Can Counterfactuals Be True?

But hang on, the foundation of Bayesianism is the counterfactual. P(A|B) = 0.6 means that "If B were true, then P(A) = 0.6 would be true". Where does the truth value of P(A) = 0.6 come from then if we are to accept Bayesianism as correct?

Oh, and to talk about "the probability that John F. Kennedy was shot, given that Lee Harvey Oswald didn't shoot him", we write:

P(Kennedy_shot|Oswald_not)

If I've understood you, this is supposed to be a high value near 1. I'm just a noob at Bayesian analysis or Bayesian anything, so this was confusing me until I realised I also had to include all the other information I know: i.e. all the reports I've heard that Kennedy actually was shot, that someone else became president, and so on.

It seems like this would be a case where it's genuinely helpful to include that background information:

P(Kennedy_shot | Oswald_not & Reports_of_Kennedy_shot) = 1 or thereabouts

And to talk about "the probability that John F. Kennedy would have been shot, if Lee Harvey Oswald hadn't shot him", we write:

P(Oswald_not []-> Kennedy_shot)

Presumably this is the case where we pretend that all that background knowledge has been discarded?

P(Kennedy_shot | Oswald_not & no_knowledge_of_anything_after_October_1963) = 0.05 or something?

Hmm, the second bit I just wrote isn't going to work, I suppose, since your knowledge of what came after the event will affect whether you believe in a conspiracy or not...

Contrary to your usual practice of including voluminous relevant links, you didn't point to anything specific for Judea Pearl. Let's give this link for his book Causality, which is where people will find the graphical calculus you rely on.

You've mentioned Pearl before, but haven't blogged the details. Do you expect to digest Pearl's graphical approach into something OB-readers will be able to understand in one sitting at some point? That would be a real service, imho.

But Judea Pearl tells me just how to compute a counterfactual, given only my beliefs about the actual world.

With Xianhang, I don't understand how you can talk about probabilities without talking about several possible worlds.

how you can talk about probabilities without talking about several possible worlds

But if probability is in the mind, and the mind in question is in this world, why are other worlds needed? Moreover (from wikipedia):

In Bayesian theory, the assessment of probability can be approached in several ways. One is based on betting: the degree of belief in a proposition is reflected in the odds that the assessor is willing to bet on the success of a trial of its truth.

Disposition to bet surely does not require a commitment to possible worlds.

semantic difference, I think. Isn't the distinction just "possible ways this world could be" versus "which of all possible worlds is this one." Is there a meaningful difference?

Eliezer: "A lot of philosophy seems to me to suffer from "naive philosophical realism" - the belief that philosophical debates are about things that automatically and directly exist as propertied objects floating out there in the void."

Well, we do this since we can't fully apprehend reality as a whole, and so must break it down into more manageable components.

I can tell my husband, "If you had not fed the cat, then I would have fed her," because I had such an intention from before the cat was fed, and I remember having said intention.

However, can I really ever know what would have happened if my husband had not fed the cat? Maybe the sun would have exploded, because reality is deterministic, and there was nothing else that could have happened, and such a blatent violation of causality would have blown open the fabric of time...

But this is not an at all useful way of thinking about the world. If we submit to fatalism then there isn't much point in trying to determine anything ourselves, including how to create an fAI and live forever... If we do it, we do it.

Likewise, counterfactuals are important for considering how different variables in our actions shape their outcomes.

"If you had hit me, I would have left you and not come back." Could be true... could be false... What's important? Don't hit her next time!

"If Oswald had not shot Kennedy, then someone else would have." What's important? We need to be very careful in protecting the safety of progressive politicians in the future, like Obama, so they don't go the way of the Kennedy... After all, it happened to Bobby too.

"But this is not an at all useful way of thinking about the world. If we submit to fatalism then there isn't much point in trying to determine anything ourselves, including how to create an fAI and live forever... If we do it, we do it."

If we do it we do it BECAUSE we try to do it, BECAUSE we try to determine it, etc. The archives here in 2008 are largely about how to deal with living in a lawful universe.

"If the federal government hadn't bought so much stuff from GM, GM would be a lot smaller today." "If the federal government hadn't bought so much stuff from GM, GM would have instead been tooling up to produce stuff other buyers did want and thus could very well have become successful that way."

???

