CAS LX 522 Syntax IQuantifiersSlide 3Slide 4QPRestrictionsSlide 7BindingScopeSlide 10Slide 11Slide 12LFQRSlide 15Slide 16Quantifiers and bindingSlide 18WCOSlide 20ACDVP ellipsisSlide 23Slide 24Slide 25Slide 26Slide 27QR and ACDWhere do quantifiers go?Adjunction to IPSlide 31Slide 32Week 13a. QRWeek 13a. QRCAS LX 522CAS LX 522Syntax ISyntax IQuantifiersQuantifiersWe interpret We interpret Bill saw everyoneBill saw everyone as asFor 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 everyoneBill saw everyone. In the . In the notation of formal logic, this is written asnotation of formal logic, 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.’.’QuantifiersQuantifiersEvery boy hates his roommate.Every boy hates his roommate.Notice that each boy hates a different Notice that each boy hates a different roommate, the roommates are specific to roommate, the roommates are specific to each boy.each boy.For every boy For every boy xx, , xx hates hates xx’s roommate.’s roommate.This means that This means that every boyevery boy doesn’t just doesn’t just mean the group of boys; rather it goes mean the group of boys; rather it goes through the set of boys and says through the set of boys and says something about each of them something about each of them individually.individually.QuantifiersQuantifiersThese phrases which don’t refer to specific These phrases which don’t refer to specific people/things in the world but rather seem to people/things in the world but rather seem to do things to sets of people/things are do things to sets of people/things are quantifiersquantifiers. Examples include:. Examples include:most studentsmost studentstwelve angry mentwelve angry menfewer than half of the membersfewer than half of the memberssome custodiansome custodiannobody in their right mindnobody in their right mindQPQPWhat 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 which studentstudent 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 propertyreally DPs with an extra property (they’re quantificational). (they’re quantificational). Sometimes people write QP, but Sometimes people write QP, but they mean ‘a quantificational DP’.they mean ‘a quantificational DP’.studentNPDPDeveryRestrictionsRestrictionsTo reiterate, quantifiers are used to say something To reiterate, quantifiers are used to say something about 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 find likes syntax, you’ll find that most (more than half) of the students you that most (more than half) of the students you checked do.checked do.For each x in students, does x like syntax? Did we For each x in students, does x like syntax? Did we answer “yes” for most of the ones we checked?answer “yes” for most of the ones we checked?QuantifiersQuantifiersTo 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 from quantifier first, and replace where it came from with a variable: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 BellNo 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 BellMary 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 likes , Mary likes xxBindingBindingA quantifier is said to A quantifier is said to bindbind its variable. That is, its variable. That is, the reference of the variable is assigned by the the reference of the variable is assigned by the quantifier.quantifier.Bill read every book.Bill read every book.For every book For every book xx, Bill read , Bill read xxIs this true? Well, let’s go through the books. Is this true? Well, let’s go through the books. Moby DickMoby Dick. Did Bill read . Did Bill read Moby DickMoby Dick? Yes. Ok, ? Yes. Ok, War War and Peaceand Peace. Did Bill read . Did Bill read War and PeaceWar and Peace? Yes. Ok, …? Yes. Ok, …ScopeScopeA 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 books.Mary, it turns out, has read all of the books.Nobody has read everything, but Mary read Nobody has read everything, but Mary read half of the books and Bill read the other half. half of the books and Bill read the other half. Every book was read by a student.Every book was read by a 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.ScopeScopeA student read every bookA student read every bookThere is a student There is a student xx such that such thatfor every book for every book yy, , xx read read yyororFor every book For every book yy, there is a student , there is a student xxsuch that such that xx read read yyIt matters which quantifier comes first in It matters which quantifier comes first in the logical form.the logical form.ScopeScopeThis is perfectly logical. A quantifier takes a set of This is perfectly logical. A quantifier takes a set of individuals and checks to see if something is true individuals and checks to see if something is true of the individual members of the set.of the individual members of the set.A student read every book.A
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