1Quantification in grammarLING 610Angelika KratzerNovember 14, 20072The beginning• Gottlob Frege1848 - 19253The Interpreter of FregeMichael DummettArticle on Frege in A Companionto Analytic Philosophy. Oxford,Blackwell, 2001, 6-20.Frege: Philosophy of Language.The Interpretation of Frege’sPhilosophy.4Creating Concept Expressions• Everyone respects Pitt’s father.everyone (!x respect("y father-of(Pitt)(y))(x))• Pitt respects everyone’s father.everyone (!x respect("y father-of(x)(y))(Pitt))• Everyone respects his own father.everyone (!x respect("y father-of(x)(y))(x))5“By attaching the universal quantifier to these threeexpressions for concepts, we obtain respectively “Forall a, a respects Pitt’s father,” “For all a, Pitt respectsa’s father,” and “For all a, a respects a’s father,” or,colloquially, “Everyone respects Pitt’s father,” “Pittrespects everyone’s father,” and “Everyone respectshis own father.” And now, in these quantifiedsentences, Frege says, the expression for the relevantconcept is part of the content of the sentence.”Dummett: Excerpt from article on Frege in Blackwell’sCompanion to Analytic Philosophy, p. 10.6A mismatch between syntax andsemantics• But then there might be concepts that arepart of the content of a sentence withoutbeing denoted by any actual constituent ofthe sentence.7The Basic Insight• Quantifier phrases must operate overpredicates (‘concept expressions’, expressionsof type <et> in our framework).• Those predicates do not necessarilycorrespond to surface constituents. Theymight have to be created by a syntactic orsemantic process.8Quantifier phrasesT(everyone)= !P#x (person(x) $ P(x))T(someone)= !P%x (person(x) & P(x))9A syntactic way of giving a QPwhat it needsQP type <<et>t>!nTP type ttntype <et>TP type t type e10A semantic way of giving a QPwhat it needsT(respect1) = !x!y respect (x)(y)T(respect2)= !Q<<et>t>!yQ (!x respect(x)(y))• Somebody respects everybody.11Accounting for ambiguitieswithout QRT(respect1) = !x!y respect(x)(y)T(respect2)= !P<<et>t> !Q <<et>t> P (!x Q (!y respect(x)(y)))T(respect3)= !P<<et>t> !Q<<et>t> Q (!y P (!x respect(x)(y)))• Somebody respects everybody.12Syntax or Semantics?Pauline Jacobson: “The(Dis)Organization of theGrammar: 25 Years. Linguisticsand Philosophy. Celebrating 25thVolume. December 2002, 601-626.13Have we gone backwards?“There is, however, one area in which we havearguably made little progress - indeed I wish tosuggest here that we have perhaps gonebackwards. And this concerns the fundamentalquestion of the overall organization andarchitecture of the grammar - in particular, howthe systems of syntax and semantics work (ordon’t work) together.”Jacobson (2002), 601.14LF“…it has almost become axiomatic in muchrecent work that there is a distinct level oflogical form which inputs the rules supplying amodel-theoretic interpretation - as opposed tohaving the model-theoretic interpretation beingdirectly supplied as syntactic expressions are‘built’. ”Jacobson (2001), 600 f.15Questions of Elegance“…there is a clear elegance to a system in whichthe grammar builds (i.e. proves as well-formed)syntactic objects in parallel with assigning theman interpretation, an elegance which is lost ifthe grammar contains two entirely separatesystems, one of which (the syntax) must ‘run’first because the other (the semantics) works onits output.”Jacobson (2002), p. 60916Questions to take home from thisdiscussion ….• Which approach is better equipped to give aninsightful account of the properties of quantifierscope?• What are the properties of quantifier scope?• What makes an account insightful?17And before we forget ….• What if we assume a Davidsonian eventsemantics and sever the external argumentfrom its verb? Do we still have a problemwith quantifier phrases in object