The problem with imagining Oswald not killing Kennedy is that we have to figure why he didn't do so. He did it for a reason. Was that reason absent? Was Oswald different in some way?

There is a chain of events before the one that we imagine changed, just as there is a chain of events after. And when we snip out that one event, it would have implications backwards in time as well as forwards. I guess this is where this Pearl model is supposed to tell us how to think about snipping out that event, with minimal backwards-in-time changes - but I can't help wondering if that isn't an arbitrary measure. Why not snip out the event with minimal forwards-in-time changes? Or why not minimize the sum of forwards and backwards changes? That last metric would surely lead to Kennedy being killed in much the same way by another person, since Kennedy living would likely have led to enormous future changes.

In more detail, suppose there was in fact no conspiracy and Oswald was a lone, self-motivated individual. It might still turn out that the simplest way to imagine what would have happened if Oswald had not killed Kennedy, would be to imagine that there was in fact a conspiracy, and they found someone else, who did the job in the same way. That would arguably be the change which would minimize total forward and backward alterations to the timeline.

Michael- my main point was that having ways of thinking about the world that are not the world itself are still useful, while trying to only see the world as it is and nothing else is not.

Yes- it's useful BECAUSE it makes us try to do it, which if we do it, we do it BECAUSE we try to determine it, which we would NOT do if we didn't consider the world as it could be, but only as it has been and as it will be.

In more detail, suppose there was in fact no conspiracy and Oswald was a lone, self-motivated individual. It might still turn out that the simplest way to imagine what would have happened if Oswald had not killed Kennedy, would be to imagine that there was in fact a conspiracy, and they found someone else, who did the job in the same way. That would arguably be the change which would minimize total forward and backward alterations to the timeline.

Hal: what you describe is called "backtracking" in the philosophical literature. It's not usually seen as legitimate, I think mostly because it doesn't correspond to what a sentence like "if X had occurred, then Y would have occurred" actually means in normal usage.

I mean, it's a really weird analysis that says "there really was no conspiracy, so if Oswald hadn't shot Kennedy, there would have been a conspiracy, and Kennedy would have been shot." :)

You could always just juxtapose a box and an arrow: □→

The archives here in 2008 are largely about how to deal with living in a lawful universe.

Lara Foster, consider the possibility that Obama's assassination would be a boon to progressivism, as JFK's death was.

Caledonian, Eliezer has discussed the lawful nature of the universe many times before. If you have some specific disagreement, I find it odd you did not express it then. Could you elaborate?

In this sort of case the motivation for the philosophical realism is that there is a real grammatical construction that's actually used in the world, and we're wondering what it's actual truth-conditions are. Maybe the best model for the semantics of this construction will involve graphical models a la Pearl. Or maybe the best semantics will require that we postulate things called possible worlds that have certain ordering properties. In either case, there will then still be a question whether the sentences ever come out true on the best semantics, or whether we're implicitly committed to certain falsehoods every time we utter the sentence. But it's far from obvious that the proper account of counterfactuals in ordinary language is in terms of some sort of computational procedure.

And actually, indicative conditionals seem to be even more problematic than counterfactuals. There's lots of explaining you need to do to just assimilate them to the material conditional, and if you try to connect them to conditional probabilities then you have to say what truth-values between 0 and 1 mean, and get around all the triviality proofs.

Conditionals in general are quite hard to deal with. But this doesn't mean you can just get away with dismissing them and say that they're never true, because of some naive commitment to everything mentioned in your semantics having to be observable in some nice direct way. If they're not true, then you have to do lots of work to say just what it is that we're doing when we go around uttering them.

The behavior of the objects in a counterfactual can be true to life, but the counterfactual as a whole can't be true.

If you have some specific disagreement, I find it odd you did not express it then.

And when the points have come up before, I've criticized them. Eliezer seems to have a very deep need for known absolutes. But the 'absolutes' he references are contingent and uncertain. For example, he frequently conflates the nature of the universe and our ideas about what the nature of the universe is. The first is consistent and universal, while the second is not, but he persists in speaking as though we had access to eternal truth. All we have is our experiences and our attempts to account for them.

Or look at this case, in which he confuses ultimate reality and our attempts to model it. The question he's asking is absurd, because the concept he's using is meaningless outside of the context it's defined in. "If X, then Y" statements are dependent upon our models - they can be said to be true to the degree that they express the output of our understanding. "If I drop an egg on the floor, then it will break" is an essentially-accurate claim even if I don't get around to dropping an egg.

