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Chapter 3-4

LING 165C Chapter Notes - Chapter 3-4: Possible World, Partial Function, Presupposition

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Dylan Bumford

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Chapter 2
2.1 Model-theoretic semantics
- Meaning are actual objects and are represented by strings of symbol. They are
model-theoretic object
- Grammar maps each linguistic expression into something beyond just a symbolic
- They are the “stuff” that is out there in the universe
2.2 Truth Conditions
- Declarative sentences are either true or false
- Truth values to declarative sentences seemed to also depend on context
- i.e [I am the president of the United States]
- It is oversimplified to say that meaning of a sentence is true or false, because
- Even once we do determine the truth value of a sentence we surely don’t want to
call that “meaning”
- Truth value can’t be determined until we know the context of utterance
2.3 Possible worlds
- We do not want all true sentences to have the same meaning
- “To know the meaning of a sentence is it know what it would take to make a sentence
true”. This involves possibilities, or possible worlds
- If the meaning of a sentence is a function from worlds to values, then all necessarily true
sentences have the same meaning
- The notion of a partial function can be used to model presupposition failure
- t denotes the set {1, 0}, where as we mean the set of worlds
- Use the notation <a, b> to mean the set of all functions whose domain is the set a and
co-domain is the set b. Thus <w, t> is set of functions from worlds to truth values
-Intension: take any expression whose meaning is a function from possible worlds to
something else; is its actual meaning, not its value in some particular world
- Possible worlds are essentially functions that maps from worlds to truth values
- Truth of a sentence is also time-dependent
- Full meaning or intension of a sentence is a function from worlds and times to truth
values (extension is the value of this function taken at some particular worlds and some
particular time)
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