Week 13a. QR CAS LX 522 Syntax I. Quantifiers We interpret Bill saw everyone as We interpret Bill saw everyone as For every person x, Bill saw x. For

Week 13a. QRWeek 13a. QR

CAS LX 522CAS LX 522Syntax ISyntax I

QuantifiersQuantifiers

We interpret We interpret Bill saw everyoneBill saw everyone as as For every person For every person xx, Bill saw , Bill saw xx..

This is the meaning. This is the This is the meaning. This is the logical formlogical form of the sentence of the sentence Bill saw Bill saw everyoneeveryone. In the notation of formal . In the notation of formal logic, this is written aslogic, this is written asx. Bill saw xx. Bill saw x‘For all ‘For all xx ( (xx a person), Bill saw a person), Bill saw xx.’.’


Every boy hates his roommate.Every boy hates his roommate. Notice that each boy hates a Notice that each boy hates a

different roommate, the roommates different roommate, the roommates are specific to each boy.are specific to each boy.

For every boy For every boy xx, , xx hates hates xx’s ’s roommate.roommate.

This means that This means that every boyevery boy doesn’t doesn’t just mean the group of boys; rather it just mean the group of boys; rather it goes through the set of boys and goes through the set of boys and says something about each of them says something about each of them individually.individually.


These phrases which don’t refer to These phrases which don’t refer to specific people/things in the world but specific people/things in the world but rather seem to do things to sets of rather seem to do things to sets of people/things are people/things are quantifiersquantifiers. Examples . Examples include:include: most studentsmost students twelve angry mentwelve angry men fewer than half of the membersfewer than half of the members some custodiansome custodian nobody in their right mindnobody in their right mind

QPQP What is the category of a What is the category of a

quantifier like quantifier like most studentsmost students?? Well, it goes basically in all the Well, it goes basically in all the

same places a DP goes. Like same places a DP goes. Like which studentwhich student or or whatwhat or or whowho..

So, like what we said for So, like what we said for whwh--phrases, phrases, quantifier phrases are quantifier phrases are really DPs with an extra really DPs with an extra propertyproperty (they’re (they’re quantificational). Sometimes quantificational). Sometimes people write QP, but they mean people write QP, but they mean ‘a quantificational DP’.‘a quantificational DP’.

studentNP

DP

Devery

RestrictionsRestrictions To reiterate, quantifiers are used to say To reiterate, quantifiers are used to say

something about something about individuals in a setindividuals in a set.. Most students like syntax.Most students like syntax. The set (sometimes, The set (sometimes, restrictionrestriction) is the set of ) is the set of

students.students. This says that, if you check This says that, if you check allall of the students of the students

individually to see if individually to see if eacheach likes syntax, you’ll likes syntax, you’ll find that most (more than half) of the find that most (more than half) of the students you checked do.students you checked do.

For each x in students, does x like syntax? For each x in students, does x like syntax? Did we answer “yes” for most of the ones we Did we answer “yes” for most of the ones we checked?checked?

QuantifiersQuantifiers To write the logical form (meaning) of a To write the logical form (meaning) of a

sentence with one of these, you put the sentence with one of these, you put the quantifier first, and replace where it came quantifier first, and replace where it came from with a variable:from with a variable:

Most students eat at Taco Bell.Most students eat at Taco Bell.For most students For most students xx, , xx eats at Taco Bell eats at Taco Bell

No administrators eat at Taco Bell.No administrators eat at Taco Bell.For no administrator For no administrator xx, , xx eats at Taco Bell eats at Taco Bell

Mary likes every flavor of ice cream.Mary likes every flavor of ice cream.For every flavor of ice cream For every flavor of ice cream xx, Mary , Mary likes likes xx

BindingBinding A quantifier is said to A quantifier is said to bindbind its variable. its variable.

That is, the reference of the variable is That is, the reference of the variable is assigned by the quantifier.assigned by the quantifier.

Bill read every book.Bill read every book.For every book For every book xx, Bill read , Bill read xx

Is this true? Well, let’s go through the Is this true? Well, let’s go through the books. books. Moby DickMoby Dick. Did Bill read . Did Bill read Moby Moby DickDick? Yes. Ok, ? Yes. Ok, War and PeaceWar and Peace. Did Bill . Did Bill read read War and PeaceWar and Peace? Yes. Ok, …? Yes. Ok, …

ScopeScope

A student read every book.A student read every book. When is this true?When is this true?