TGGP- While JFK's assassination may or may not (LBJ???) have been good for progressivism, RFK's was certainly NOT. Nixon won, and then we had drug schedules, and watergate, and all that bullshit...

Here's a counterfactual to consider: What would the world have been like if Bobby Kennedy had been president instead of Nixon?

Still think it would be a good thing for progressivism if Obama is shot and McCaine becomse prez?

Lots of counterfactuals are statements about how we think the world is connected together. We tell stories. We make analogies and metaphors.

Do you think Oswald killed Kennedy because he had free will and he chose to independent of anything else? If Kennedy died because somebody powerful and important wanted to have him killed, then if Oswald hadn't taken the job somebody else surely would have. Maybe somebody else did and we picked up Oswald by mistake.

If Oswald did it for reasons that might influence other people too, then somebody else might very well have been influenced similarly to Oswald. Were there 5 independent lone nuts ready to kill Kennedy? 50? 500? We don't know because the first one to do it, succeeded. If we could re-run the experiment a hundred times and it was Oswald 20% of the time versus Oswald 100% of the time, that would tell us something. If it was Oswald 30% of the time and nobody 70%, that would tell us something else. But we can't rerun the experiment even once.

We can say what we think might have happened, based on our experience with other things applied as similes and metaphors to that one. It isn't reliable. But it's central to the way we think all the time.

Lara Foster, consider the possibility that Obama's assassination would be a boon to progressivism, as JFK's death was.

Where is your evidence that JFK's death helped "progressivism"?

How do you know what would have happened to progressivism if JFK had died considerably later?

Isn't this an example of the fallacy we're talking about?

"But Judea Pearl tells me just how to compute a counterfactual, given only my beliefs about the actual world."

This is actually a subtle issue. The procedure given in the book assumes (a) full knowledge of the precise causal mechanisms (which you never know in practice) and (b) the distribution over all unobserved variables (which you don't know by definition). Surprisingly, it is possible to compute certain counterfactuals using ONLY the distribution over observable variables (which is typically what you get). You can check my thesis for details if you wish.

Completely tangential: many, many years ago, shortly after reading Hofstadter's discussion of counterfactuals in GEB that starts with him driving through a cloud of bees, I accidentally dropped a bowl on the ground.

The bowl shattered into fragments, and I said "Well, it's a good thing I'm me instead of being that bowl!"

It was quite some time before I lived that down.

I was somewhat confused by this post, the language of it. I resolved my confusion, which came through applying more quantitative reasoning to it. Yet, my revised view is the largest deviation from (the appearance of) Eliezer's message I've yet had that has stuck around; past such differences revealed themselves to be flawed under more reflection. (If this view had been internalized it could generate the wording in the post, but the wording of the post doesn't seem to strongly imply it.) I know that going forward I'm going to hold my revised interpretation unless some other evidence presents itself, so I'm going to stick my neck out here in the case that I am mistaken and someone can correct me.

But so long as we have a lawful specification of how counterfactuals are constructed - a lawful computational procedure - then the counterfactual result of removing Oswald, depends entirely on the empirical state of the world.

A counterfactual does not depend (directly) on the actual state of the world, but on one's model of the world. Given a model of the world and a method of calculating counterfactuals we can say whether a counterfactual is mathematically or logically correct. But like the phrase "'snow is white' is true," or "the bucket is true," we can also put forward the proposition that the actual world corresponds to such a state, that our models match up to reality, and ask how likely it is that this proposition is true, with probabilistic beliefs. So we can assign probabilities to the proposition "'If Oswald hadn't shot Kennedy, Kennedy would not have died' is true."

From the post Qualitatively Confused:

To make a long story short, it turns out that there's a very natural way of scoring the accuracy of a probability assignment, as compared to reality: just take the logarithm of the probability assigned to the real state of affairs.

(emphasis added)

We never actually receive "confirmation" that "snow is white," at least in the sense of obtaining a probability of exactly 1 that "'snow is white' is true". Likewise, we never receive confirmation that a counterfactual is true; we just increase the probabilities we assign to it being true.

(I worked out some simple math that allows you to score a probabilistic expectation even if you can't gain full confirmation of what happened, which does nice things like having the same expected score of the basic model, but I won't go into it here, assuming that such math already exists and wasn't the point. I don't disagree with presenting the simpler model, as it works just fine.)

