{
  "compose": 1,
  "id": "hk7-quantification",
  "title": "Quantification & Grammar (§7.1–7.3, §7.5)",
  "subtitle": "Heim & Kratzer — object quantifiers in situ (RaiseO) vs. by movement (QR+PA), scope, binding",
  "notation": "hk",
  "domain": {
    "multiLetterNames": true,
    "constants": {
      "e": "j m x1 x2"
    },
    "variables": {
      "e": "x y z",
      "et": "f g P Q X Y",
      "t": "p q"
    }
  },
  "lexicon": [
    {
      "words": [
        "John"
      ],
      "denotation": "j"
    },
    {
      "words": [
        "Mary"
      ],
      "denotation": "m"
    },
    {
      "words": [
        "linguist"
      ],
      "denotation": "Lx.linguist(x)"
    },
    {
      "words": [
        "publisher"
      ],
      "denotation": "Lx.publisher(x)"
    },
    {
      "words": [
        "offended",
        "offend"
      ],
      "denotation": "Ly.Lx.offend(x,y)"
    },
    {
      "words": [
        "knows",
        "know"
      ],
      "denotation": "Ly.Lx.know(x,y)"
    },
    {
      "words": [
        "everybody"
      ],
      "denotation": "Lf.Ax[f(x)]"
    },
    {
      "words": [
        "somebody"
      ],
      "denotation": "Lf.Ex[f(x)]"
    },
    {
      "words": [
        "every",
        "Every"
      ],
      "denotation": "Lf.Lg.Ax[f(x) -> g(x)]"
    },
    {
      "words": [
        "some",
        "Some"
      ],
      "denotation": "Lf.Lg.Ex[f(x) ∧ g(x)]"
    },
    {
      "words": [
        "no",
        "No"
      ],
      "denotation": "Lf.Lg.~Ex[f(x) ∧ g(x)]"
    },
    {
      "words": [
        "he1",
        "him1",
        "his1",
        "himself1"
      ],
      "denotation": "x1"
    },
    {
      "words": [
        "he2",
        "him2",
        "his2",
        "himself2"
      ],
      "denotation": "x2"
    }
  ],
  "rules": {
    "composition": {
      "functionApplication": true,
      "nonBranchingNodes": true,
      "predicateModification": true,
      "predicateAbstraction": true
    },
    "typeShifts": [
      "raiseO",
      "raiseS"
    ],
    "quantifierRaising": true
  },
  "exercises": [
    {
      "title": "A. Object quantifiers in situ (RaiseO) — §7.1–7.2",
      "instructions": "The verb wants an individual object (⟨e,⟨e,t⟩⟩) but a quantifier is ⟨⟨e,t⟩,t⟩, so FA fails. RaiseO lifts the verb's type ⟨e,⟨e,t⟩⟩ → ⟨⟨⟨e,t⟩,t⟩,⟨e,t⟩⟩ so the quantifier fits in situ — no movement. (This is the book's own endnote-7 exercise, p. 205 — the Montague-style verb entry H&K invite you to define; their illustrated §7.2.1 variant retypes the quantifier instead.)",
      "items": [
        {
          "sentence": "John offended every linguist.",
          "tree": "[.S [.DP John ] [.VP [.V offended ] [.DP [.D every ] [.NP linguist ] ] ] ]",
          "targets": [
            "∀x[linguist(x) → offend(j,x)]"
          ],
          "reading": {
            "section": "7.2"
          }
        },
        {
          "sentence": "Mary offended some linguist.",
          "tree": "[.S [.DP Mary ] [.VP [.V offended ] [.DP [.D some ] [.NP linguist ] ] ] ]",
          "targets": [
            "∃x[linguist(x) ∧ offend(m,x)]"
          ],
          "reading": {
            "section": "7.2"
          }
        },
        {
          "sentence": "John knows everybody.",
          "tree": "[.S [.DP John ] [.VP [.V knows ] [.DP everybody ] ] ]",
          "targets": [
            "∀x[know(j,x)]"
          ],
          "reading": {
            "section": "7.2"
          }
        }
      ]
    },
    {
      "title": "B. Object quantifiers by movement (QR + PA) — §7.3",
