features can be part of a DP that has an mation that is all that is inside it – and perhaps this allows it to be pronounced as overt NP. Tis would be a language, then, which allows DPs like (40). apronoun. (40) DP

D NP

the ϕ NP

sing fem woman

Wecanusepredicateconjunctiontoputthepartsofthedeterminer’s complement together. If DPs like this are available – and if DPs can Agree with ϕ features, then this seems plausible – we should expect languages that build relative clauses as in (41).

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Landau, Idan. 2004. Chain resolution in Hebrew V(P)-fronting. In Proceedings of References the North East Linguistic Society 34,ed.KeirMoultonandMatthewWolf,vol- ume 2, 357–372. University of Massachusetts at Amherst: Graduate Linguistic Student Association. Aoun, Joseph, Lina Choueiri, and Norbert Hornstein. 2001.Resumption, move- Landau, Idan. 2006. Chain resolution in Hebrew V(P)-fronting. Syntax 9:32–66. ment, and derivational economy. Linguistic Inquiry 32:371–403. Sauerland, Uli. 2008.OnthesemanticmarkednessofPhi-features. In Phi theory, Bianchi, Valentina. 2000. Teraisinganalysisofrelativeclauses: a reply to Borsley. ed. Daniel Harbour, David Adger, and Susana Béjar, 57–82.Oxford: Oxford Linguistic Inquiry 31:123–140. University Press. Elbourne, Paul D. 2005. Situations and individuals.MITPress. Kayne, Richard S. 1994. Teantisymmetryofsyntax. Cambridge, Massachusetts: Schachter, Paul. 1973.Focusandrelativization.Language 49:19–46. MIT Press. Vergnaud, Jean-Roger. 1974.Frenchrelativeclauses.Doctoral Dissertation, Mas- Kratzer, Angelika. 2009.Makingapronoun:Fakeindexicalsaswindows into the sachusetts Institute of Technology. properties of pronouns. Linguistic Inquiry 40:187–237.

10 Towards a Multidominant Theory of Movement Lecture Three: Questions Kyle Johnson University College London University of Massachusetts at Amherst 22 June 2016

Todaywe’llstarttotakeacloserlookathowmovementstructures are semantically (3) λp ∃xxis a child & p = she kissed x interpreted. Our focus will be Wh Movement. Simple wh-questions have the shape in (1), on the multidominant model of So, the challenge is to get this kind of meaning out of (1). movement that we’re exploring. Tecentralproblemamultidominantdefnition of movement poses is that it baldly predicts that the single meaning that is associatedwiththemoveditem (1) (I know) which child she kissed. should be found in both of its positions. Tat works fne for moved heads, but CP it isn’t what we want from questions. Instead, we must associate the moved wh- phrase with both a binder meaning and a variable meaning. Te frst person to CP XP appreciate, and try to solve, this problem is Elisabet Engdahl. In Engdahl (1980), what she proposes is that the moved wh-phrase has two C TP X meanings, and they are introduced at their two positions. Temeaning intro- duced in the lower position must be a variable. But it should also provide a way of explaining “reconstruction,” one of the manifestations of Semantic Displacement DP TP that is found in wh-movement. she T VP (4)Whichpictureofhimselfshouldnooneputonhiswebsite? Note that it is the position from which movement has occurred that matters. V DP

(5) a. Which picture of himself does this indicate that no one should kissed D NP bring?

b. *Which picture of himself does the thing no one heard indicate I which N should bring?

c. * Which picture of himself indicates that no one should bring it? child Engdahl (1980)suggesteddoingthatbylettingtheNPpartofthemovedwh- Astandard,simple,viewofthemeaningofquestionsisthatthey denote a set of phrasebeinterpretedinitslowerposition.Wecanspeculate that the NP part is not propositions, each proposition ofering a kind of answer in those cases where the interpreted in its higher (spoken) position however, since inthispositionitisnei- question is answer-seeking. Tis is the view introduced by Hamblin and modifed ther c-commanded by its binder, nor meets the locality condition that anaphors by Kartunnen. One way of representing a set is with the λ-operator, which can be typically impose on their antecedents. used to represent a function. Tere is another, somewhat less obvious, difculty involved in capturing these (2) λxP(x)=thatfunctionwhich,whenappliedtoa,givesP(a)is reconstruction cases. Tis problem is easier to appreciate incasesinvolvinguni- true (or, P(a)=1). versal quantifcation, like that in (6). Afunctioncanbeequatedwiththesetofthingsthatthatfunction holds of. For (1), for instance, we can give the question a denotation like: Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

(6) CP Her idea, then, is that in the lower position, a wh-phrase is interpreted as a func- tion that can contain a variable within it. Tevaluesthisfunction gives can de-

DP CP pend on the value given to the variable it contains. Tat’s how in (8)thedonkeys are made to vary with the values given to everyone.Indeed,itisthisfunctionthat D NP C TP we can see questions as asking for the identity of. (10) a. Which picture did you say you’d show every girl? which picture of himself shouldn’t DP TP λp ∃fp= you said you’d show every girl the x [ f (y)](x) anyone T VP f might be: Sally → the picture of the Eifel tower VP PP Mary → the picture of the Milkmaid Myrtle → the picture of hot-rods V t on his website f might be: her favorite picture !t" ≈ picture-of-himself(x) put f might be: If we adopt a Hamblin/Kartunnen style analysis of questions, and make the NP part of the moved phrase interpreted in its unmoved position,thenfor(6)we the picture of George Clooney might get an interpretation along the lines of (7). Some questions describe functions that can only depend on thevaluesgivento nearby quantifers. (7) λp ∃x p=notanyone should put picture-of-himself(x)onhiswebsite. (7) characterizes the question as seeking the identity of a single picture with the (11)Whichwholenumberdoeseverywholenumberprecede? expansive property of being of a bunch of guys, none of whom should put it on Te only function in the actual worlds that ftthisquestionareones like its suc- their website. Tat’s not what we want. We want something that allows the pictures cessor, which vary as according to the value give every whole number. to vary with the variable it contains. Te anaphoric connection between a moved We get from this model an account of why the trace can only get a value that phrase and its trace must be capable of carrying this duty. Elisabet Engdahl gave varies with the values given to expressions which c-command it. us a way of doing that. What she suggests is that the wh-phrase in the lower position gets an inter- (12) Which picture did you show the guy every girl knows? pretation like the defnite description in examples of “donkey anaphora,” like that *λp ∃fp= you showed the guy every girl knows the x [ f (y)](x) in (8). f can’t be: (8)Everyonewhoownsadonkeylovesthe/thatdonkey. Sally → the picture of the Eifel tower → Tese defnite descriptions also act like restricted variables. Following Cooper Mary the picture of the Milkmaid (1979), she adopted the view that they have buried within them a function that Myrtle → the picture of hot-rods picks out individuals which the restrictor donkey tells us are donkeys. In (8), that f can’t be: function is something like “owned by y.” her favorite picture (9)Everyone who owns a donkey loves the x,suchthat f (x),&donkey(x) f can be: f =ownedbyy the picture of George Clooney

