### 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.

## 7 Comments:

I doubt that epistemic frames of reference are needed.

How about the following as a recipe for counterfactuals?

Change actuality to make the counterfact true, and then see what CAUSAL differences follow. (In effect, hold the causal laws fixed, plus all particular facts apart from those that are causally downstream from the counterfact.)

Then it's true that, when the (indeterministic) coin comes down heads, 'you would have won, if you'd bet heads'. Even though the actual outcome wasn't determined, that outcome is causally independent of which way you bet, so gets held fixed.

Cf this case: you are stuck on the M4, and so miss your plane. The plane crashes because of engine failure (indeterministically and unlikelily) half-way to Paris. Still on the M4, you look at your watch and say 'if I'd caught the plane, I'd be in Paris already'. Not true. You'd be dead.

Of course, my suggestion is no good for Lewisians who want to analyse causation in terms of counterfactuals.

So much the worse for Lewisians.

Maybe this was what Lee Walters was arguing to start with. If so, sorry for coming in late.

David's suggestion is similar to that of Schaffer (analysis 2004) and Bennett. Edgington suggests this as a way out for closest worlds people too.

I want to bite the bullett and say these counterfactuals are false although assertable - if I'd caught tha plane and everything was otherwise the same then I'd be dead. But if I'd caught the plane we cannot assume everything is otherwise the same even those facts causally independent of me making the flight.

Others disagreed and thought when we assert counterfactuals this is precisely what we do - hold those facts constant that we sensibly can (causaly independent facts) and see what follows.

I failed to convince anyone of my position so must go back to the drawing board.

If I called heads a t, a time when it is indeterminate whether the coin lands heads, then it is indeterminate whether I win the bet. All sides should agree to this. I think this is sufficient to undermine the truth of "if I had called heads at t I would have won". I cannot, although nor can my opponents, establish the falsity (truth) of this conditional without begging the question as to what counts as the closests worlds.

If, like Bennett, you accept the conditional, "If you tossed the coin, it would have come down heads" in an indeterministic world where the coin does come down heads, then I think I can force you to accept the falsity of the "if bet heads then won".

Any takers?

I tend to find David's recipe very tasty, partly because it gives the right answers to the truth of counterfactuals, but mainly because it is compatible with my epistemic frame analysis.

The recipe directs that we should "change actuality to make the counterfact true then see what causal differences follow" But this is impossible for any counterfactual. If we successfully managed to change actuality, then the counterfactual wouldn't be counterfactual anymore. The best we can do is change our best model of actuality, which consists of everything we know minus the counterfacts negation and facts causally downstream according to our best causal laws. This is pretty well what I mean by an epistemic frame of reference.

I think I am with Lee on the indeterministic case. Its just that indeterminism is empirically falsified when the coin comes down heads, since it is determinate that the coin came down heads on this occasion. So Davids recipe works. But suppose the coin wasn't tossed. Is the law of excluded middle applicable to the counterfactual

"if you had bet heads you'd have won"?

I don't think it can be. The best answer is to say that this counterfactual is 50% true and 50%false. This preserves Lees bullet biting whilst also leaving intact the intuition that if the coin had been tossed and had landed heads, then the counterfactual would have been true. (I think this is a countercounterfactual, which isn't the same as a fact)

I'm not quite sure what kinds of cases Lee has in mind.

Suppose that in the actual (indeterministic) world A tosses a coin, B calls 'tails', the coin lands heads.

I assert (with Bennett and Edgington (good company)) that: if B had called 'heads', B would have won.

That's because I take B's call to have no causal influence on the coin, and so I hold fixed the fact that the coin landed heads.

On the other hand, I don't assert that: if B had tossed the coin (rather than A), it would have landed heads.

That's because B tossing the coin rather than A certainly does have a causal influence on the coin.

Lee also says that my view can't defeat his without begging the question about which worlds are closest.

I don't think that we arrive at counterfactual judgements via judgements about closeness of worlds. (Even Lewis admits this--the similarity metric needed to do a poss worlds semantics for counterfactuals is not at all intuitive.) Rather, there's some other grounds for counterfactual judgements, and this then imposes a similarity metric on poss worlds.