      "instructions": "The alternative repair MOVES the object quantifier, adjoining it above the clause with a co-indexed trace. Predicate Abstraction over the trace makes the remnant a ⟨e,t⟩ property — a fit argument for the raised quantifier. Same truth conditions as RaiseO.",
      "items": [
        {
          "sentence": "John offended every linguist.",
          "tree": "[.S [.DP [.D every ] [.NP linguist ] ] [.LP 1 [.S [.DP John ] [.VP [.V offended ] [.DP t1 ] ] ] ] ]",
          "targets": [
            "∀x[linguist(x) → offend(j,x)]"
          ],
          "reading": {
            "section": "7.3"
          }
        },
        {
          "sentence": "Mary knows some publisher.",
          "tree": "[.S [.DP [.D some ] [.NP publisher ] ] [.LP 1 [.S [.DP Mary ] [.VP [.V knows ] [.DP t1 ] ] ] ] ]",
          "targets": [
            "∃x[publisher(x) ∧ know(m,x)]"
          ],
          "reading": {
            "section": "7.3"
          }
        }
      ]
    },
    {
      "title": "C. Scope ambiguity & inverse scope — §7.5.1",
      "instructions": "With two quantifiers, movement derives BOTH scope orders; the in-situ proposals the book considers predict only the linear one (p. 194; richer in-situ type regimes exist, n. 24). Raise the quantifiers in either order; PA gives two non-equivalent LFs. Build the LF for each reading.",
      "items": [
        {
          "sentence": "Somebody offended everybody. (linear: ∃ > ∀)",
          "tree": "[.S [.DP somebody ] [.LP 1 [.S [.DP everybody ] [.LP 2 [.S [.DP t1 ] [.VP [.V offended ] [.DP t2 ] ] ] ] ] ] ]",
          "targets": [
            "∃x[∀y[offend(x,y)]]"
          ],
          "reading": {
            "section": "7.5.1"
          }
        },
        {
          "sentence": "Somebody offended everybody. (inverse: ∀ > ∃)",
          "tree": "[.S [.DP everybody ] [.LP 2 [.S [.DP somebody ] [.LP 1 [.S [.DP t1 ] [.VP [.V offended ] [.DP t2 ] ] ] ] ] ] ]",
          "targets": [
            "∀y[∃x[offend(x,y)]]"
          ],
          "reading": {
            "section": "7.5.1"
          }
        },
        {
          "sentence": "Some publisher offended every linguist. (inverse: ∀ > ∃)",
          "tree": "[.S [.DP [.D every ] [.NP linguist ] ] [.LP 2 [.S [.DP [.D some ] [.NP publisher ] ] [.LP 1 [.S [.DP t1 ] [.VP [.V offended ] [.DP t2 ] ] ] ] ] ] ]",
          "targets": [
            "∀y[linguist(y) → ∃x[publisher(x) ∧ offend(x,y)]]"
          ],
          "reading": {
            "section": "7.5.1"
          }
        }
      ]
    },
    {
      "title": "D. Quantifiers that bind pronouns — §7.5.3",
      "instructions": "When the raised subject's trace and a pronoun share an index, PA abstracts over both, binding the pronoun as a variable. Raise the subject (index 1) over a clause whose object pronoun is himself₁.",
      "items": [
        {
          "sentence": "Every publisher offended himself.",
          "tree": "[.S [.DP [.D every ] [.NP publisher ] ] [.LP 1 [.S [.DP t1 ] [.VP [.V offended ] [.DP himself1 ] ] ] ] ]",
          "targets": [
            "∀x[publisher(x) → offend(x,x)]"
          ],
          "reading": {
            "section": "7.5.3"
          }
        },
        {
          "sentence": "Some linguist knows himself.",
          "tree": "[.S [.DP [.D some ] [.NP linguist ] ] [.LP 1 [.S [.DP t1 ] [.VP [.V knows ] [.DP himself1 ] ] ] ] ]",
          "targets": [
            "∃x[linguist(x) ∧ know(x,x)]"
          ],
          "reading": {
            "section": "7.5.3"
          }
        }
      ]
    }
  ],
  "reading": {
    "format": "latex",
