Questions: Wh-Movement and Operator Quantification

Question 1

In the sentence 'What did Alice say that Bob thought Carol had eaten?', where is the word 'what' semantically interpreted?

• A. At the front of the clause, where it modifies the matrix verb 'say' — specifying what was said
• B. As the object of 'eaten' — what Carol ate — because that is where the gap occurs in the base structure
• C. As a discourse-level topic that floats freely and is not tied to any specific argument position
• D. At the edge of each embedded clause it crosses, binding multiple argument positions simultaneously

Answer: (B)

Despite appearing at the front of the sentence, 'what' is semantically interpreted as the object of 'eaten' — the thing Carol ate. This is the defining feature of long-distance dependency: the form (surface position) and the meaning (base position gap) are at different structural locations. The wh-phrase moves to the front but leaves a semantic gap in the deep object position of 'eaten', and the operator-variable relationship spans the entire distance. This is not stylistic — it reflects the genuine syntactic displacement that gives wh-movement its theoretical significance.

Question 2

A student argues: 'Chinese doesn't front wh-phrases — they stay in place — so Chinese doesn't have the operator-variable structure that English questions show.' What is the problem with this argument?

• A. The student is wrong because Chinese actually does front wh-phrases, just in a phonologically silent way not visible in surface word order
• B. The student is correct — wh-in-situ languages genuinely lack operator-variable semantics for questions
• C. Chinese speakers show sensitivity to the same island constraints in scope interpretation as English speakers, suggesting the operator-variable relationship exists even without overt fronting
• D. Operator-variable structure is a property of formal logic rather than natural language syntax, so the argument does not apply to either Chinese or English

Answer: (C)

The cross-linguistic evidence from wh-in-situ languages is decisive. Chinese and Japanese speakers do not front wh-phrases, but their scope judgments respect the same island constraints that block wh-extraction in English. If the constraint were purely about word order movement, in-situ languages would show no island sensitivity — but they do. This convergence across typologically different languages suggests the operator-variable relationship is the deep grammatical primitive, and that overt fronting is one surface strategy for expressing it. Some frameworks (LF movement, Agree) posit covert movement; others treat in-situ as direct operator binding — but all agree the semantic relationship is present.

Question 3

The sentence 'What did you read a book that discussed?' is grammatically ill-formed in English because extracting a wh-phrase from within a complex NP violates a syntactic island constraint.

• T. True
• F. False

Answer: True

This is the complex NP island (also called the complex noun phrase constraint). The NP 'a book that discussed ___' is a noun with an embedded relative clause modifier. Wh-extraction from within this structure is blocked — the relative clause constitutes an island that traps any movement from inside it. The sentence is ungrammatical because speakers recognize that 'what' cannot coherently be interpreted as the object of 'discussed' across that boundary. Island constraints are among the most robust grammatical generalizations, holding across languages and even (partially) for wh-in-situ languages in scope interpretation.

Question 4

The wh-phrase in 'What did Alice eat?' is semantically interpreted at its surface position — at the front of the clause — because that is where it appears in the sentence.

• T. True
• F. False

Answer: False

This reverses the central insight of wh-movement analysis. The wh-phrase appears at the front (Spec,CP) due to movement, but it is semantically interpreted as the object of 'eat' — the position where it was base-merged and where the gap appears. The semantic interpretation follows the base position (the variable bound by the operator), not the surface position. 'What did Alice eat?' means 'For what x, Alice ate x?' — the 'what' scopes over the clause from the front, but x occupies the object position. Form and meaning are decoupled, which is the defining property of long-distance dependency.

Question 5

What evidence shows that wh-movement creates a genuine semantic operator-variable relationship rather than merely reordering words stylistically?

Model answer: Two types of evidence are decisive. First, long-distance binding: in 'What did Alice say that Bob thought Carol had eaten?', the fronted 'what' must be interpreted as the object of 'eaten' across multiple clause boundaries — no stylistic account can explain why a word at the front of the sentence is semantically connected to a gap many clauses away. Second, cross-linguistic island sensitivity: Chinese and Japanese speakers keep wh-phrases in their base positions (no overt fronting) yet show the same sensitivity to island constraints in scope interpretation as English speakers. If movement were merely stylistic, in-situ languages would show no island effects. The consistent pattern across languages shows the operator-variable relationship is the grammatical primitive, and overt fronting is just one expression of it.

The formal semantic representation captures what is happening: 'What did Alice eat?' has the logical structure ιx[eat(Alice, x)], where x is a variable bound by the wh-operator at the front of the clause. This operator-variable isomorphism between syntax and logic is not a coincidence — it is one of the strongest arguments that syntax and formal semantics are deeply integrated. The island constraints further reinforce this: the domains within which operators can bind variables are syntactically defined, meaning the grammar has built-in locality conditions on operator-variable relationships that cannot be explained by pragmatics or information structure alone.