Language and coordination
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Language and Coordination. Convention in the Theory of Meaning. Connotes. Dog. Dog. Mind. Idea of a Dog. Conventional Relation. Dog. Dog. Mind. Idea of a Dog. The Absurdity of Fit. The “convention” that associates an idea with a word can’t just be due to the person using the word.

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Language and Coordination

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Language and coordination

Language and Coordination


Convention in the theory of meaning

Convention in the Theory of Meaning


Language and coordination

Connotes

Dog

Dog

Mind

Idea of a Dog


Language and coordination

Conventional Relation

Dog

Dog

Mind

Idea of a Dog


The absurdity of fit

The Absurdity of Fit

The “convention” that associates an idea with a word can’t just be due to the person using the word.

This is because you can use a word wrongly, even if it’s in accord with your idea.


Language and coordination

Personally Associates

Dog

Dog

Mind

Idea of a Dog


Language and coordination

Still Means

Dog

Dog

Mind

Idea of a Dog


Language and coordination

Connotes

“Dagger”

Dagger

Mind

Experience of a wound


Language and coordination

Conventional Relation

“Dagger”

Dagger

Mind

Experience of a wound


Language and coordination

Personally Associates

“Dagger”

Dagger

Mind

Experience of a wound


Language and coordination

Still Means

“Dagger”

Dagger

Mind

Experience of a wound


Language and coordination

Connotes

Dog

Dog

Mind

Definition of “Dog”


Language and coordination

Conventional Relation

Dog

Dog

Mind

Definition of “Dog”


Language and coordination

Personally Associates

Dog

Dog. n. A deer, a female deer.

Dog

Mind

Definition of “Dog”


Language and coordination

Still Means

Dog

Dog. n. A deer, a female deer.

Dog

Mind

Definition of “Dog”


The causal historical theory

The Causal-Historical Theory

Even in the case of the causal-historical theory (where there is no denotation), it seems as though what the community calls things is important.


Language and coordination

Let’s call that place ‘Mogadishu’

Madagascu

Madagishu

Madagascar

Madagasceir

Denotation


The use theory

The Use Theory

What about the use theory? Doesn’t Horwich explicitly argue that meaning is not a conventional relation, but rather a natural one?


Indication

Indication

Smoke means (indicates the presence of) fire.


The use theory1

The Use Theory

means

and

AND


Horwich i s wrong

HorwichIs Wrong

But Horwich is wrong: the connection between smoke and fire is grounded in the laws of the universe.

The connection between a word and the concept it expresses is wholly conventional.


The use theory2

The Use Theory

gift

GIFT

POISON

gift


Game theory

Game Theory


Decisions

Decisions

Sometimes what happens to us depends entirely on what we do, and not on what other people do.

This doesn’t mean that decision making in such cases is easy or trivial. For example, suppose someone’s life is on the line, and it is my job to decide whether to convict or acquit them.


Decision under risk

Decision under Risk


Decision theory

Decision Theory

A number of factors are relevant here:

  • How likely do I think it is that the person committed the crime?

  • How much worse is it to convict an innocent person than to let a guilty one go?

    Decision theory is devoted to telling us how to act when we must make decisions under risk.


Games

Games

Sometimes what happens to us does depend on what others do as well.

  • Whether I have a good time tonight depends not just on whether I go to the party, but on whether other people come too.

  • Whether I win a chess match depends not just on the moves I make, but the moves my opponent makes as well.

  • Whether nuclear disarmament is good depends on whether my enemies disarm as well.


The disarmament game

The Disarmament Game


Numbers

Numbers

In game theory we usually use numbers to represent the value of an outcome.

I won’t go into how we assign the numbers… let’s say we just make them up.


The disarmament game1

The Disarmament Game


Equilibria

Equilibria

An equilibrium point is a square on the grid where no player can improve his position through unilateral deviation.

Unilateral deviation is when one player changes strategy and all the other players do not.


The disarmament game2

The Disarmament Game

?


The disarmament game3

The Disarmament Game

?


The disarmament game4

The Disarmament Game


The disarmament game5

The Disarmament Game

?


The disarmament game6

The Disarmament Game

?


The disarmament game7

The Disarmament Game


The disarmament game8

The Disarmament Game

?


The disarmament game9

The Disarmament Game

?


The disarmament game10

The Disarmament Game


The disarmament game11

The Disarmament Game

?


