Questions: Quantifier Interaction and Multiple Quantification

Question 1

Consider 'Every professor admires some philosopher.' What is the inverse scope reading, and why is it harder to access than the surface scope reading?

• A. The inverse reading — there is a specific philosopher every professor admires — is harder because it requires the existential quantifier to be raised above the universal at Logical Form, a more complex derivation than the default surface-order interpretation
• B. The inverse reading — each professor admires a different philosopher — is harder because existential quantifiers always take narrow scope by semantic convention
• C. There is no inverse reading — English quantifiers always scope in left-to-right order, so only the surface scope reading exists
• D. The inverse reading — there is a specific philosopher every professor admires — is harder because universal quantifiers semantically outrank existential ones

Answer: (A)

The surface scope reading (∀x∃y: every professor has some philosopher they admire, possibly different) is the default because it matches the left-to-right syntactic order. The inverse reading (∃y∀x: there's one philosopher all professors admire) requires the existential to be covertly raised above the universal at Logical Form — a more complex derivation. This is not a semantic law but a syntactic preference: more complex LF derivations are less accessible, which is why inverse scope requires contextual pressure to obtain.

Question 2

The phenomenon of inverse linking — where an embedded quantifier like 'some university' in 'Every student in some university passed' can take wide scope over the containing quantifier — supports which theoretical claim?

• A. That surface word order directly encodes the logical form of a sentence, with no covert movement required
• B. That existential quantifiers always outscope universals when they appear in embedded positions
• C. That scope is determined at an abstract level of Logical Form where quantifiers can be raised from syntactically embedded positions, not simply read off from surface structure
• D. That inverse linking is a pragmatic inference rather than a grammatical phenomenon

Answer: (C)

In 'Every student in some university passed,' the phrase 'some university' is syntactically embedded inside the subject DP. Yet the reading 'there is a university such that every student in it passed' is available — giving 'some university' wide scope over 'every student.' Since this contradicts a surface-order account, it motivates Quantifier Raising: the existential is covertly moved to a higher LF position where it c-commands the universal. Inverse linking is one of the strongest arguments that scope is a property of an abstract syntactic level, not surface strings.

Question 3

In 'Every student read some book,' the surface scope reading (each student read a possibly different book) is generally easier to access than the inverse scope reading (there is one book every student read).

• T. True
• F. False

Answer: True

Surface scope follows the left-to-right order of quantifiers in the sentence and requires no covert movement — it is the default interpretation. Inverse scope requires Quantifier Raising of the existential above the universal, a more complex derivation. This asymmetry is well-documented experimentally: the inverse scope reading requires contextual support (e.g., a context where one book was assigned) to be salient.

Question 4

Since logic allows quantifiers to scope in any order, natural languages also permit speakers to freely choose any scope ordering for multiple quantifiers in a sentence.

• T. True
• F. False

Answer: False

Logical notation is free to write quantifiers in any order, but natural language is constrained by grammar. Syntactic structure creates a preferred surface scope; inverse scope requires more complex derivations and is sometimes unavailable. Cross-linguistic data shows further constraints: some languages (e.g., Chinese, Hindi) are more 'scope rigid' and rarely allow inverse readings without special morphology. The availability of scope interpretations is governed by grammatical resources, not just logical possibility.

Question 5

What is the Quantifier Raising (QR) hypothesis, and what grammatical evidence motivates it?

Model answer: QR is the proposal that quantifier phrases are covertly moved (at the level of Logical Form) to a position where they c-command their scope domain, even if they remain in their surface syntactic position in pronunciation. Evidence includes: (1) the availability of inverse scope readings that cannot be derived from surface order; (2) inverse linking, where embedded quantifiers take wide scope over containing phrases; (3) cross-linguistic scope rigidity, which can be explained by differences in how freely QR applies across languages.

QR is 'covert' movement — it does not affect pronunciation but does affect interpretation. This is why 'Every student read some book' sounds the same whether you mean the surface or inverse reading, yet the two are semantically distinct. The theoretical move of positing Logical Form as a level of syntactic representation distinct from both surface structure and phonological form is motivated precisely by these scope facts.