Language and Coordination
Convention in the Theory of
Meaning
Connotes
Dog
Mind
Idea of a Dog
Dog
Conventional Relation
Dog
Mind
Idea of a Dog
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.
This is because you can use a word wrongly, even if it’s in accord with
your idea.
Personally Associates
Dog
Mind
Idea of a Dog
Dog
Still Means
Dog
Mind
Idea of a Dog
Dog
Connotes
“Dagger”
Mind
Experience of
a wound
Dagger
Conventional Relation
“Dagger”
Mind
Experience of
a wound
Dagger
Personally Associates
“Dagger”
Mind
Experience of
a wound
Dagger
Still Means
“Dagger”
Mind
Experience of
a wound
Dagger
Connotes
Dog
Mind
Definition of
“Dog”
Dog
Conventional Relation
Dog
Mind
Definition of
“Dog”
Dog
Personally Associates
Dog
Dog. n. A deer,
a female deer.
Mind
Definition of
“Dog”
Dog
Still Means
Dog
Dog. n. A deer,
a female deer.
Mind
Definition of
“Dog”
Dog
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.
Let’s call that
place ‘Mogadishu’
Madagishu
Madagascu
Madagasceir
Madagascar
Denotation
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
Smoke means (indicates the
presence of) fire.
The Use Theory
means
AND
and
Horwich Is 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 Theory
GIFT
POISON
gift
gift
Game Theory
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
Innocent
Guilty
Conviction
Very Bad
Good
Acquittal
Good
Bad
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
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
Country 2
Disarm
Don’t Disarm
Great
Amazing
Country 1
Disarm
Great
Terrible
Bad
Don’t Disarm
Good
Acceptable
Acceptable
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 Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
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 Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
?
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
?
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
?
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
?
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
?
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
?
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
0
?
Don’t Disarm
5
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
0
Equilibrium
Don’t Disarm
5
0
Dominance
A dominant strategy is one where a player gets a better outcome,
regardless of what the other player does.
The Disarmament Game
Country 2
Dominant
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Dominant
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Dominant
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-15
-5
Don’t Disarm
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-5
Not Dominant
Don’t Disarm
-15
5
0
0
The Disarmament Game
Country 2
Disarm
Don’t Disarm
10
15
Country 1
Disarm
10
-5
Not Dominant
Don’t Disarm
-15
5
0
0
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
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 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 Dilemma
Prisoner 2
Confess
Stay Silent
-5
-10
Prisoner 1
Confess
-5
0
0
Stay Silent
-10
-1
-1
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 Dilemma
Prisoner 2
Confess
Stay Silent
-5
-10
Prisoner 1
Equilibrium
Confess
-5
0
0
Stay Silent
-10
-1
-1
The Prisoner’s Dilemma
Prisoner 2
Confess
Stay Silent
-5
-10
Prisoner 1
Equilibrium
Confess
-5
0
0
-1
Clearly Better!
Stay Silent
-10
-1
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
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
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
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
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
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
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
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
Person 2
Place 1
Place 2
1
0
Person 1
Place 1
1
0
0
Place 2
0
1
1
The Meaning Game
Person 2
“Dog”
“Chien”
1
0
Person 1
“Dog”
1
0
0
“Chien”
0
1
1
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