Mary, it turns out, has read all of the Mary, it turns out, has read all of the books.books.

Nobody has read everything, but Mary Nobody has read everything, but Mary read half of the books and Bill read the read half of the books and Bill read the other half. Every book was read by a other half. Every book was read by a student.student.

There are two meanings here, the There are two meanings here, the sentence is ambiguous between two sentence is ambiguous between two logical forms.logical forms.

ScopeScope

A student read every bookA student read every bookThere is a student There is a student xx such that such that

for every book for every book yy, , xx read read yyororFor every book For every book yy, there is a student , there is a student xx

such that such that xx read read yy It matters which quantifier comes It matters which quantifier comes

first in the logical form.first in the logical form.

ScopeScope This is perfectly logical. A quantifier takes a This is perfectly logical. A quantifier takes a

set of individuals and checks to see if set of individuals and checks to see if something is true of the individual members of something is true of the individual members of the set.the set.

A student read every book.A student read every book. (Namely, Mary)(Namely, Mary) In the set of students, we find that it is true that In the set of students, we find that it is true that

for at least one student for at least one student xx: : xx read every book read every book.. In the set of students, we find that it is true that In the set of students, we find that it is true that

for at least one student for at least one student xx:: In the set of books, we In the set of books, we find that it is true that for each book find that it is true that for each book yy, , xx read read yy..

There is a student There is a student xx such that for every book such that for every book yy, , xx read read yy..

x x students students : : y y booksbooks: : xx read read yy..

ScopeScope A student read every book.A student read every book. (They were all (They were all

covered, though not necessarily by one covered, though not necessarily by one student)student) In the set of books, we find that it is true that In the set of books, we find that it is true that

for each book for each book xx: : a student read a student read xx.. In the set of books, we find that it is true that In the set of books, we find that it is true that

for each book for each book xx:: In the set of students, we find In the set of students, we find that it is true that for at least one student that it is true that for at least one student yy, , yy read read xx..

For every book For every book xx, there is a student , there is a student yy such that such that yy read read xx..

x x booksbooks: : y y studentsstudents: : yy read read xx..

LFLF

We think about this kind of ambiguity in We think about this kind of ambiguity in much the same way we think aboutmuch the same way we think aboutMary heard a dog bark in the house.Mary heard a dog bark in the house. (either Mary was in the house or the dog was)(either Mary was in the house or the dog was)

This (above) is a This (above) is a syntacticsyntactic ambiguity, ambiguity, depending on where the PP depending on where the PP in the housein the house is attached.is attached.

If there are two different interpretations, If there are two different interpretations, there are two different there are two different structuresstructures. Two . Two different LFs.different LFs.

QRQR

Sue read every book.Sue read every book.For every book For every book xx, Sue read , Sue read xx..

After Spellout, the quantifier After Spellout, the quantifier movesmoves to to a position above the sentence, so a position above the sentence, so there is then a direct mapping there is then a direct mapping between the structure and the logical between the structure and the logical form.form.

[every book][every book]ii [ [IPIP Sue read Sue read ttii ]. ].

QRQR



As with As with whwh-movement, the -movement, the tracetrace is is the variable at logical form—moving the variable at logical form—moving quantifiers is a way to establish a quantifiers is a way to establish a quantifier-variable structure.quantifier-variable structure.

QRQR



This movement is called This movement is called Quantifier RaisingQuantifier Raising ( (QRQR), and it ), and it happens to happens to everyevery quantifier quantifier before LF.before LF.

Quantifiers and bindingQuantifiers and binding

Every girl aced her exams.Every girl aced her exams. [Every girl][Every girl]ii [ [ ttii aced her aced herii exams] exams] For every girl For every girl xx, , xx aced aced xx’s exams’s exams

Not only the trace of QR, but also Not only the trace of QR, but also pronouns, can be bound by the pronouns, can be bound by the quantifier, their referent quantifier, their referent determined by the quantifier.determined by the quantifier.

Quantifiers and bindingQuantifiers and binding

[Every girl][Every girl]ii [ [ ttii aced her aced herii exams] exams] Binding (assigning reference) is subject to c-Binding (assigning reference) is subject to c-

command. A quantifier can only assign command. A quantifier can only assign reference to a variable (its trace and possibly reference to a variable (its trace and possibly other pronouns) which it c-commands.other pronouns) which it c-commands.