The disarmament game12

The Disarmament Game

Equilibrium


Dominance

Dominance

A dominant strategy is one where a player gets a better outcome, regardless of what the other player does.


The disarmament game13

The Disarmament Game

Dominant


The disarmament game14

The Disarmament Game

Dominant


The disarmament game15

The Disarmament Game

Dominant


The disarmament game16

The Disarmament Game

Not Dominant


The disarmament game17

The Disarmament Game

Not Dominant


Equilibria as solutions

Equilibria as Solutions

An equilibrium strategy is a “solution” to a game. It’s what we predict will happen, and it’s what “rational” players will choose.

John Nash proved that there’s always an equilibrium (if we allow mixed strategies).


The prisoner s dilemma

The Prisoner’s Dilemma

Two people are arrested for a crime. The police do not have enough evidence to convict them of that crime, but they can convict them of a lesser crime, and send them to prison for a year.


The prisoner s dilemma1

The Prisoner’s Dilemma

However, they are offered the chance to confess to the more serious crime:

  • If Prisoner 1 confesses and Prisoner 2 does not, 1 goes free and 2 gets a long prison sentence.

  • If Prisoner 2 confesses and Prisoner 1 does not, 2 goes free and 1 gets a long prison sentence.

  • If both confess, each gets a 5 year sentence.

  • If neither confess, both get a 1 year sentence.


The prisoner s dilemma2

The Prisoner’s Dilemma


Confessing is dominant

Confessing is Dominant

Player 1 can reason as follows:

If 2 confesses, I’m better off confessing, because 5 years in prison is better than 10.

If 2 doesn’t confess, then I’m better off confessing, because 0 years in prison is better than 1.

Therefore, I should confess.


The prisoner s dilemma3

The Prisoner’s Dilemma

Equilibrium


The prisoner s dilemma4

The Prisoner’s Dilemma

Equilibrium

Clearly Better!


The evolution of morality

The Evolution of Morality

Some philosophers have suggested that the point of moral rules is to avoid rational-but-worse outcomes. Cases where it’s good for you if you do X, but bad if everyone does X.

  • Don’t rat out your friends.

  • Put trash in the garbage cans.

  • Let passengers alight first.

  • Wait your turn in line.

  • Don’t steal.

  • Don’t kill people over disagreements.


Coordination problems

Coordination Problems


Example 1 meeting

Example 1: Meeting

Suppose two people want to meet, but they have no way of communicating with each other.

It does not matter where they go, as long as they go to the same place.


Example 2 driving

Example 2: Driving

Cars have just come to our country. We have plenty of roads to drive on, but sometimes they are winding and we cannot see who is coming.

It doesn’t matter what side of the street we drive on– right or left– as long as everyone drives on the same side.


Example 3 searching

Example 3: Searching

Suppose we are camping and need firewood. It would be bad if any of us searched places that others have already looked. Thus we each want to cover different ground.

It doesn’t matter to any person which direction he goes in, as long as he goes in a direction no one else goes in.


Example 4 dressing fashion

Example 4: Dressing/ Fashion

We are all going to a party. It would be bad to dress in suits if everyone at the party is wearing blue jeans and t-shirts. Similarly, it would be bad to wear jeans and a t-shirt to a party where everyone was wearing suits.

It doesn’t matter to us what we wear as long as we are wearing what everyone else is wearing.


Example 5 money

Example 5: Money

Throughout history, people have used different things as money: gold, silver, sea shells, salt (whence ‘salary’), goats, cigarettes (in prison), coins and paper currency.

It doesn’t matter to me what I accept in exchange for my goods and labor as long as it’s what everyone else accepts (as long as I can spend it).


Example language

Example? Language

Suppose I want to talk about dogs.

It doesn’t matter what word I use, so long as it’s the word everyone else uses to talk about dogs.


Suggestion

Suggestion

Maybe language is a coordination problem and can be understood through game theory! Here are some thoughts about what’s similar in these cases:

  • The solutions to all our problems are equilibrium points. (For example: no one benefits by unilaterally deviating from the rule “drive on the left”).

  • There are multiple equilibrium points. (Example: drive on the left OR drive on the right).


The meeting game

The Meeting Game


The meaning game

The Meaning Game


Conventions

Conventions

The problem here is different from the Prisoner’s Dilemma. There we had to move people away from an equilibrium point to a different point.

In coordination problems we have to get everyone to the same equilibrium. Next time we’ll talk about how conventions are used to solve coordination problems


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