Semantics

December 3, 2010

The “Maxims” of Conversation• General Principle: be cooperative

• The maxims are not rules;

• They can be obeyed, dis-obeyed, or even flouted.

• Flouting a maxim =

• Disobeying it in a way that is obvious to the listener.

• Flouting is meant to draw attention to the fact that you’re disobeying the maxim.

• can indirectly provide information to the listener.

• However: the maxims can also be dis-obeyed without the listener noticing.

Maxims, Reviewed• Maxim #1: Relevance.

• = say things that are relevant to the topic under discussion.

• Prevents randomness and incoherence.

• Maxim #2: Quality.

• Don’t say what you believe to be false.

• Don’t say what you can’t back up.

• Maxim #3: Quantity.

• Make your contribution as informative as is required.

• Do not make your contribution more informative than is required.

Flouting Quantity• Stating necessary truths, (tautologies, or analytic sentences) is an example of flouting the maxim of quantity.

• War is war.

• Either Bob will come, or he won’t.

• If she does it, she does it.

Maxim #4: Manner• The maxim of manner: be clear.

• This one breaks down into four parts:

• Avoid obscurity

• Avoid ambiguity

• Be brief

• Be orderly

• A flouting example:

At the concert last night, Jessica Simpson produced a series of sounds corresponding somewhat to the score of “The Star Spangled Banner”.

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.”

One Possible World

This is the world.

One Possible World

This is the world.

Mars Venus Pluto

Earth

Mercury Saturn

Jupiter The Moon

Neptune

Uranus The Death Star

These are different things in the world.

One Possible World

Mars Venus Pluto

Earth

Mercury Saturn

Jupiter The Moon

Neptune

Uranus The Death Star

is a planet this is a predicate

Another Possible World

Mars Venus

Earth Pluto

Mercury Saturn

Jupiter The Moon

Neptune

Uranus The Death Star

is a planet this is a predicate

Another Possible World

Mars Venus

Earth

Mercury Saturn

Jupiter 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

expressions referent

“The Mona Lisa”

“La Joconde”

“La Gioconda”

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.

is a planet

Mars Venus Pluto

Earth

Mercury Saturn

Jupiter The Moon

Neptune

Uranus The Death Star

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