Language and Coordination

Convention in the Theory of Meaning

Mind Idea of a Dog Dog Connotes Dog

Mind Idea of a Dog Dog Conventional Relation 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.

Mind Idea of a Dog Dog Personally Associates Dog

Mind Idea of a Dog Dog Still Means Dog

Mind Experience of a wound Dagger “Dagger” Connotes

Mind Experience of a wound Dagger “Dagger” Conventional Relation

Mind Experience of a wound Dagger “Dagger” Personally Associates

Mind Experience of a wound Dagger “Dagger” Still Means

Mind Definition of “Dog” Dog 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.

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’ MadagascarMadagasceir Madagascu Madagishu 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 and AND means

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 GIFT gift POISON

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 InnocentGuilty ConvictionVery BadGood Acquittal GoodBad

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 Country 1 DisarmDon’t Disarm Disarm Great Amazing Terrible Don’t Disarm Bad Good 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 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm

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 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm ?

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm Equilibrium

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 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm Dominant

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm Dominant

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm Dominant

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm Not Dominant

The Disarmament Game Country 2 Country 1 DisarmDon’t Disarm Disarm Don’t Disarm Not Dominant

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 Prisoner 1 ConfessStay Silent Confess Stay Silent 0 -10

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 Prisoner 1 ConfessStay Silent Confess Stay Silent Equilibrium

The Prisoner’s Dilemma Prisoner 2 Prisoner 1 ConfessStay Silent Confess Stay Silent Equilibrium Clearly Better!

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 Person 1 Place 1Place 2 Place Place

The Meaning Game Person 2 Person 1 “Dog”“Chien” “Dog” “Chien”

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