### Jonny on Lee Walters on counterfactuals

Lee Walters gave a talk today at (The legendary) William Bynoe’s Metaphysics Group on my favourite topic: counterfactuals. Unfortunately I had to go just when it was getting interesting so this is a counterfactual post about what I would have said if I had been there.

I’ll jump straight to the controversy. I bet five pounds on tails. The coin comes up heads. Now we have the counterfactual.

1) If I had bet on heads I would have won.

First up: does this sentence express a true proposition? Intuitions please. (Yes it does)

A quick word on why this is important. It seems that a good theory of counterfactuals should make 1) come out true given that the coin actually came up heads. However, the problem lies in trying to give an account of counterfactuals where you hold the past fixed up to the point where the counterfact antecedent happens and then forward from there following the expected causal consequences of the counterfact. (I’ve just made up the word “counterfact” meaning the antecedent of a counterfactual, in this case that I bet on heads). But if I had bet heads, at the time of betting given that coin tosses are indeterministic, then the chance of me winning would have only been ½. So the counterfactual should come out as

2) If I had bet on heads I might have won and I might have lost.

Lee bites the bullet and says that 1) is in fact false. But this is only on the assumption that the consequent was indeterministic. I don’t understand objective probability, nor what indeterministic means in any non epistemic sense. I believe that all probability is relative to an epistemic frame of reference. If we specify the frame of reference the problem goes away.

So as far as I knew at the time, I might have lost with a bet on heads; but I now know that had I bet on heads I would have won. Here 1) and 2) are compatible.

My analysis of counterfactuals is that a counterfactual is relative to an epistemic frame of reference. The epistemic frame of reference includes any facts that are known to the relevant subject minus any counterfacts and their causal consequences specified or tacitly assumed. The relevant subject would normally be the speaker, but could be the subject of a counterfact action.

An example to show the plausibility of this view.

Person 1. If you’d bet on heads you’d have won.

Person 2. Yes, but there is no way I could have known that. As far as I knew at the time, if I had have bet on heads, I could have lost.

The agreement between person 1 and 2 shows that the epistemic frame of reference changes the truth conditions of the counterfactual, since otherwise person 1 and person 2 are asserting inconsistent counterfactuals.

Suppose Person 1 said before the toss but after Person 2 has bet on tails:

“If you had have bet on heads you would be going to win”

I think the most natural interpretation of this counterfactual is that it is true if the coin comes up heads. It is a bit difficult to parse because Person 1 would not be in a position to know that the coin was to come up heads so the knowledge norm of assertion forbids him from asserting it. But if we take a rigged horse race or a non gambling situation it becomes more plausible.

If you’d have caught the train, you would be going to arrive on time.

If you’d only have bet on Black Beauty, you’d be buying us all a drink tonight.

The point is that 1) is true if the fact that the coin is heads is fixed in our epistemic frame of reference. It is false otherwise.

One last example. Persons 1 and 2 enter into a gambling den and are offered a bet of £2000 on either heads or tails for the next toss of a coin. Being puritans they walk out in disgust without waiting to see whether the coin came up heads or tails.

Person 1 says; 1) “If you had bet on heads, you would have won.”

I think that Person 1 is in no position to assert this, but if he did it would have been true if and only if the coin had landed heads. Because in his epistemic frame of reference the coin landed heads has a probability of 50%, person 2 could rebuke him by saying. “No, you are wrong, I could just as easily have lost.” This is because from their epistemic frame of reference, it is true that if they had bet on heads they would have had a 50% chance of winning and it is therefore false that if they had bet on heads they would have won.

I’ll jump straight to the controversy. I bet five pounds on tails. The coin comes up heads. Now we have the counterfactual.

1) If I had bet on heads I would have won.

First up: does this sentence express a true proposition? Intuitions please. (Yes it does)

A quick word on why this is important. It seems that a good theory of counterfactuals should make 1) come out true given that the coin actually came up heads. However, the problem lies in trying to give an account of counterfactuals where you hold the past fixed up to the point where the counterfact antecedent happens and then forward from there following the expected causal consequences of the counterfact. (I’ve just made up the word “counterfact” meaning the antecedent of a counterfactual, in this case that I bet on heads). But if I had bet heads, at the time of betting given that coin tosses are indeterministic, then the chance of me winning would have only been ½. So the counterfactual should come out as

2) If I had bet on heads I might have won and I might have lost.

Lee bites the bullet and says that 1) is in fact false. But this is only on the assumption that the consequent was indeterministic. I don’t understand objective probability, nor what indeterministic means in any non epistemic sense. I believe that all probability is relative to an epistemic frame of reference. If we specify the frame of reference the problem goes away.

So as far as I knew at the time, I might have lost with a bet on heads; but I now know that had I bet on heads I would have won. Here 1) and 2) are compatible.

My analysis of counterfactuals is that a counterfactual is relative to an epistemic frame of reference. The epistemic frame of reference includes any facts that are known to the relevant subject minus any counterfacts and their causal consequences specified or tacitly assumed. The relevant subject would normally be the speaker, but could be the subject of a counterfact action.

An example to show the plausibility of this view.

Person 1. If you’d bet on heads you’d have won.

Person 2. Yes, but there is no way I could have known that. As far as I knew at the time, if I had have bet on heads, I could have lost.

The agreement between person 1 and 2 shows that the epistemic frame of reference changes the truth conditions of the counterfactual, since otherwise person 1 and person 2 are asserting inconsistent counterfactuals.

Suppose Person 1 said before the toss but after Person 2 has bet on tails:

“If you had have bet on heads you would be going to win”

I think the most natural interpretation of this counterfactual is that it is true if the coin comes up heads. It is a bit difficult to parse because Person 1 would not be in a position to know that the coin was to come up heads so the knowledge norm of assertion forbids him from asserting it. But if we take a rigged horse race or a non gambling situation it becomes more plausible.

If you’d have caught the train, you would be going to arrive on time.

If you’d only have bet on Black Beauty, you’d be buying us all a drink tonight.

The point is that 1) is true if the fact that the coin is heads is fixed in our epistemic frame of reference. It is false otherwise.

One last example. Persons 1 and 2 enter into a gambling den and are offered a bet of £2000 on either heads or tails for the next toss of a coin. Being puritans they walk out in disgust without waiting to see whether the coin came up heads or tails.

Person 1 says; 1) “If you had bet on heads, you would have won.”

I think that Person 1 is in no position to assert this, but if he did it would have been true if and only if the coin had landed heads. Because in his epistemic frame of reference the coin landed heads has a probability of 50%, person 2 could rebuke him by saying. “No, you are wrong, I could just as easily have lost.” This is because from their epistemic frame of reference, it is true that if they had bet on heads they would have had a 50% chance of winning and it is therefore false that if they had bet on heads they would have won.