Semantics 2 Syntax Semantics Interface Ling 400 Sentence

Sentence Meaning and Truth Conditions • It is not easy to say what a

Principle of Compositionality • Idea: You know the meaning of a complex expression (including

Our assumptions so far • proper name --> the object it denotes • common

Assume that VP denotes a collection (“set”) of things • Intransitive verbs (and all

Truth conditions of a simple sentence “John sings” is true just in case the

VP conjunction (VP and VP) VP VP conj VP sings and dances means intersection

VP disjunction (VP or VP) Intersection is optional VP VP conj VP sings or

Two meanings of or? • Some say that or has an inclusive meaning (represented

Counterfactuals • If kangaroos had no tails, they would topple over. • If Oswald

Sentences with Quantifiers Every dog barks. No cat laughs. cats dogs barks Dogs are

Sentences with Quantifiers cats Every dog barks. No cat laughs. dogs barks This means

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Semantics 2: Syntax. Semantics Interface Ling 400

Sentence Meaning and Truth Conditions • It is not easy to say what a sentence means. • The meaning of sentence S can be thought of as the truth conditions for S • “George W. Bush is in the White House. ” • If you know its meaning, then you know how to go about checking its truth conditions, and vice versa.

Principle of Compositionality • Idea: You know the meaning of a complex expression (including sentences) because you know the meanings of its parts (words). • You somehow put together “word meanings” to get to the meaning of the whole, and this process relies on the syntactic structure.

Our assumptions so far • proper name --> the object it denotes • common noun --> the set of all things that have the property/quality in question What about verbs?

Assume that VP denotes a collection (“set”) of things • Intransitive verbs (and all other VPs) denote (“mean”) collections (“sets”) of things. E. g. sings means/denotes (the set of) those who sing:

Truth conditions of a simple sentence “John sings” is true just in case the individual John is an element of the collection (set) of those who sing. John must be in there somewhere. Sentence of the form “NP VP” is true just in case the meaning of NP is an element of the meaning of VP.

VP conjunction (VP and VP) VP VP conj VP sings and dances means intersection Mary sings and dances is true just in case …

VP disjunction (VP or VP) Intersection is optional VP VP conj VP sings or dances means union (the whole thing) Mary sings or dances is true just in case …

Two meanings of or? • Some say that or has an inclusive meaning (represented by union — taking the “whole thing” including the overlap (intersection)) • Others say that or has an exclusive meaning (i. e. , A or B and not both) • For our purpose of exposition, we adopt the latter.

Counterfactuals • If kangaroos had no tails, they would topple over. • If Oswald had not killed Kennedy, someone else would have. • Truth conditions: Assume that the antecedent is true. Otherwise, the hypothetical situation is almost the same as the real world. On these assumptions, the consequent (main clause) is true.

Sentences with Quantifiers Every dog barks. No cat laughs. cats dogs barks Dogs are completely contained in those that bark. no overlap those who laugh

Sentences with Quantifiers cats Every dog barks. No cat laughs. dogs barks This means that some dogs do not bark. those who laugh This means that some cats laugh.