1. Semantics 2: Syntax-Semantics Interface
Ling400

2. 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.

3. 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.

4. 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?

5. 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:

6. 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.

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

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

9. 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.

10. 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.

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

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