Semantics - Basesproduced.com

Semantics
April 5, 2012

The Last Details
• Semantics/pragmatics homework will be posted after
class today.
• Will be due next Thursday
• Future plans:
• Today: semantics
• Tuesday of next week - wrap up semantics
• Thursday: some comments on language preservation
• With a guest speaker!
• + an opportunity to ask some review questions
• Semantics homeworks will be graded by Monday of final
exam week (the 16th)

Moving On
• There are several different ways to study meaning in
language:
1. Pragmatics
The meaningful use of linguistic expressions in
conversation and discourse.
2. Compositional Semantics
How the meaning of phrases and sentences is built up
from the meanings of individual words.
3. Lexical Semantics
The meaning of individual words, and how they’re
related to one another.

Here’s a question…
• What is “meaning”?
• No, really. What is it? Any ideas?
• The meaning of “meaning” seems to be very complex
and hazy.
• For today, we’ll try to figure out what “meaning” means
for a small, simple set of data and then work from there.
• We’ll be doing compositional semantics.
• …and we’ll focus on the literal meaning of linguistic
expressions, for now.

Possible Worlds
• Consider this idea: we live in one of many possible
different worlds.
• There are certain true statements we can make about the
world in which we live. For instance:
If you jump up, you fall down.
The sun is about 93 million miles away.
Mars is a planet.
It’s chilly outside.
I am teaching linguistics 201.
Hobbits do not exist.

Possible Worlds
• In other possible worlds, different statements might be
true. For instance:
If you jump up, you fly off the surface of the Earth.
The sun has become a black hole.
Pluto is a planet.
The weather in Calgary is always nice.
I am married to Scarlett Johansson.
A hobbit named Frodo stole my wedding ring.

What is truth?
• How do we know that some of these statements are true,
while others are not?
• What does it mean for something to be true?
• Let’s consider the philosophical question this way:
• What sorts of things can be true?
• (hint: think in syntactic terms)
• Can a noun be true? A verb? An adjective?
*Is it true that dog?
*Is it true that escape?
*Is it true that happy?

What is truth? (part 2)
• How about verb phrases or noun phrases?
*Is it true that {make copies}?
*Is it true that {destruction of the city}?
• Whole sentences?
Is it true that Pluto is a planet?
• Declarative sentences can be true.
e.g., “Hobbits do not exist.”
...as opposed to interrogative or imperative sentences
(questions or commands)

A Theory of Truth
• Declarative sentences are also known as propositions.
• Let’s assume that a proposition is true if:
• the information it imparts about the world is actually the
way the world is.
• A philosophical definition:
• truth is the correspondence of propositions to facts.
• This is called the correspondence theory of truth.
• Q: What kind of information can a proposition provide
about the world?

Subjects, Predicates
• Let’s consider declarative sentences with this form:
S → NP VP
• We already know that the NP is called the subject.
• Let’s call the VP the predicate.
• Subjects refer to “persons, places or things”.
• Predicates (roughly) describe relationships between the
persons, places or things.
• Subjects are what’s in the world;
• Predicates are “the way the world is.”

This is the world.
One Possible World

One Possible World
Mars Venus Pluto
Earth
Mercury
Neptune
Jupiter
Uranus
Saturn
The Moon
The Death Star
This is the world.
These are different things
in the world.

One Possible World
Mars Venus Pluto
Earth
Mercury
Neptune
Jupiter
Uranus
Saturn
The Moon
The Death Star
is a planet
this is a predicate

Another Possible World
Mars
Venus
Earth Pluto
Mercury Saturn
Jupiter
Neptune
Uranus
The Moon
The Death Star
is a planet
this is a predicate

Another Possible World
Mars
Mercury
Earth
Jupiter
Venus
Saturn
The Moon
is a planet
this is a predicate

Reference
• Note that the expression “Jupiter” is not the planet Jupiter
itself;
• It’s just a linguistic convention we can use to refer to
the actual thing.
• The actual thing (in the world) is the referent of the word
“Jupiter”.
• Another example:
“Barack Obama”
expression
referent

Reference: Another Example
“The Mona Lisa”
“La Joconde”
“La Gioconda”
expressions
referent
Remember: languages can be arbitrary.