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What we need to do now is put into the meaning of the phrase in thelowerposi- (15) ιxx= g(n) ∧ fower(x)= tion the contribution that the restrictor — the NP — makes. DP Te frst step we can take, then, is to reïnvoke Engdahl’s idea that the trace lef by movement is semantically like a donkey-type DP. Let’s start by considering the D λxx= g(n) ∧ fower(x)= syntax, and semantics, of these expressions. NP Ifwestartwithamodelofdonkey-typeDPslikethatofered in Cooper (1979), the we will want to build in a function whose arguments can be bound. We should λxx= g(n) λx fower(x)= notice that it is not just defnite descriptions that can have this interpretation in NP donkey anaphora sentences, but personal pronouns can as well: n (13) a. Every man who owns a donkey kisses it. N b. Every man who owns a donkey kisses the donkey. fower c. Every man who owns a donkey kisses that donkey. (16) !the" = λP ιxP(x) = ,defned only if there is a unique x We should build into pronouns, traces and defnite descriptions a functional such that P(x) =  meaning, then, and to the extent that this relation is the same in all these cases, we (17) !fower" = λx fower(x)= will want an explanation for why it travels in this particular pack. A commonplace idea about explaining the similarity between pronouns and defnite descriptions Tedenotationfor(15)isonlydefned if there is a unique x which is both g(n) is to adopt the view we saw yesterday that pronouns are the way defnite descrip- and a fower. Tis expresses the presupposition that we saw defnite descriptions tions are pronounced when they contain just ϕ features. Let’s look at such a way invoke. I will ignore that part of the meaning for the rest of this lecture. that builds on Heim (2013), Fox (1999), Elbourne (2005), Chierchia (1995) and An index can be a function, along with its arguments; when the index is a Rullmann and Beck (1998). function, I will represent it with “f .” Tis is what we have in (13b).1 Te frst innovation will be to let a defnite description come with an index. I (13b) Every man who owns a donkey kisses the donkey. will adopt the view in Fox (2003)whereindicesaretreatedaskinds of adjectives. ιxx= g( f )(g(z)) ∧ donkey(x)= (We will see evidence for this view in the lectures on QR.) An index is a variable DP that gets interpreted either by being bound or by way of a function that assigns a free variable a referent in the discourse. Tefunctionthatdoes this is sometimes called “an assignment function,” and it is standardly represented with “g.” Fox’s D λyy= g( f )(g(z)) ∧ donkey(y) =  idea, then, is that an index is a predicate that holds of those things that the assign- NP ment function or binder make the index refer to. So just as the adjective “red,” for the instance, is a predicate that holds of all those things that are red, the index “n” is λyy= g( f )(g(z)) λy donkey(y)= apredicatethatholdsofallthosethingsthatgorabinderassigns “n” to. NP f(z) (14) a. !red" = λx red(x)=1 N b. !n" g = λxx= g(n) donkey Adefnite description that has an index in it will look like (15). Notice that there are two variables here: f and z. f is a free variable, and will get its value from g. In this context, g assigns to f avalueparaphrasedby“ownedby” 1 Giving determiners funtional indices like this is in Chierchia (1995).

3 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

z,bycontrast,willbeboundbyevery man,andthat’showwegetthedonkeysthis (18) Which book about her should no linguist forget? defnite description refers to to vary with the men. Tecasein(13a) is parallel. Tesolediference being that the NP contains just ∃f ¬∃y linguist(y)= ∧ y should forget ϕ features in (13a). ιxx= f (y) ∧ book_about_y(x)= CP (13a) Every man who owns a donkey kisses it. ιxx= g( f )(g(z)) ∧ sing(x)= λP∃fP( f )= λ ¬∃y linguist(y)= ∧ y should forget DP DP ιxx= g()(y) ∧ book_about_y(x)= CP D λyy= g( f )(g(z)) ∧ sing(y) =  λP∃fP( f )= NP NP D C ¬∃y linguist(y)= ∧ y should forget ιxx= g()(y) ∧ book_about_y(x)= the book which about her TP λyy= g( f )(g(z)) λy sing(y)= NP DP TP f(z) N no linguist T VP

it should V ιxx= g()(g()) ∧ book_about_her(x)= rd (Note that I assume here that neuter 3 person are unmarked features, so it is forget DP merely singular.) So, this is how a normal donkey-type DP looks. We can imagine that some- D λxx= g()(g()) ∧ thing like this is what Engdahl would assign to the meaning of a moved wh-phrase book_about_her(x)= in its lower position. In its higher position, we’ll want the wh-phrase to intro- which NP duce a binder that will bind f . Tis will make the questions about the identity of those functions. We can do that by assigning a denotation to which that makes it a () NP binder, and then apply that denotation in the higher position. If we were to revert to the copy theory of movement for a moment, and represent syntactically these book about her two denotations, we’d get something like (18). Note that the NP book about her in the higher copy is not semantically inter- preted there. It can’t be, since the pronoun it contains must be interpreted within the scope of no linguist if it is to be interpreted as a variable. I’ve indicated that this NP isn’t semantically interpreted in this position withthedashedline. What’s missing from (18)isthesetofpropositionspart.Allwe’ve got here is a sentence that existentially quantifes over functions — functions that pick out books about x that no x, x a linguist, should forget. What we want is the set of such propositions. Let’s hold of on completing this picture for a little while.

2 See Fox (1999). Tere are others, all closely related to Fox’s. Two of them are found in Sauerland (1998, 2004)andRomero(1998), as well asEngdahl(1980, 1986).

4 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

Te standard account of the semantics of movement does precisely what we (20) ∃f ¬∃ylinguist(y)= ∧ yshould forget see in (18). Tat account is due to Danny Fox,2 who adopts a copy theory of move- ιxx= f (y) ∧ book_about_y(x)= ment and assumes that there is a rule which converts the lower copy into some- CP thing that matches what we have in the lower position of (18). He calls that rule “Trace Conversion,” and the way he formulates it is in (19), whichisslightlydif- λP ∃f .P( f )= λ.¬∃y linguist(y)=1 ∧y should forget ferent from how I’ve built the meaning of the lower copy, but close enough to be QP ιxx= g()(y) ∧ book_about_y(x)= roughly equivalent. CP λP ∃f .P( f ) ce onversion (19)Tra C Q C TP In ϕ′ interpret ϕ as a function that maps,

x,tothemeaningofϕ[x/n]. should DP TP DPn ϕ no linguist T VP ...DPn ... V ϕ[x/n] is the result of replacing the head of every constituent bearing the index n in ϕ with the head the ,whoseinterpretation,!the ", is: ιxx= g()(g()) ∧ x x book_about_her (x)= forget λP ∶ P(x).x.  DP (adapted from Fox 2003,(52): 111) What this rule says is that the two copies of which can get diferent interpreta- D NP tions in the diferent places they reside in. We can’t do this on amultidominant picture of movement because there aren’t two which’s: there’s just the one in to () NP diferent positions. Even if we were forced to a diferent solution, however, I think we should be worried about the power of a rule like Trace Conversion. book Te picture I’d like to replace these with is one that says that wh-movement about her involves putting together a defnite description of the sort that we see in donkey anaphora, with a Q morpheme that produces the question and binds the variable On this view, technically what has moved is just the DP portionthatisinterpreted in the defnite description. Tat Q morpheme is going to be the X in our parses as a variable. Tis denotation it supplies to the object position of forget. Tat DP for questions. As a frst approximation, I suggest something like (20). has merged with the higher Q, which is the binder of the index within the DP in object position. It has merged with that Q, but its denotation is not computed there. I’ve indicated that with the dotted line. As a consequence, the QP in the higher position has the same meaning as the Q which heads it. Weneedtodeterminewherein(20)thequestionwordwhich is inserted. I am going to assume that it is the D position of the DP that gets matched to the ques- tion word. We need this because it is possible for which to show up on unmoved DPs, as in (21). (21)Whichstudentaskedwhichquestion?

5 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

But I want the form this D has to refect the fact that there is the question mor- 1 Alternatives pheme, Q, in the sentence. We need to ensure that when Q is present, there is a which.SoIsuggestthatweletwhich be the exponent of the Q morpheme. When To get these remaining pieces, I’ll start by looking at how questions are formed in the exponent of some morpheme is expressed at the position that another mor- (some) wh-in-situ languages. In these languages, the D that is found in the lower pheme has, we say that “Agreement” holds between them. So I will assume that DP and the Q that binds of the variable in these lower expressions map onto sep- Agree holds between Q and the D containing which. arate morphemes. In Japanese, for instance, a morpheme on the verb marks the scope of a question, and in the position of the variable is an interrogative phrase. (22) CP (23) (Kimi-wa) dono-gakusei-ga nattoo-o tabe-tagatte-iru-to (you-top) which-student-nom natto-acc eat-desirous-be-C QP CP omoimasu-ka? Q C TP think-Q (Which student do you think wants to eat natto?)