    "markdown": "# Chapter 7 · Quantification and Grammar\n\nSubject quantifiers compose by FA. Object quantifiers do not: a type mismatch.\nCh. 7 gives two repairs and weighs them (§7.5).\n\n## 7.1 The problem of quantifiers in object position\n\nIn (\\ref{obj}) the verb is `⟨e,⟨e,t⟩⟩`, the object `⟨⟨e,t⟩,t⟩`: neither sister has\nthe other in its domain, FA yields no value for the VP (p. 179).\n\n\\begin{derivation}\n[[offended]]        = λy . λx . offend(x,y)=1    : <e,<e,t>>\n[[every linguist]]  = λg . ∀x[linguist(x)=1 → g(x)=1]   : <<e,t>,t>\n\\end{derivation}\n\n\\ex<obj> John offended every linguist.\n\\xe\n\n## 7.2 Repair in situ: flexible types (RaiseO)\n\nLeave the quantifier in place; retype. The book's illustrated variant retypes the\nquantifier — \"We will illustrate the first possibility here. You are invited to try\nout the second on your own\" (p. 180; the \"type-shifted homonym of *every*\", p. 187).\nThe second, verb-retyping variant is endnote 7's exercise, credited to Montague\n(p. 205) — and is what RaiseO implements: `⟨e,⟨e,t⟩⟩ → ⟨⟨⟨e,t⟩,t⟩,⟨e,t⟩⟩`, then FA\ntwice, no movement.\n\n\\begin{derivation}\n[[John offended every linguist]]  = ∀x[linguist(x)=1 → offend(j,x)=1]   : t\n\\end{derivation}\n\n## 7.3 Repair by movement: Quantifier Raising + PA\n\nMove the object, adjoin it above the clause, leave a co-indexed trace; PA (ch. 5)\nturns the remnant into `⟨e,t⟩`, and the quantifier applies. LF: *[every linguist]\n1 [John offended t₁]* (p. 186).\n\n\\begin{derivation}\n[[John offended t1]]      = offend(j,x)=1            : t\n[[1 [John offended t1]]]  = λx . offend(j,x)=1       : <e,t>   (PA)\n[[(QR) every linguist …]] = ∀x[linguist(x)=1 → offend(j,x)=1]   : t   (FA)\n\\end{derivation}\n\n\"We have obtained the correct result… without resorting to a type-shifted homonym\nof 'every'\" (p. 187). Same truth conditions either way — so why movement?\n\n## 7.5.1 Scope ambiguity and inverse scope\n\n*Somebody offended everybody* (\\ref{scope}) \"has two readings, not just one\"\n(p. 194): linear (one offender for all) and inverse (each was offended, offenders\npossibly different). Raising the quantifiers in either order gives both LFs; the\nin-situ proposals the book considers predict only the linear reading (p. 194).\n\n\\begin{derivation}\n[[Somebody offended everybody]]  (linear)   = ∃x . ∀y . offend(x,y)=1   : t\n[[Somebody offended everybody]]  (inverse)  = ∀y . ∃x . offend(x,y)=1   : t\n\\end{derivation}\n\nH&K stop short of calling this decisive: richer type regimes derive inverse scope\nin situ (n. 24: Hendriks; Cooper storage); the §7.5 arguments' \"ultimate force is\nvery difficult to assess\"; \"we could not possibly purport here to give decisive\nevidence in favor of a pure movement approach\" (p. 194); pending independent\nmotivation, \"the choice seems to be just a matter of taste\" (p. 193).\n\nEngine note: the book's ⟦everybody⟧/⟦somebody⟧ quantify over persons (p. 180); our\nentries range over all of Dₑ.\n\n\\ex<scope> Somebody offended everybody.\n\\xe\n\n\\ex Some publisher offended every linguist.\n\\xe\n\n## 7.5.3 Quantifiers that bind pronouns\n\nA raised quantifier binds a co-indexed pronoun: PA abstracts over trace and pronoun\nat once. *[every publisher] 1 [t₁ offended himself₁]* (\\ref{bound}):\n\n\\begin{derivation}\n[[t1 offended himself1]]      = offend(x,x)=1            : t\n[[1 [t1 offended himself1]]]  = λx . offend(x,x)=1       : <e,t>   (PA)\n[[Every publisher … himself]] = ∀x[publisher(x)=1 → offend(x,x)=1]   : t\n\\end{derivation}\n\n\\ex<bound> Every publisher offended himself.\n\\xe\n\n> **Beyond this chapter.** Antecedent-contained deletion needs an ellipsis\n> mechanism we do not model; see §7.5.2 (p. 198)."
  }
}