I think we use counterfactual judgements to keep track of what causally depends on what (v useful for planning, ascribing responsibility, making certain inferences . . .) Given this, the recipe 'hold the causal laws fixed, plus all particular facts apart from those that are causally downstream from the counterfact, and see what follows' seems entirely natural. It doesn't need any further justification in terms of poss worlds or anything like that.

David's view has then consequence that the truth of the counterfactual depends on whether or not the consequent is causally downstream from the counterfact. I doubt that there is necessarily a fact of the matter whether A is causally downstream from B when B did not in fact happen. Let's suppose that Jim is unlucky. The following rule is true in all cases: "Whenever Jim places a bet he loses" Let's say he doesn't believe this himself and consequently loses many bets in his life. On this occasion he bets heavily on tails and the coin comes up heads. He then says "If I had bet on heads I would have won". But what he said here could be false. The reasoning here is that because he loses every time he places a bet, he would have lost whatever bet he had placed.

Now it seems that the truth of the counterfactual depends on whether the rule "Jim never wins a bet" is counterfactual supporting. If in the actual world Jim never wins a bet, there is nothing in the world which can decide the matter. We could decide the matter this way, if "Jim never wins a bet" is a causal law, then it supports counterfactuals, if it is just an accidental generalisation, then it does not. This is fine by me. It means that whether a counterfactual is true depends on which true generalisation count as laws in your model of the world. I see no reason why there can't be two perfectly adequate models of the world such that "Jim is unlucky" is a causal law in one but just a true generalisation in the other. The proposition "If Jim had bet heads he would have won" is true relative to one epistemic frame of reference and false relative to the other. It won't do to be platonic realist about causal laws either, because many heuristics and rules of thumb are counterfactual supporting.

Example, "If it was John who was marrying July he would have turned up late". This is true if you accept the rule that John is usually late is counterfactual supporting, false otherwise.

There is an interesting point which david's "would the counterfact have made a difference" approach addresses.

Some quantum events (not coin tosses) are thought to be truly indeterminate. Coin tosses are merely unpredictable.

With truly indeterminate events it is not wholly obvious that even if exactly the same preconditions occured the outcome would have been the same. All that is given is that the probability of an outcome would be the same. This makes any talk of 'if you had done this then that' or 'in a possible world in which things were thus this would have happened' difficult. I am not sure it is true to claim in relation to a truly indeterministic event that "even though the outcome wasn't determined, that outcome is causally independent of which way you bet so gets held fixed".

It is however in certain circumstances true to claim that changing a given factor (how you bet, for example) would have no effect on the outcome even if that outcome is undetermined.

Where does this get us with the man facing a truly indeterminate coin toss (e.g. some heads or tails machine triggered by nuclear decay)? He bets heads; the machines says tails. We say to him "had you bet tails you would be rich". If all we mean is that his betting tails would not have changed the outcome of the coin toss then what we say is true. If we mean 'If you had bet tails and if the machine had said tails then you would be rich' then we have said something true but rather uninformative. If we mean 'If everything had been exactly the same other than that you bet tails then the machine would have said tails and you would be rich' then I suggest we have said something false for we cannot make that claim about truly indeterminate events

Here's what I take to be a sound argument with a counterfactual conclusion.

1. If I bet heads on the toss of a coin and the coin comes up heads then I win the bet.

2. This coin toss came up heads.

Therefore:

3. If I had bet heads on this coin toss I would have won the bet.

Here is another sound argument.

1. If I bet heads on the toss of a coin that has a 50% chance of coming up tails, then I have a 50% chance of losing the bet.

2. This coin toss had a 50% chance of landing tails.

Therefore

3. If I had bet heads on this coin toss, I would have had a 50% chance of losing.

Lee I guess is pointing out that the conclusions of these arguments are incompatible, therefore the first argument is invalid.

I guess anonymous's point is that in indeterminist quantum events, the second argument is valid therefore the first argument is invalid. However, if indeterminism is true of (some) coin tosses then both arguments should be valid, since both second premises are true.

The coin DID land heads and the probability that the coin landed tails IS 50%. What is needed is an interpretation of probability that can handle this seeming contradiction. In my view, this constitutes an argument against objective chance.

Post a Comment

<< Home