should DP TP We might think of these languages as having the same syntax that I’ve given to English questions, but with a small diference in how the syntax-to-morphology no linguist T VP works. In Japanese, the D and Q are mapped onto separate morphemes and, per- haps relatedly, the shared DP is spelled out in the lower of its two positions.3 Al- agree V ternatively, we could see the Q and the DP as being completely independent, and there being no remerge/movement in these examples. forget Interestingly,though,inthesekindsofquestionsthereis (sometimes) a kind of DP intervention efect that does not arise in overt movement cases. Tis shows up for some dialects of Korean, according to Beck and Kim (1997). According to them, which NP the presence of man (‘only’) in (24)isresponsiblefordestroyingtherelationship between nuku and ni,therebycausingthissentencetobeill-formed. book (24)*Minsu-mannuku-lûl po-ss-ni? about her Minsu-only who-acc see-Pst-Q Te which-phrase in (22)haspaths.TegrammarofEnglishrequiresthatthe ‘Who did only Minsu see?’ linearization choose the path that includes QP, and this is why the wh-phrase is Beck (2006)providesanexplanationfortheseinterventionefects — sometimes linearized according to its status as part of the Specifer of CP. called “Beck Efects” — that gives to questions a slightly diferent semantics than Okay, that’s a start. We’ve got two things lef to do before we’llhaveacomplete I have adopted. Her semantics will, it turns out, provide the missing pieces to our picture. picture so far. So I will modify what we have to bring it in line with her analysis. 1.Wheredoesthesetofpropositionspartofthemeaningcomefrom in ques- Her leading idea follows Hamblin (1973)morecloselythanitdoes Kartunnen tions? in the Hamblin/Kartunnen style account of questions. Hamblinsuggestedthatthe question word in questions introduces not a variable that gets bound of,butin- 2.WhatcausesQandDPtomergeintheparticularwayindicatedin(22)? stead introduces “alternatives” that the set of propositionswhichmakesaquestion vary on. Tese alternative generating terms have also been used by Rooth(1985)to model focus. What will go wrong in (24)isthatthefocussensitive operator man

3 See Adger and Ramchand (2005), Kratzer and Shimoyama (2002), Hagstrom (1998, 2000), Kishimoto (2005), and Cable (2010).

6 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016 will interfere with the question particle ni’s access to the alternatives generated by (27) CP nuku.Let’stakeabrief,sketchy,lookatthis. TeideainRooth(1985) is that focused items have, in addition to their “nor- QP !CP"= ∅ f mal” denotation another denotation that certain operators like only interact with. !CP" ={noone recommended ιxx= f () ∧ book(x) =  T ′ at other denotation – its focus value – is a set made up of alternatives to the Q no one recommended ιxx= f () ∧ book(x) =  ′′ term. In something like (25), then, Sally has a normal semantic value that allows no one recommended ιxx= f () ∧ book(x) = ,...} it to refer to Sally, and the focus semantic value in (25b). CP (25)SheonlyvisitedSally. F C TP a. !Sally" =theindividualnamedSally b. !Sally"f = { Jerry, Max, Sam, Sean, Mary,...} DP TP Phrases that contain terms with a focus semantic value inherit a focus semantic value by composing their normal denotation with the term in a point-wise fash- no one T !VP" = ∅ !VP"f ={forgetιxx= f () ∧ book(x) = , ion. In the case of a verb composing with its object, the verb will compose with ′ each of the alternatives in the focus semantic value of the object by function ap- forget ιxx= f () ∧ book(x) = ,...} plication, and produce a set of alternative VP meanings. VP

f (26) !visited Sally" = { visited Jerry, visited Max, visited Sam, visited Sean, vis- {ιxx= f () ∧ book(x) = , V ited Mary,...} ιxx= f ′() ∧ book(x) = , ′′ !visited Sally" = visited(Sally) ιxx= f () ∧ book(x) = ,...}forget DP Rooth then gives only ameaningthat,whencombinedwiththeVP,returnsthe same ordinary semantic value that the VP has, but adds that all the members of D NP the focus semantic value of the VP are false. TeideainBeck(2006)istoletthewh-wordshavethesamefocussemantic which f () book value that focussed items do. But she suggests that they have no regular semantic value. Tis will cause the phrases they are contained in to have only focus se- Now, Beck’s proposal is that the Q morpheme, among perhaps other things, con- mantic values: they will be sets of alternatives that vary only with respect to the verts the focus semantic value of its sister into a normal semantic value. Tis gives value given to the wh-word. We are letting the part of a wh-wordthattheques- us (28). tion abstracts over be a function. If we leave all the rest of oursystemthesame,but import Beck’s idea that the function in the wh-word is an alternative generator, rather than a variable. We’ll get representations like that indicated in (27).

7 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

(28) !CP"={noone recommended ιxx= f () ∧ book(x) =  (29)WhodidonlyMinsusee? ′ no one recommended ιxx= f () ∧ book(x) =  ′′ We need to make it matter where the wh-phrase gets spelled out —thatiswhat no one recommended ιxx= f () ∧ book(x) = ,...} !CP"f = ∅ distinguishes the Korean example from the English one. We havetolearnabout QR before I can address that problem, so we have to leave this question unan- CP swered for a while. QP !CP"= ∅ f !CP" ={noone recommended ιxx= f () ∧ book(x) =  ′ Q no one recommended ιxx= f () ∧ book(x) =  ′′ no one recommended ιxx= f () ∧ book(x) = ,...} CP

C TP

DP TP

no one T !VP" = ∅ !VP"f ={forgetιxx= f () ∧ book(x) = , forget ιxx= f ′() ∧ book(x) = ,...} VP

{ιxx= f () ∧ book(x) = , V ιxx= f ′() ∧ book(x) = , ′′ ιxx= f () ∧ book(x) = ,...}forget DP

D NP

which f () book

Asetofalternativesshouldbethoughtofasalongdisjunction: each member in the set is a separate disjunct. Tis means that the set of alternatives Beck assigns to a question is semantically equivalent to an existential quantifcation over func- tions. We have achieved the denotation for questions that we wanted. What goes wrong in (24), then, is that man (‘only’) manipulates the focus se- mantic value of the clause its in before the question morpheme can get its hands on it. Interestingly, English doesn’t have these kinds of intervention efects. Some- thing parallel to (24)isperfectlygrammatical.

8 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

What we need now is an answer to the question why Q merges with the DP CP in English questions. For this, I need to turn to work by Seth Cable and Hadas Kotek. In Cable QP CP (2007), he studies questions of the sort that Korean and Japanese illustrate, but his object of study is Tlingit, a Na-Dené language spoken in Western Canada Q C TP and Southeastern Alaska. Like Korean, Tlingit has a wh-determiner and another morpheme — I’ll call it Q — in its questions. Like English, the wh-phrase moves should DP TP overtly to the lef edge of the question sentence. But, interestingly, unlike Korean or Japanese, the Q morpheme does not show up in what we might associate with no linguist T VP the C position. Instead, it is merged with some phrase that contains the wh-phrase. (30)illustrates. V (30) Aadóo yaagú sá ysiteen? agree who boat Q you.saw.it? DP forget ‘Whose boat did you see’ (Cable 2007,(212)–(213): 155-6) DP DP In (30), the Q particle, sá,hasmergedwithaDP,insideofwhichliesthewh-word: aadóo. Tewholethinghasmovedtothelef edge of the sentence. which NP D NP (31) CP f () NP s book about her DP CP  philosopher DP Q C TP Now, Tlingit sá has to have a diferent semantics than we need for our En- glish/Japanese/Korean questions, because it can show up in non-questions as well. aadóo yaagú sá ysiteen (34) Tléil aadóo yaagú sá xwsateen. whose boat you saw t  not whose boat Q I.saw.it Moreover, Cable argues that the Q morpheme is in an Agreement relationship ‘I didn’t see anyone’s boat.’ with the wh-word, and that there are locality conditions on that agreement rela- (Cable 2007,(187): 141) tion that determine where the Q particle can be merged. Very roughly, that locality Cable gives it a semantics in Tlingit that, like what we need, operates on the fo- condition can be described with (32). cus semantic values of its complement and converts them into regular semantic (32)QcanagreewithDonlyifthereisnolexicalitemthatc-commands D but values. In Tlingit, though, its existential force is derived from a higher, silent, op- not Q. erator. My suggestion, then, is that English Q has the semantics of the Q found in Korean, but the syntax of that found in Tlingit. He argues that Pied-Piping in English arises because the phrase that moves in Tis how a multidominant model of wh-movement can be formulated. It har- English has a Q morpheme merged with it in just the way that Tlingit sá does. (33) bors two problems, though. One is the one already acknowledged that we should illustrates. expect English wh-questions to show Beck efects. Because thewh-phraseisse- (33)Whichphilosopher’sbookabouthershouldnolinguistforget? mantically interpreted in just its lower position, even whenithasovertlymoved,