Her brother said that every girl aced her examsHer brother said that every girl aced her exams.. The things which a quantifier c-commands are The things which a quantifier c-commands are

said to be in itssaid to be in its scope. scope.

Quantifiers can only bind variables in their Quantifiers can only bind variables in their scope.scope.

WCOWCO

Now, let’s look at weak crossover again.Now, let’s look at weak crossover again. Every girl likes her roommate.Every girl likes her roommate. For every girl For every girl xx, , xx likes likes xx’s roommate.’s roommate. Her roommate likes every girl.Her roommate likes every girl. For every girl For every girl xx, , xx’s roommate likes ’s roommate likes xx.. Why can’t the second sentence have Why can’t the second sentence have

this meaning?this meaning?

WCOWCO

[Every girl][Every girl]ii [ [IPIP ttii likes her likes herii roommate]. roommate]. For every girl For every girl xx, , xx likes likes xx’s roommate.’s roommate.

[Every girl][Every girl]ii [ [IPIP her herii roommate likes roommate likes ttii ]. ]. For every girl For every girl xx, , xx’s roommate likes ’s roommate likes xx..

Answer: WCO again.Answer: WCO again. But WCO is about But WCO is about moving a quantifier over a variable—so if moving a quantifier over a variable—so if WCO rules out this meaning, there must WCO rules out this meaning, there must have been movement. have been movement. There must have There must have been QRbeen QR. A movement we couldn’t see.. A movement we couldn’t see.

ACDACD

Here’s another reason to believe in Here’s another reason to believe in QR, QR, antecedent contained deletionantecedent contained deletion. . This one’s kind of complicated, so This one’s kind of complicated, so hang on tight.hang on tight.

First, we need to talk about First, we need to talk about VP ellipsisVP ellipsis..

Mary bought a record, and Bill did too.Mary bought a record, and Bill did too. [[IPIP Mary -ed [ Mary -ed [vvPP buy a record]] and buy a record]] and

[[IPIP Bill -ed [ Bill -ed [vvPP buy a record]] too. buy a record]] too.

VP ellipsisVP ellipsis

Mary bought a record and Bill Mary bought a record and Bill bought a tapebought a tape. ≠ . ≠ Mary bought a Mary bought a record and Bill did too.record and Bill did too.

VP ellipsis is allowed VP ellipsis is allowed when a when a preceding VP is identicalpreceding VP is identical..

To To interpretinterpret this, you need to use this, you need to use the content of the preceding VP.the content of the preceding VP.

Mary bought a record and Bill did Mary bought a record and Bill did (buy a record) too.(buy a record) too.


We will consider the process of VP ellipsis to We will consider the process of VP ellipsis to be one of be one of deletion under identitydeletion under identity..

Underlyingly:Underlyingly:-ed [-ed [vvPP Mary sleep] and -ed [ Mary sleep] and -ed [vvPP Bill sleep] too. Bill sleep] too.

Spellout, LF:Spellout, LF:Mary -ed [Mary -ed [vvPP tt sleep] and Bill -ed [ sleep] and Bill -ed [vvPP tt sleep] too sleep] too

Pronunciation:Pronunciation:Mary -ed [Mary -ed [vvPP tt sleep] and Bill -ed [ sleep] and Bill -ed [vvPP tt sleep] too sleep] tooMary slept and Bill did tooMary slept and Bill did too


So, as long as two VPs in sequence So, as long as two VPs in sequence look identicallook identical (where traces of (where traces of movement look identical to one movement look identical to one another—they sound the same), another—they sound the same), we we are allowed to pronounce the are allowed to pronounce the second one second one very quietlyvery quietly..

Like an extreme case ofLike an extreme case ofMary bought a record andMary bought a record and

Bill Bill bought a record bought a record too.too.


Note that Note that identityidentity is actually fairly abstract. is actually fairly abstract. John slept and Mary will too.John slept and Mary will too. John slept and Mary will John slept and Mary will sleepsleep too. too.

Spellout:Spellout:John -ed [John -ed [vvPP tt sleep] and Mary will [ sleep] and Mary will [vvPP tt sleep] toosleep] too Also, further support for “affix hopping” being Also, further support for “affix hopping” being

“part of pronunciation”; the V doesn’t “part of pronunciation”; the V doesn’t inherentlyinherently have a tense suffix. have a tense suffix.