Extension
• A predicate is a set of referents in some possible world.
• This set of referents is known as a predicate’s extension.
Mars Venus Pluto
Earth
Mercury
Neptune
Jupiter
Uranus
Saturn
The Moon
The Death Star
is a planet

Finding the Truth
• With this framework in place, we have a formula for
figuring out whether or not a proposition is true.
• Formula: a proposition is true if the referent of its
subject is contained in the extension of its predicate.
• Consider the proposition: Pluto is a planet.
• The subject’s referent is:
• The predicate’s extension includes:
• Therefore, “Pluto is a planet” is a false proposition.

Truth Values
• In any possible world, a proposition may have one of two
different truth values.
• “Pluto is a planet” may be false.
or
• “Pluto is a planet” may be true.
• We can calculate a proposition’s truth value when we
know:
• what its subject refers to
• the extension of its predicate
• ...in some possible world

More Expressions
• Note: a number of different expressions can refer to the
same thing in the world.
The 43rd President of the United States
The former owner of the Texas Rangers
George H.W. Bush’s oldest son
“43”
“Shrub”
• George W. Bush is the referent of all of these expressions.

There is no Santa Claus
• Note that there are some expressions which have no
real-world referent:
Santa Claus
The Easter Bunny
A Unicorn
Frodo Baggins
The King of the United States
• Q: Are these meaningless expressions?

Sense
• Expressions like “The President of the United States”
have different referents in different possible worlds.
• Consider the referents of this expression in three
possible (past) worlds:
1805: Thomas Jefferson
1905: Teddy Roosevelt
2005: George W. Bush
• Idea: the sense of an expression is the set of its referents
in all possible worlds.
• (Note: the textbook refers to the sense of an expression
as its “intension”.)

Another Example
• From 1979-1999, the expression “8th planet from the
Sun” technically referred to Pluto.
• In all possible worlds, however, the expression “8th
planet from the Sun” refers to:
• the planet which is eighth-most distant from the Sun

Meaning
• Corollary: expressions like “Santa Claus” are not
meaningless, even though they have no referents in this
world.
• Their meaning, or “sense”, is their set of referents in all
possible worlds.
• ⇒ You can talk about Santa Claus because you know
what the world would be like if he existed.

Truth Conditions
• Within this framework, we can now make the following
claim:
• The meaning of a proposition is the set of all possible
worlds in which that proposition is true.
• Another way of saying the same thing:
The meaning of a proposition is the set of conditions in
which that proposition is true.
• I.e., its truth conditions.
• When you know the meaning of a proposition, you know
the conditions under which it can be true.

Rehashed Ad Nauseum
• Check out this possible world:
“It can only be the thought of verdure to come, which
prompts us in the autumn to buy these dormant white
lumps of vegetable matter covered by a brown papery
skin, and lovingly to plant them and care for them. It is a
marvel to me that under this cover they are labouring
unseen at such a rate within to give us the sudden
awesome beauty of spring flowering bulbs. While winter
reigns the earth reposes but these colourless green ideas
sleep furiously.”
--C. M. Street

Compositionality
• By the way:
The idea that the meaning of a sentence can be
calculated from the meaning(s) of its parts is the
principle of compositionality.
• Consider this sentence:
The President of the United States is a white male.
• Is this true? How do you know?
• How about this sentence:
Santa Claus is a white male.

Types of Sentences
• Propositions may be distinguished on the basis of the
kinds of worlds in which they may be true.
1. Synthetic propositions may be true or false,
depending on the state of affairs in the world.
2. Analytic propositions are always true, no matter
what the state of the world.
3. Contradictions are always false, no matter what the
state of the world.
• Quick Write check.

Meaning Summary
• Reference: the actual thing in the world an expression
picks out.
• Extension: a set of referents (= a predicate) in some
possible world.
• Sense: what an expression refers to in all possible worlds.
• Truth: a proposition is true if the referent of its subject is
contained in the extension of its predicate.
• Meaning:
• The meaning of a proposition is the set of conditions in
which that proposition is true.
• Truth conditions