9 Kyle Johnson Towards a Multidominant Theory of Movement 22 June 2016

just like Korean, its lower position should be separated fromitshigherposition Elbourne, Paul D. 2005. Situations and individuals.MITPress. by a focus marked thing. Tat is not the case: Engdahl, Elisabet. 1980. Te syntax and semantics of questions in Swedish. Doc- (35)WhodidonlyMinsuvisit? toral Dissertation, University of Massachusetts, Amherst, Massachusetts. Engdahl, Elisabet. 1986. Constituent questions.Dordrecht,TeNetherlands:D. Asecond,related,problemisthatweshouldexpecteverything within a moved Reidel Publishing Company. T wh-phrase to obligatorily be interpreted in its lower. is means we should get the Fox, Danny. 1999.Reconstruction,bindingtheory,andtheinterpretation of same disjoint reference efect in both the examples of (36). chains. Linguistic Inquiry 30:157–196. (36) a. * She hates a book that Mary brought. Fox, Danny. 2003.Onlogicalform.InMinimalist syntax, ed. Randall Hendrick,

b. Which book that Mary brought does she hate. 82–123. Oxford: Blackwell Publishers. Hagstrom, Paul. 1998.Decomposingquestions.DoctoralDissertation, Mas- But that isn’t the case. Both of these examples suggest that a moved wh-phrase is sachusetts Institute of Technology, Cambridge, Massachusetts. not interpreted wholly in its lower position. Hagstrom, Paul. 2000. Temovementofquestionparticles.InProceedings of the TesolutiontotheseproblemsthatIwillexploreissuggestedin Kotek (2014). North East Linguistic Society, ed. Masako Hirotani, Andries Coetzee, Nancy She suggests that the derivations that form wh-questions in English can involve a Hall, and Ji-yung Kim, 275–286. Rutgers University: Graduate Linguistic Stu- QR step. Tat is, she suggests that the wh-phrase can frst QR past a focus marked dent Association. term, or a disjoint reference trigger, and from that QR’d position wh-move. To see how that solution might work, we will frst have to learn how to do QR in a Hamblin, Charles. 1973. Questions in Montague grammar. Foundations of Lan- multidominant theory. guage 10:41–53. Heim, Irene. 2013. Functional readings without type-shifed noun phrases. Un- published paper, MIT. Kishimoto, Hideki. 2005.Wh-in-situandmovementinSinhalaquestions.Natu- References ral Language and Linguistic Teory 23:1–51. Kotek, Hadas. 2014.Composingquestions.DoctoralDissertation, Massachusetts Adger, David, and Gillian Ramchand. 2005.Mergeandmove:Wh-dependencies Institute of Technology. revisited. Linguistic Inquiry 36:161–193. Kratzer, Angelika, and Junko Shimoyama. 2002.Indeterminatepronouns: Te Beck, Sigrid. 2006.Interventionefects follow from focus interpretation. Natural view from Japanese. In Proceedings of the Tokyo conference on psycholinguis- Language Semantics 14:1–56. tics,ed.YukioOtsu,volume3, 1–25.Tokyo:HituziSyobo. Beck, Sigrid, and Shin-Sook Kim. 1997.Onwh-andoperatorscopeinKorean. Romero, Maribel. 1998.Focusandreconstructionefects in wh-phrases. Doctoral Journal of East Asian Linguistics 6:339–384. Dissertation, University of Massachusetts, Amherst. Cable, Seth. 2007. TegrammarofQ:Q-particlesandthenatureofwh-fronting, Rooth, Mats. 1985.Associationwithfocus.DoctoralDissertation, University of as revealed by the wh-questions of Tlingit. Doctoral Dissertation, Mas- Massachusetts, Amherst. sachusetts Institute of Technology, Cambridge, Massachusetts. Rullmann, Hotze, and Sigrid Beck. 1998.Presuppositionprojection and the in- Cable, Seth. 2010. Te grammar of Q: Q-particles, Wh-Movement and Pied-Piping. terpretation of which-questions. In Proceedings of SALT VIII,ed.Devon Oxford University Press. Strolovitch and Aaron Lawson, 215–232. Ithaca, NY: CLC Publications. Chierchia, Gennaro. 1995. Dynamics of meaning. Chicago: University of Chicago Sauerland, Uli. 1998. Te meaning of chains. Doctoral Dissertation, Mas- Press. sachusetts Institute of Technology, Cambridge, Massachusetts. T Cooper, Robin. 1979. einterpretationofpronouns. InSyntax and Seman- Sauerland, Uli. 2004. Te interpretation of traces. Natural Language Semantics tics 10:SelectionsfromtheTird Groningen Round Table,ed.FrankHenyand 12:63–127. H. Schnelle, 61–92. New York: Academic Press.

10 Towards a Multidominant Theory of Movement Lecture Four: Quantifier Raising Kyle Johnson University College London University of Massachusetts at Amherst 23 June 2016

Quantifer Raising is the rule that allows the quantifcational determiner every (4) ∀y.y is a bank → a guard stood in front of y in (1)tobeinterpretedinapositionhigherthanwhereitispronounced. Tis IP is required to give us the interpretations where the indefnite’s value varies as a function of the universal quantifer. λP.∀y.y is a bank → P(y) λ a guard stood in front of  QP IP (1) A guard stood in front of every bank. In it original formulation – which I think goes back to Chomsky (1977), but is every bank DP IP usually credited to May (1977)–movementisallowedtocreatethe representation in (2)“covertly”from(1). a guard I VP (2) IP V PP QP IP  stood P DP every bank DP IP in N PP aguard I VP front P DP V PP of x stood P DP TeproposalinFox(2002)istousethecopytheoryofmovementand do “Trace Conversion” on the lower copy. in N PP

front P DP

of x Astandardsemanticsforevery gives us the interpretation in (4). (3) !every" = λQ.λP.∀yQ(y) → P(y) Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

(5) ∀y.y is a bank → aguardstands (7) ∀y.y is a bank → aguardstands in front of ιx, x = y such that x is a bank in front of ιx, x = y such that x is a bank IP IP

λQ.∀y.y is a bank → Q(y) λn. a guard stands in front λn. a guard stands in front λQ.∀y.y is a bank → Q(y) QP of ιx, x = n such that x is a bank of ιx, x = n such that x is a bank QP IP* IP* every bank Q DP IP DP IP ∀ aguard I VP aguard I VP

V PP V PP

stand P DP stand P DP

in N PP in N PP

front P ιx.x = g(n) front P ιx.x = g(n) ∧ x is a bank ∧ x is a bank of DP of DP

everyn bank D NP (6) Trace Conversion the n NP Interpret [DP DNP]as[DP the n NP].

Trace Conversion causes the lower copy to be interpreted as a defnite description bank with a variable. the gets pronounced as every when it shares an NP with ∀ TeproposalinJohnson(2012)istotranslatethisintoamultidominant struc- ture without changing the semantics. Tat’s done by sharing the NP part with two Note that on all these accounts, the NP part of the moved phrase is inter- separate heads: a defnite determiner downstairs and a quantifer upstairs. preted in both of its positions. Unlike what we saw for questions, the NP part of the moved phrase must be interpreted in its higher position ifwearetorestrict the quantifcation. We can see that this is a desirable outcomebyconsideringthe fact that (8) does not allow an inverse scope reading. (8) A guard stands in front of every picture of himself. Because picture of himself must be interpreted together with the universal quan- tifer, it cannot be interpreted lower than where the universal quantifer is inter- preted. And because himself must be interpreted within the scope of aguard,the result is that the universal quantifer must too. We should keep a semantics for the