ACDACD

Now, consider a DP with a relative clause:Now, consider a DP with a relative clause: the record [whichthe record [whichii Mary bought Mary bought ttii ]. ].

Bill likes [the record which Mary bought].Bill likes [the record which Mary bought].

Bill likes the record which Mary bought and Bill likes the record which Mary bought and Sue does too.Sue does too.

Bill likes the record which Mary bought and Bill likes the record which Mary bought and Sue does (like the record which Mary Sue does (like the record which Mary bought) too.bought) too.

ACDACD

Bill likes every book Mary does.Bill likes every book Mary does. Bill [Bill [vvPP likes every book likes every book OpOpii Mary [ Mary [vvPP likes likes

ttii ]]. ]]. vvP:P: likes [every book likes [every book OpOp Mary likes Mary likes t t ]] vvP:P: likes likes tt Those aren’t the same. VP ellipsis Those aren’t the same. VP ellipsis shouldn’t shouldn’t

work, but yet it does.work, but yet it does. The deleted VP is The deleted VP is contained contained in the in the

antecedent VPantecedent VP ( (antecedent-contained antecedent-contained deletiondeletion))

QR and ACDQR and ACD But now let’s consider what QR would do.But now let’s consider what QR would do. Every book that Mary likesEvery book that Mary likes is a quantifier. is a quantifier. Quantifiers have to move up past the subject by Quantifiers have to move up past the subject by

LF.LF. Bill likes every book Mary does.Bill likes every book Mary does. Spellout:Spellout:

Bill [Bill [vvPP likes [every book likes [every book OpOpjj Mary [ Mary [vvPP likes likes ttjj ]]]. ]]]. LF:LF:

[every book [every book OpOpjj Mary [ Mary [vvPP likes likes ttjj ]] ]]ii Bill [ Bill [vvPP likes likes ttii ].].

But now the VPs But now the VPs areare identical. identical. So if we believe in QR, we can explain ACD So if we believe in QR, we can explain ACD

sentences in a natural way.sentences in a natural way.

Where do quantifiers go?Where do quantifiers go?

Every student left.Every student left. [Every student][Every student]ii [ [IPIP ttii left ] left ] We need a variable in subject We need a variable in subject

position, so QR must be moving the position, so QR must be moving the quantifier out of IP, to somewhere quantifier out of IP, to somewhere higher then IP.higher then IP.

Believe me that it is also moving Believe me that it is also moving somewhere somewhere lowerlower than CP. than CP.

Adjunction to IPAdjunction to IP

In order to In order to accommodate this, we accommodate this, we need to formulate a need to formulate a new position to which new position to which quantifiers move.quantifiers move.

This position is going This position is going to be to be adjoined to IPadjoined to IP..

vPI

I

IP

subj

IP

QP

Adjunction to IPAdjunction to IP One difference between QR One difference between QR

(adjunction to IP) and movement to (adjunction to IP) and movement to SpecIP is in the motivations.SpecIP is in the motivations.

Moving to SpecIP or moving to Moving to SpecIP or moving to SpecCP is motivated by some need SpecCP is motivated by some need of Iof I (EPP: SpecIP must be filled)(EPP: SpecIP must be filled) or or CC ([+WH] C needs a [+WH] in its ([+WH] C needs a [+WH] in its specifier)specifier)..

Moving a quantifier (QR) is Moving a quantifier (QR) is required because the required because the quantifierquantifier needs to get out of the IP (for needs to get out of the IP (for interpretation). IP interpretation). IP itself itself has no need has no need for quantifiers.for quantifiers.

vPI

I

IP

subj

IP

QP

Adjunction to IPAdjunction to IP So, we could say that moving to So, we could say that moving to

Spec is something that happens if Spec is something that happens if the moving thing is the moving thing is pulledpulled (I is (I is pulling up a subject to satisfy its pulling up a subject to satisfy its own needs, not the needs of the own needs, not the needs of the moving subject)moving subject) or or pushedpushed (quantifiers move to satisfy their (quantifiers move to satisfy their own needs, not the needs of the I)own needs, not the needs of the I)..

An XP that is An XP that is pulledpulled up goes into up goes into Spec.Spec.

An XP that is An XP that is pushedpushed up adjoins. up adjoins.

vPI

I

IP

subj

IP

QP

Documents

Week 13a. QR CAS LX 522 Syntax I. Quantifiers We interpret Bill saw everyone as We interpret Bill saw everyone as For every person x, Bill saw x. For