A professor says: 'Every student passed an exam.' Under one reading, this requires that all students took the same exam. Under another, each student could have passed a different exam. Which analysis correctly explains where these readings come from?
AThe ambiguity is pragmatic — listeners resolve it based on context, and there is really only one syntactic structure
BThe word 'an' is semantically vague and can mean either 'one specific' or 'some arbitrary'
CQuantifier Raising at Logical Form creates two distinct syntactic structures with different scope relations, producing genuinely different truth conditions
DThe ambiguity arises from the passive/active distinction — passive voice would eliminate one reading
The ambiguity is structural, not pragmatic or lexical. Quantifier Raising (QR) at Logical Form — the covert syntactic level interfacing with semantic interpretation — moves quantified NPs to scope positions. If 'an exam' raises higher than 'every student,' it takes wide scope and the wide-scope-existential reading results: one specific exam was passed by all students. If 'every student' takes wide scope, the wide-scope-universal reading results: for each student, there exists some (potentially different) exam they passed. These are distinct LF representations with genuinely different truth conditions, not just different emphases of a single meaning.
Question 2 Multiple Choice
Under the wide-scope-universal reading of 'Every student solved a problem,' what is the truth condition?
AThere is one particular problem that every student solved (∃y∀x: problem(y) ∧ student(x) → solved(x,y))
BEvery student solved at least one problem, though different students may have solved different problems (∀x∃y: student(x) → problem(y) ∧ solved(x,y))
CEvery student solved every problem (∀x∀y: student(x) ∧ problem(y) → solved(x,y))
DAt least one student solved at least one problem (∃x∃y: student(x) ∧ problem(y) ∧ solved(x,y))
The wide-scope-universal reading (∀x∃y) means: for every student x, there exists some problem y such that x solved y. Different students may have solved different problems. This is the weaker, more easily satisfied reading. The wide-scope-existential reading (∃y∀x) is stronger: one particular problem was solved by every student. A free-choice assignment satisfies the ∀x∃y reading (everyone solved a problem, possibly different ones). A class that all solved problem #7 satisfies both. The two readings can diverge sharply, making the ambiguity real and consequential.
Question 3 True / False
Scope ambiguity in sentences like 'Nearly every student read a book' is purely pragmatic — the grammar generates one meaning, and listeners use context to determine which reading was intended.
TTrue
FFalse
Answer: False
This is the core misconception the topic addresses. Scope ambiguity is structural — it arises from genuinely distinct Logical Form representations generated by Quantifier Raising. The two readings have genuinely different truth conditions: the wide-scope-existential reading requires one specific book read by all students, while the wide-scope-universal reading requires only that each student read some book (possibly different ones). These conditions can diverge sharply in real situations — a class assigned the same novel versus a free-reading period. The ambiguity is not resolved by context inferring a single meaning; it is a grammatically generated structural ambiguity.
Question 4 True / False
Constraints on Quantifier Raising — such as the inability to raise quantifiers out of syntactic islands — parallel constraints on overt wh-movement, suggesting QR is a genuine syntactic operation rather than merely a semantic notation.
TTrue
FFalse
Answer: True
This convergence is theoretically significant. Overt wh-movement is blocked from extracting out of syntactic islands — complex NPs, adjunct clauses, etc. If QR shows the same island sensitivity, it suggests that QR is not merely a semantic bookkeeping device but a real syntactic operation subject to the same universal grammar constraints as overt movement. This has implications for the architecture of grammar: the syntax-semantics interface is not a clean boundary but a level (Logical Form) where syntactic operations continue to apply.
Question 5 Short Answer
Explain why the two readings of 'Every student read a book' have genuinely different truth conditions, and give a real situation where one reading is satisfied but the other is not.
Think about your answer, then reveal below.
Model answer: The wide-scope-universal reading (∀x∃y: every student x read some book y) is satisfied if every student read at least one book — each student's book can be different. The wide-scope-existential reading (∃y∀x: some specific book y was read by every student x) requires that one particular book was read by all students — a much stronger claim. In a free-reading period where students self-select books, the ∀x∃y reading is satisfied (everyone read something) but the ∃y∀x reading is not (there is no one book read by all). In a class where everyone reads the assigned novel, both readings are satisfied.
The key insight is that these are not different emphases but logically distinct claims — one can be true while the other is false. This is what makes it a genuine structural ambiguity, not vagueness. Quantifier Raising at Logical Form generates two distinct LF representations: in one, 'a book' adjoins above 'every student' (taking wide scope); in the other, 'every student' takes wide scope. Each LF corresponds to a distinct truth condition. Listeners perceive both readings as available — a fact that scope theory must explain and that pragmatics alone cannot account for.