2 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

universal quantifer – the standard one will do – that has this efect. Rather than (12) ∀y.[y is a human that Sherlock accused] → Joan accused ιx.x = y ∧ x is a human Trace Conversion, this model separates the two meanings of QR:thequantifca- IP tional part (=Q) from the variable part (=D). Q, then, has the denotation that the other models ascribe to every. every is the way that the defnite determiner gets λn Joan accused ιx.x = n ∧ x is a human λQ.∀y [y is a human that pronounced when its expressing the presence of a universal quantifer somewhere IP Sherlock accused] → Q(y) else. QP But unlike questions, we cannot rely on Agreement to characterize when the DP IP defnite determiner is in the right relation to Q to be pronounced as every. Be- Q NP cause Q does not c-command every,wecannotuseAgreement.So,that’sanopen Joan I VP problem we will have to solve: ∀ CP V ιx.x = g(n) (9)HowtogetDand∀ to jointly spell out as every ∧ x is a human that Sherlock did △ DP QR is thought to be responsible for resolving ACD. accused (10) Joan accused everyone that Sherlock did △. D NP △ = accused x the n NP Tat’s because there seems to be a match between the scope of thequantifer and the size of the VP that can be elided. (see Williams (1977)andSag(1976).) one △ (11)JoanwantstoeateverythingSherlockdoes. Fox and Nissenbaum (1999) argues that this is the same syntax we see for “ex- a. every » want traposition from NP,” as in (13). i. Everything that Sherlock wants to eat is something that is de- (13) John accused everyone yesterday that Sherlock did △. sirable for Joan to eat. ii. ? Everything that Sherlock eats is something that is desirable for Joan to eat. b. want » every i. Eating everything that Sherlock eats is what is desirable for Joan. ii. * Eating everything that Sherlock wants to eats is what is desirable for Joan. On the copy theory and multidominant theories of movement, this isn’t trivial. If the NP part of a QR’d phrase is semantically in both the lowerandhigherpo- sition, then we might expect a relative clause to be in both those positions too. Tat would not resolve ACD. Fox (2002)arguesthatLateMergeisresponsible for resolving the ellipsis.

3 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

(14) ∀y.[y is a human that Sherlock accused] → Joan accused ιx.x = y ∧ x is a human (18) a. We met every biker yesterday who has ever ridden on these trails. IP b. * We met some biker yesterday who has ever ridden on these trails.

λn Joan accused ιx.x = n ∧ x is a human λQ.∀y [y is a human that Moreover, we can fnd examples where the relative clause cannot be interpreted IP Sherlock accused] → Q(y) as if it hadn’t moved out of the VP, and yet even here it behaves like it is part of QP the restrictor of the universal quantifer. DP IP Q NP (19) a. Kim bought every book yesterday that she’d ever been told to △. Joan I VP b. * Kim bought some books yesterday that she’d ever been told to △. ∀ CP (Overfelt 2015a, (32): 36) VP yesterday Tere are other subtle efects of Extraposition from NP that follow from our that Sherlock did △ syntax. One that Fox (2015)discussesisacontrastin(20) frst noticed, to my V ιx.x = g(n) knowledge, by Rochemont and Culicover (1990). ∧ x is a human accused DP (20) a. Mary saw an alleged mouse from Mars yesterday. b. Mary saw an alleged mouse yesterday from Mars. D NP Te fact reported in Rochemont and Culicover (1990)isthatfrom Mars isn’t al- the n NP leged in (20b), but can be in (20a). Tis suggests that the extraposed PP must be related to a position in the DP that is higher than alleged. Tat’s achieved in our one system with the representation in (21). Overfelt (2015b) points out that this analysis of clausal extraposition from NP solves the mystery of why relative clauses do not seem to be movable otherwise: (15)*Tat Sherlock accused, John accused everyone. And, as Overfelt (2015a) demonstrates, this also accounts for why an extraposed relative behaves semantically as if it is part of the restrictor for the quantifer with respect to NPI licensing. TeNPIever is licensed when it is in the restrictor of the quantifer every,butnotwhenitisinthenuclearscopeofevery. (16) a. We met every biker who has ever ridden on these trails. b. *We met every biker while he has ever ridden on these trails. Tis is a fact about every, and not a fact about relative clauses more generally, as we can see from the contrast in (17). (17) a. We met every biker who has ever ridden on these trails. b. *We met some biker who has ever ridden on these trails. Tis is preserved under extraposition:

4 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

(21) ∃y. y is an alleged mouse from Mars ∧ Mary saw ιx.x = y ∧ y is an alleged mouse (22) ∃y. y is an alleged mouse from Mars IP ∧ Mary saw ιx.x = y ∧ x is an alleged mouse from Mars IP λn Mary saw ιx.x = n ∧ n is an alleged mouse λQ.∃y.y an alleged IP mouse from Mars ∧ Q(y) λn Mary saw ιx.x = n ∧ x is an alleged λQ.∃y.y an alleged QP mouse from Mars mouse from Mars ∧ Q(y) DP IP IP QP Q NP Mary I VP DP IP Q ∃ PP VP yesterday Mary I VP ∃ from Mars V ιx.x = g(n) VP yesterday ∧ x is an alleged mouse saw DP V ιx.x = g(n) ∧ x is an alleged D NP saw mouse from Mars DP the n NP D NP alleged NP the n NP mouse alleged NP By contrast, the case in (20a) can have the structure in (22), whichwouldallow from Mars to be what is alleged. mouse from Mars Tis is roughly the characterization of the situation that is in Culicover and Rochemont (1990). Fox (2002) argues, following Baltin (1987), that relative clauseswhichhave ACD in them are always extraposed. Tat is, he argues that the position a rela- tive clause is pronounced in is the position that resolves its ellipsis. One piece of evidence on behalf of that idea is (23), which is from Tiedeman (1995). (23) a. * I said that everyone you did △ arrived. b. Isaidthateveryonearrivedthatyoudid △. △ =saidthatx arrived (Fox 2002,(35b), (36b): 77) Tewordorderin(23a) requires that the relative clause be inside the VP headed by said,whereasin(23b), it’s possible for the relative clause to be outside this VP.

5 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

If QR moves things rightwards, as these examples would suggest, it is ofen very (28) VP difcult to tell when the relative clause is in or outside the VP. In ( 24), it could have moved string-vacuously out of the VP, and in (25), the PP could have itself QPn VP moved farther to the right than the relative clause is. Q V CP (24)She[read every book ] that you did. VP ! ∀ said C TP (25)She[read every book ] that you did to me. VP ! that DP TP What this means for us is that we need the linearization schemetoassignto (26)thestringin(27), and to (28)thestringin(29). NP D arrived (26) VP NP n the QP VP n NP CP Q NP V CP one that you did △ ∀ CP said C TP (29) She said that everyone that you did △ arrived If we fnd a way of ensuring that the NP which is a sister to the D always gets △ that you did that DP TP linearized according to the path that contains DP,then this contrast does, indeed, emerge. (Tough the fact that the QR’d material shows up to the right of its sister, NP D arrived rather than to the lef,doesnot.) Tis is the method of accounting for QR in a multidominant framework that NP n the Johnson (2012)suggests.FoxandJohnson(2016)triestoshowhow this method captures a puzzle that Perlmutter and Ross (1970)discover: one (27) She said that everyone arrived that you did △ (30)Amanenteredtheroomandawomanwentoutwhowerequitesimilar. (Perlmutter and Ross 1970,(3), p. 350) Terelativeclausehereseemstoberelatedtobothsubjectsoftheprecedingcoör- dinaton. We’re going to look at a slightly diferent example because it’s difcult to be sure in (30)thatwehavearestrictiverelativeclause.Tat’s clearer, I think, in (31). (31)Everywomanissmilingandeverymanisfrowningwhocameintogether. Tis has the same meaning as (32). (32)Everywomanandmanwhocameintogetheraresmilingandfrowning respectively.

