Questions: Montague Semantics

Question 1

What is the core principle that makes Montague semantics 'compositional'?

• A. The meaning of a sentence is memorized as a whole unit.
• B. The meaning of a complex expression is derived from the meanings of its parts and the syntactic rules that combine them.
• C. Every word denotes an individual object in the world.
• D. Sentences are translated into informal paraphrases before interpretation.

Answer: (B)

Compositionality (the Fregean principle) holds that sentence meaning is a function of sub-expression meanings and their mode of combination. This is what allows Montague semantics to give a recursive, rule-by-rule account of meaning rather than listing meanings for infinitely many sentences.

Question 2

In Montague semantics, a noun phrase like 'most student' and a proper name like 'John' both denote the same semantic type — they both pick out individual entities in the model.

• T. True
• F. False

Answer: False

Proper names like 'John' can be treated as denoting individuals (type e), but quantificational NPs like 'every student' denote generalized quantifiers — functions from sets to truth values (type <<e,t>,t>). One of Montague's key insights is that NPs must be assigned a uniform type, which requires lifting proper names to the generalized quantifier type as well.

Question 3

How does lambda abstraction allow a transitive verb phrase like 'loves Mary' to combine with a subject to produce a sentence meaning?

Model answer: The VP 'loves Mary' is represented as λx. loves(x, mary) — a function waiting for an individual argument. When applied to the subject denotation (e.g., john), beta-reduction yields loves(john, mary), a proposition with a truth value.

Lambda abstraction creates a 'slot' for the missing argument. The subject saturates that slot via function application. This is how syntactic constituency directly drives semantic composition: combining two phrases corresponds to applying a function to an argument.