6 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

Tetheoryofrelativeclauseextrapositionthatwehaveispartofatheoryabout (37) ∀y couple(y)=1 → a friend of y QR, so what we expect in (31) is that QR has (somehow) related the subjects of the thinks that ιx max(woman(x)=1 ∧ x ≤ y) conjuncts to a DP that the relative clause modifes. Tis, it turns out, is possible dances better than ιx max(man(x)=1 ∧ x ≤ y) on the present theory of QR, when we add to it one additional hypothesis. TP But before adding that hypothesis, I have to show you one necessary refne- ment. We’ve modeled the “trace” lef by QR as a defnite description equipped with DP TP an index, and we’ve given a semantics for the index that makes it a kind of adjec- tive: it is the property of being identical to what the assignment function maps the every couple λ a friend of  thinks index onto. But we can see from examples like (33)thatthemeaning of an index that ιx max(woman(x)=1 ∧ x ≤ ) in a defnite description is not exactly that. dances better than ιx max(man(x)=1 ∧ x ≤ )) TP (33)Afriendofeverycouple thinks that the woman dances better than the man. DP TP Instead, we need to let an index hold of things that are part of what the assignment function assigns to the index. a friend of x  T VP

g (34) !n" = λx [x ≤ g(n)],where“≤”meansequaltoorpartof. V CP I need to also reveal to you now another fact about the meaning of the that we can see when it heads a plural DP. In a sentence like (35), we need to ensure that the thinks C TP set that the students refers to includes all the students in the context of utterance. that DP TP (35) Testudentsareirritated. ιx max(woman(x)=1 ∧ x ≤ g()) Te meaning of the builds in a maximality operator that ensures the phrase it T VP heads refers to every individual that satisfes the property denoted by the NP it D NP contains. (It invokes a similar presupposition, namely that it can refer only when V AP there is just one set of individuals in the context that has everything that satisfes the  woman the property denoted by the NP.) So let’s build this into our meaning of the. dances A PP

(36) !the" = λP.ιx max(P(x)), defned when there is exactly one x max(P(x)). better P DP max(P(x)) = [P(x) =  ∧∀y[P(y) =  → y ≤ x]] ιx max(man(x)=1 ∧ than x ≤ g()) Tat will give (33)themeaningin(37). D NP

the  man

With these refnements to the meaning of a defnite description that comes with an index, we now add a theory of coördination. Tis theory has two parts. Te frst is (38).

7 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

(38) If two merged phrases are of the same morpho-syntactic kind, then (40) TP prepend and to the last part of the second. ∀y [y is woman⊕man ∧ y came in together] → ∧ ∧ DP → DP [ιx max(x is a woman x ≤ y) is smiling and ιx max(x is a man x ≤ y) is frowning]

D NP D NP TP QP λQ∀y [y is woman⊕man ∧ y came in together] → Q(x) the NP NP the NP NP TP λ ιx max(x is a woman ∧ x ≤ ) is smiling NP Q and ιx max(x is a man ∧ x ≤ ) is frowning cats NP NP cats NP NP λxxis woman⊕man CP ∀ TP IP NP dogs elephants dogs and elephants who came in together DP → DP DP TP and TP ιx max(x is a woman D NP D NP ∧ x ≤ g()) T VP DP TP ιx max(x is a man the AP NP the AP NP D NP is smiling ∧ x ≤ g()) T VP

AP AP mice AP AP mice every  NP D NP is frowning λxxis a woman fat hairy fat and hairy every  NP woman λxxis a man Tesecondpartisthethesisthatthereisaprocesswhichderives the sums reading of conjoined NPs from Predicate Modifcation. (See Winter 2001 and man Champollion 2015.) Tis is the structure that Zhang (2007) argues is correct for the Perlmutter/Ross (39) DP → DP examples, and it emerges out of our theory of QR, once we grant this theory of coördination. To the extent that this is successful, I think we can see it as evi- D λx woman(x)=1 ∧ man(x)=1 D λx woman⊕man(x)=1 dence for a multidominant theory of movement. Tis isn’t a structure that would NP NP be easily achievable on a, say, copy theory of movement. the the NP NP NP NP

woman and man woman and man woman⊕man holds of a plurality x if x contains a woman and a man. QR now provides the following structure for (31).

8 Kyle Johnson Towards a Multidominant Theory of Movement 23 June 2016

Johnson, Kyle. 2012.Towardderivingdiferences in how Wh movement and QR References are pronounced. Lingua 122:529–553. May, Robert. 1977. Tegrammarofquantifcation. Doctoral Dissertation, Mas- sachusetts Institute of Technology. Baltin, Mark. 1987.Doantecedent-containeddeletionsexist? Linguistic Inquiry Overfelt, Jason. 2015a. Extraposition of NPIs from NP. Lingua 164:25–44. 18:579–596. Overfelt, Jason. 2015b. Rightward movement: A study in locality. Doctoral Dis- Champollion, Lucas. 2015.Tenmenandwomengotmarriedtoday: noun coordi- sertation, University of Massachusetts at Amherst. nation and the intersective theory of conjunction. Journal of Semantics 1–62. Chomsky, Noam. 1977. Essays on form and interpretation.Amsterdam,Te Perlmutter, David, and John Robert Ross. 1970.RelativeClauses with Split An- Netherlands: North-Holland Publishing Company. tecedent. Linguistic Inquiry 1:350. Culicover, Peter W., and Michael S. Rochemont. 1990.Extraposition and the com- Rochemont, Michael, and Peter W. Culicover. 1990. English focus constructions plement principle. Linguistic Inquiry 21:23–47. and the theory of grammar.Cambridge:CambridgeUniversityPress. Fox, Danny. 2002.Antecedent-containeddeletionandthecopy theory of move- Sag, Ivan. 1976.Deletionandlogicalform.DoctoralDissertation, Massachusetts ment. Linguistic Inquiry 33:63–96. Institute of Technology. Fox, Danny. 2015. Te alleged reading of certain sentences with extraposed mod- Tiedeman, Robyne. 1995. Some remarks on antecedent contained deletion. In ifers – evidence for embedded late merge. MIT. Minimalism and Linguistic Teory, ed. Shosuke Haraguchi and Michio Funaki, Fox, Danny, and Kyle Johnson. 2016.QRisrestrictorsharing.InProceedings of 67–103.Tokyo:HituziSyobo. the 33rd West Coast Conference on Formal Linguistics,ed.Kyeong-minKim, Williams, Edwin. 1977.Discourseandlogicalform.Linguistic Inquiry 8:101–139. Pocholo Umbal, Trevor Block, Chan Queenie, Tanie Cheng, Finney Kelli, Winter, Yoad. 2001. Flexibility principles in Boolean semantics.Cambridge,Mas- Mara Katz, Sophie Nickel-Tompson, and Shorten Lisa, 1–16. sachusetts: MIT Press. Fox, Danny, and Jon Nissenbaum. 1999.Extrapositionandscope:acaseforovert Zhang, Niina Ning. 2007. Te syntactic derivations of split antecedent relative QR. In Proceedings of the West Coast Conference on Formal Linguistics 18,ed. clause constructions. Taiwan Journal of Linguistics 5:19–48. Sonya Bird, Andrew Carnie, Jason D. Haugen, and Peter Norquest, 132–144. Somerville, Massachusetts: Cascadilla Press.

9 Towards a Multidominant Theory of Movement Lecture Five: QR and derivations Kyle Johnson University College London University of Massachusetts at Amherst 24 June 2016

We lef with a theory of QR that had these parts. ∀y.y is a bank → aguardstands in front of ιx, max(x ≤ y such that x is a bank) (1) !the" = λP.ιx max(P(x)), defned when there is exactly one x max(P(x)). IP max(P(x)) = [P(x) =  ∧∀y[P(y) =  → y ≤ x]] (2) !n" g = λx [x ≤ g(n)],where“≤”meansequaltoorpartof. λn. a guard stands in front λQ.∀y.y is a bank → Q(y) of ιx, max(x ≤ n such that x is a bank) QP (3) !∀" = λQ.λP.∀yQ(y) IP* (4)QR Q DP IP a. Merge QP with a λ expression, ∀ b. Make the NP part of that QP dominate the sister of the index the λ aguard I VP binds, c. Make the exponent of the head of QP be the D whose sister contains V PP the index bound by the λ. stand P DP (5) A guard stands in front of every bank. in N PP

front P ιx.max(x ≤ g(n) ∧ x is a bank) of DP

D NP

the n NP

bank Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

We saw that this theory gave us a way of capturing the Perlmutter/Ross examples: (6)Everywomanissmilingandeverymanisfrowningwhocameintogether. TP ∀y [y is woman⊕man ∧ y came in together] → [ιx max(x is a woman ∧ x ≤ y) is smiling and ιx max(x is a man ∧ x ≤ y) is frowning]

TP QP λQ∀y [y is woman⊕man ∧ y came in together] → Q(x) TP λ ιx max(x is a woman ∧ x ≤ ) is smiling NP Q and ιx max(x is a man ∧ x ≤ ) is frowning λxxis woman⊕man CP ∀ TP IP NP who came in together DP TP and TP ιx max(x is a woman e. * Most women are smiling and every man is frowning who came in ∧ x ≤ g()) T VP DP TP ιx max(x is a man together. D NP is smiling ∧ x ≤ g()) T VP f. ? Most women are smiling and most men are frowning who came in together. every  NP D NP is frowning g. * Every woman is smiling and Few men are frowning who came in λxxis a woman together. every  NP h. few women are smiling and few men are frowning who came in woman λxxis a man together.

man i. * No woman is smiling and every man is frowning who came in together. Tis predicts, correctly, that the exponents of the quantifer in each DP must be j. Nowomanissmilingandnomanisfrowningwhocamein the same, a fact noted by Moltmann (1992), McKinney-Bock (2013), andZhang together. (2007). Link (1984)’s hydras teach us that (4c) needs changing. (7) a. * A woman is smiling and every man is frowning who came in together. (8)Everywomanandeverymanwhocameintogetherarenowdancing. b. Awomanissmilingandamanisfrowningwhocameintogether. Tis should be given the same meaning that (9)has. c. * Every woman is smiling and some man is frowning who came in (9)Everywomanandmanwhocameintogetherarenowdancing. together. d. Somewomanissmilingandsomemanisfrowningwhocamein We want the expressions every woman and every man to be predicates which sum together. in the same way that woman and man do. Tis means that every cannot be !the". Isuggestthatwetakeevery to be the index. Our new theory of QR:

2 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

(10)QR a. Put QP in the Specifer of LP, a phrase headed by a term that intro- duces a λ binder, b. QP agrees with L which agrees with the index it binds, c. Make the sister of Q dominate the sister of Q’s exponent: theindex. Tis gives us (11). (11) LP

LP agree QP

L TP Q

λ DP TP ∀

aspeakerT VP

V DP

annoys D NP agree !the"  NP

every student Note that the head that holds !the" is (always?) silent. My role model for (10a) and (10b) is subject agreement: (12) TP

DP TP

the girls T VP agree agree V AP

are sleepy Hydras can now be given the structure in (13)onthenextpage.

3 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

(13) ∀y [y is woman⊕man] → [ιx max(x is [woman ∧ ≤ y]⊕[man ∧ ≤ y] ∧ x came in together)] are now dancing LP

LP λQ∀y [y is woman⊕man] → Q(y) =  QP L TP λxxis woman⊕man Q λ ιx max(x is [woman ∧ ≤ g()]⊕[man ∧ ≤ g()] TP NP ∧ x came in together) ∀ DP are now dancing

D λxxis [woman ∧ ≤ g()]⊕[man ∧ ≤ g()] ∧ x came in together !the" NP

λxxis [woman ∧ ≤ g()]⊕[man ∧ ≤ g()] λxxcame in together NP CP

λxxis a woman who came in together ∧ x ≤ g() and λxxis a man NP ∧ x ≤ g() NP  NP λxxis a woman  NP every λxxis a man woman every man

Note that “[woman ∧ ≤ y]⊕[man ∧ ≤ y]” is a predicate that holds of a plurality x if x contains a woman who is part of y and a man who is part of y.

4 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

Note that Hydras are just special cases of the Perlmutter/Ross examples, ones (17)...whichbooknooneforgot. in which the relative clause is merged with the NP building theDPandnotthe !CP"={noone forgot ιx max(x ≤ f () ∧ book(x) = ) NP building the QP.We expect, therefore, that the exponents of the quantifer will ′ no one forgot ιx max(x ≤ f () ∧ book(x) = ) be the same in hydras as well, and as Link (1984), Zhang (2007), and Moltmann ′′ no one forgot ιx max(x ≤ f () ∧ book(x) = ), ...} (1992)note,thisseemstobecorrect. !CP"f = ∅ (14) a. * A woman and every man who’dagreed to dance with each other got CP out on the foor. QP !CP"= ∅ b. A woman and a man who’d agreed to dance with each other got out f !CP" ={noone forgot ιx max(x ≤ f () ∧ book(x) = ) on the foor. ′ Q no one forgot ιx max(x ≤ f () ∧ book(x) = ) c. * Every woman and some man who’dagreed to dance with each other ′′ no one forgot ιx max(x ≤ f () ∧ book(x) = ), ...} got out on the foor. CP d. Some woman and some man who’dagreed to dance with each other got out on the foor. C TP e. * Most women and every man who’dagreed to dance with each other

got out on the foor. DP TP f. ? Most women and most men who’d agreed to dance with each other got out on the foor. no one T !VP" = ∅ f g. * Every woman and few men who’d agreed to dance with each other !VP" = {forget ιx max(x ≤ f (g()) ∧ book(x) = ), got out on the foor. ′ h. Few women and few men who’d agreed to dance with each other forget ιx max(x ≤ f (g()) ∧ book(x) = ), ...} got out on the foor. VP i. * No woman and every man who’d agreed to dance with each other {ιx max(x ≤ f (g()) ∧ book(x) = ), V got out on the foor. ′ ιx max(x ≤ f (g()) ∧ book(x) = ), ′′ j. No woman and no man who’d agreed to dance with each other got ιx max(x ≤ f (g()) ∧ book(x) = ), ...} forget out on the foor. DP We detoured into QR in order to explore the idea that it might be used in the way that Kotek (2014)doesinformingderivationsforwhmovement. Kotek D NP adopts a semantics for questions that uses alternatives and combines it with QR to explain why we don’t get the expected intervention efects.Let’sfrst update which f () book our system for questions. I’ve added our new idea about what indices mean to the In languages in which a question can be formed with a wh-phrase in situ, this special index that we used for questions, and I’ve updated ourmeaningforthe computation fails because no one is one of the things that breaks the set of alter- defnite determiner as well. natives from percolating up. (We looked at an example paralleltothisonewith (15) which = !the" = λP ιx max(P(x)) only Minsu as subject, which also blocks the alternatives from percolating up.) Te subject here is one of the class of things that produces “Beck efects.” So there is a (16) Teindexinawh-phraseis: ′ problem in giving English the same kind of meaning that we givequestionswith !f(x)" g, f ={λxx≤ f (g(x)), λxx≤ f (g(x)),...} wh-in-situ. Kotek’s idea is that we solve that with QR.

5 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

We can see that a wh-phrase is an expression that can undergo QRfromcases like (18). (18) Which woman won’t read which book that you have △. So let’s redesign wh-phrases so that they are quantifcational expressions. We’ll make the which-phrase that we speak exactly like the defnite descrip- tions with indices in them that we have made the quantifcational phrases that we speak. Teindexinwh-phrase,however,willbeoneofthosethatcanbeavariable over functions that takes another variable as its argument. (19) !f(n)" g = λx.x ≤ g( f )(g(n)) Like all indices, this a predicate that holds true of anythingthatisapartoftheset of things which the function f picks out given the value given to n.Unlikewhat we had before, this function f won’t be an alternative generator, it will be a garden variety variable over functions. TealternativegeneratorwillbeintheDPthatQRs.I’llassign that meaning to which,andI’llwhich combine with a predicate, like other determiners that QR do, but rather than take that predicate as an argument it will use that predicate to introduce a presupposition. Here’s a stab at that: (20) !which" = λP.{f , f ′, f ′′,...},defned if P( f ) =  f is a function that picks an entity So, for instance: (21) {f , f ′, f ′′ ...} DP

λP{f , f ′, f ′′,...} λx book(x)=1 D NP

which book where !D" and !DP" are defned only if the thing that f picks out is a book. Imakethisfunctiondefned only if the thing f picks out is something that !NP" holds of so that the content of NP will restrict what f can range over. Tat this can be done with a presupposition in this way is what Heim (2013)suggests. Okay, putting this altogether, here’s how Wh-movement will look. We’ll QR a wh-phrase, and wh-move that QR’d phrase.

6 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

(22) !CP"o = {noone forgot ιx max(λxx≤ f () ∧ x is a book), ′ no one forgot ιx max(λxx≤ f () ∧ x is a book), ′′ no one forgot ιx max(λxx≤ f () ∧ x is a book),...} !CP" f = ∅ CP

CP QP

C !TP" f = Q {noone forgot ιx max(λxx≤ f () ∧ x is a book), ′ no one forgot ιx max(λxx≤ f () ∧ x is a book), ′′ no one forgot ιx max(λxx≤ f () ∧ x is a book),...} !TP"o = ∅ TP

f ′ ′′ λ no one forgot !DP*" ={f , f , f ,...} ιx max(λxx≤ () ∧ x is a book) !DP*"o = ∅ LP DP*

L no one forgot D ιx max(λxx≤ g()() ∧ x is a book) λ TP which

DP TP

no one T VP

V ιx max(λxx≤ g()(g()) ∧ x is a book) DP forgot D λxx≤ g()(g()) ∧ x is a book NP !the" 2(3) NP

book DP* and every node above it has a value only if the entity f picks out is a book.

7 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

Tese structures allow us to do late merge too: (23)WhichbookthatJohnbroughtdoesherecommend? !CP"o = {he recommend ιx max(λxx≤ f () ∧ x is a book), ′ he recommend ιx max(λxx≤ f () ∧ x is a book), ′′ he recommend ιx max(λxx≤ f () ∧ x is a book),...} !CP" f = ∅ CP

CP QP

C !TP" f = Q {he recommend ιx max(λxx≤ f () ∧ x is a book), ′ he recommend ιx max(λxx≤ f () ∧ x is a book), ′′ he recommend ιx max(λxx≤ f () ∧ x is a book),...} !TP"o = ∅ TP

f ′ ′′ λ he recommend !DP*" ={f , f , f ,...} ιx max(λxx≤ () ∧ x is a book) !DP*"o = ∅ LP DP*

L he recommend D NP ιx max(λxx≤ g()() ∧ x is a book) λ TP which CP

DP TP that John brought

he T VP

V ιx max(λxx≤ g()(g()) ∧ x is a book) DP recommend D λxx≤ g()(g()) ∧ x is a book NP !the" 2(3) NP

book DP* and every node above it has a value only if f is a book that John brought.

8 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

Let’s consider now how pied-piping will work. (24)Onwhichtabledidnoonestand? Teproblemherewillbeftting our theory – which is designed toletvariablesonlybeDPs–toacasewheresomethingotherthan a DP moves. One solution, indicated in the parse on the next page, is to let the preposition move semantically vacuously.

9 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

(25) !CP"o = {noone stand on ιx max(λxx≤ f () ∧ x is a table), ′ no one stand on ιx max(λxx≤ f () ∧ x is a table), ′′ no one stand on ιx max(λxx≤ f () ∧ x is a table),...} !CP" f = ∅ CP

CP QP

C !TP" f = Q {noone stand on ιx max(λxx≤ f () ∧ x is a table), ′ no one stand on ιx max(λxx≤ f () ∧ x is a table), ′′ no one stand on ιx max(λxx≤ f () ∧ x is a table),...} !TP"o = ∅ TP

f ′ ′′ λ no one stand on !PP*" ={f , f , f ,...} ιx max(λxx≤ () ∧ x is a table) !PP*"o = ∅ LP PP*

′ ′′ L no one stand on { f , f , f ,...} ιx max(λxx≤ g()() ∧ x is a table) DP* λ TP D DP TP which no one T VP

V PP

stand P ιx max(λxx≤ g()(g()) ∧ x is a table) DP on D λxx≤ g()(g()) ∧ x is a table NP !the" 2(3) NP

table DP* and every node above it has a value only if f is a table. 10 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

Teprepositionis“latemerged”intotheQR’dterm,butitisn’t semantically Another way we could do that is to revert to something closer to the trace theory interpreted in that position. To model the diference betweenlanguageslikeEn- of movement and let the PP in the lower position get translatedintoavariableof glish which allow Pied-Piping as well as preposition stranding and languages, like the same semantic type that the PP has. But that will wrongly predict that refex- those descended from Latin, which don’t allow preposition stranding we can fnd ives inside the PP cannot be bound from their lower position. a way of constraining what Q can attach to. Tis is what Cable (2010)suggests, (27)OnwhichphotoofherselfhasMaryputaframe? though the method he proposes is incompatible with our multidominant repre- sentations. CP Tis may look alarmingly complex, but there are few alternatives. If the vari- able that is bound in these cases corresponds to the argument of the preposition, PP CP then every syntax-to-semantics mapping is going to do something like what (25) does. On the copy theory of movement, for instance, the copy that is spoken in the on which photo C TP higher position will have to be designed so that the semanticsignorestheprepo- of herself sition, and that is precisely what (25)isexpressing.TeonlywayIcanseetoavoid has DP TP this consequence is to adopt a theory of movement that would allow the PP to be translated into a variable in its lower position. One way wecoulddothatisto Mary T VP interpret the PP in situ and use the alternative type semantics for questions that IdescribedonWednesday.Butthatwouldwronglypredictthatweshouldget VP PP Principle C efects in examples like (26).

(26) On which table that John hates will he stomp? V DP x CP put aframe C TP We need a syntax that will for part of the moved phrase to be interpreted below and part of it to be interpreted above, and that is difcult to achieve on a syntax Q DP TP that translates the moved PP into some particular semantic object. What we need is something that allows the DP within that PP to be broken apart. And that is he T VP what our syntax achieves. For the case in (26), for instance, we can do plain old late merge of the relative clause. will V PP

stomp P DP

on D NP

which NP CP

table that John hates

11 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

(28) !CP"o = {he will stomp on ιx max(λxx≤ f () ∧ x is a table), ′ he will stomp on ιx max(λxx≤ f () ∧ x is a table), ′′ he will stomp on ιx max(λxx≤ f () ∧ x is a table),...} !CP" f = ∅ CP

CP QP

C !TP" f = Q {he will stomp on ιx max(λxx≤ f () ∧ x is a table), ′ will he will stomp on ιx max(λxx≤ f () ∧ x is a table), ′′ he will stomp on ιx max(λxx≤ f () ∧ x is a table),...} !TP"o = ∅ TP

f ′ ′′ λ he will stomp on !PP*" ={f , f , f ,...} ιx max(λxx≤ () ∧ x is a table) !PP*"o = ∅ LP PP*

′ ′′ L he will stomp on { f , f , f ,...} ιx max(λxx≤ g()() ∧ x is a table) DP* λ TP D NP DP TP which CP he T VP that John hates V PP

stomp P max(λxx≤ g()(g()) ∧ x is a table) DP on D λxx≤ g()(g()) ∧ x is a table NP !the" 2(3) NP

table DP* and every node above it has a value only if f is a table and John hates f .

12 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

Sauerland (1998)discoveredthatitispossibleforonemovedwh-phrase to have a part that is just interpreted in the lower position and another part that is just interpreted in the higher position. An example of that kind is(29). (29)WhichpictureofhersthatJohnbroughtshouldheshowtonowoman? Our system will give this the representation in (30). (30) CP

CP QP

C TP Q

should LP DP

L TP D NP

λ DP TP which CP

he T VP that John brought

VP PP

V DP to no one

give D NP

!the" 3(2) NP

pictures of hers

13 Kyle Johnson Towards a Multidominant Theory of Movement 24 June 2016

References

Cable, Seth. 2010. Te grammar of Q: Q-particles, Wh-Movement and Pied-Piping.OxfordUniversityPress. Heim, Irene. 2013. Functional readings without type-shifed noun phrases. Unpublished paper, MIT. Kotek, Hadas. 2014.Composingquestions.DoctoralDissertation, Massachusetts Institute of Technology. Link, Godehard. 1984.Hydras.onthelogicofrelativeclauseconstructions with multiple heads. In Varieties of Formal Semantics, ed. Fred Landman and Frank Veltman, 151–180.Reidel. McKinney-Bock, Katherine. 2013.Derivingsplit-antecedentrelativeclauses.University of Pennsylvania Working Papers in Linguistics 19. Moltmann, Friederike. 1992.Coordinationandcomparatives.DoctoralDissertation,MIT. Sauerland, Uli. 1998. Temeaningofchains.DoctoralDissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts. Zhang, Niina Ning. 2007. Te syntactic derivations of split antecedent relative clause constructions. Taiwan Journal of Linguistics 5:19–48.

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