A small comment... Pearl's treatment works fine for "forward-tracking" counterfactuals, where the only allowed changes in the counterfactual world are in the future of the change (i.e. after the point of surgery). However, regular counterfactuals require a bit of "back-tracking" to make the counterfactual scenario plausible in the first place.

Consider these statements:

1. "If Gore had been president during 9/11 he'd have reacted differently, and the US wouldn't have invaded Iraq"
2. "If Gore had been president during 9/11 then he'd have been sworn in as president back in January 2001"
3. "If Gore had been president during 9/11 he'd have been blinking in shock at having suddenly teleported to Air Force One, and wondering why everyone was calling him Mr President"
4. "If Gore had been president during 9/11 he'd have been recently sworn in as president, owing to changing party, Dick Cheney dying of a heart attack, Bush appointing him as vice-president, and then himself dying of shock".

Statement 1 is a forward-tracking counterfactual and arguably true. But the usual way of understanding it to be true assumes that 2 is also true, which is a back-tracking counterfactual (it involves re-writing approximately a year of history before 9/11).

Statement 3 is the only statement consistent with no back-tracking at all, and corresponds to Pearl's approach of performing surgery on the causal graph at 9/11. (This is generally physically impossible, or at least physically absurd, since it involves tearing the graph apart and inserting a new state with no causal relation to the previous states.)

Statement 4 is an odd sort of compromise; it's at least not physically impossible or absurd, and involves the bare minimum of back-tracking (to a political crisis a few days before 9/11). But it is clearly not the best way to understand the counterfactual.

Eliezer you never defined what a counterfactual actually is, so I got the following from the internet:

A counterfactual is a conditional statement:

(Philosophy / Logic) a conditional statement in which the first clause is a past tense subjunctive statement expressing something contrary to fact, as in if she had hurried she would have caught the bus.

As usual, I'm late to the discussion.

The probability that a counterfactual is true should be handled with the same probabilistic machinery we always use. Once the set of prior information is defined, it can be computed as usual with Bayes. The confusing point seems to be that the prior information is contrary to what actually occurred, but there's no reason this should be different than any other case with limited prior information.

For example, suppose I drop a glass above a marble floor. Define:

sh = “my glass shattered”

f = “the glass fell to the floor under the influence of gravity”

and define sh_0 and f_0 as the negations of these statements. We wish to compute

P(sh_0|f_0,Q) = P(sh_0|Q)P(f_0|sh_0,Q)/P(f_0|Q),

where Q is all other prior information, including my understanding of physics. As long as these terms exist, we have no problem. The confusion seems to stem from the assumption that P(f_0|sh_0,Q) = P(f_0|Q) = 0, since f_0 is contrary to our observations, and in this case seemingly mutually exclusive with Q.

But probability is in the mind. From the perspective of an observer at the moment the glass is dropped, P(f_0|Q) at least includes cases in which she is living in the Matrix, or aliens have harnessed the glass in a tractor beam. Both of these cases hold finite probability consistent with Q. From the perspective of someone remembering the observed event, P(f_0|Q) might include cases in which her memory is not trustworthy.

In the usual colloquial case, we’re taking the perspective of someone running a thought experiment on a histroical event with limited information about history and physics. The glass-dropping case limits the possible cases covered by P(f_0|Q) considerably, but the Kennedy-assassination case leaves a good many of them open. All terms are well defined in Bayes’ rule above, and I see no problem with computing in principle the probability of the counterfactual being true.

Who cares if they are true, unless by true you mean useful - having predictive validity. In that case, the answer to are there examples of counterfactual thinking being useful is yes.

"We continue to use counterfactual thoughts to change our future behavior in a way that is more positive, or behavior intention. This can involve immediately making a change in our behavior immediately after the negative event occurred. By actively making a behavioral change, we are completely avoiding the problem again in the future. An example, is forgetting about Mother’s Day, and immediately writing the date on the calendar for the following year, as to definitely avoid the problem.[15] Goal-directed activity

In the same sense as behavior intention, people tend to use counterfactual thinking in goal-directed activity. Past studies have shown that counterfactuals serve a preparative function on both individual and group level. When people fail to achieve their goals, counterfactual thinking will be activated (e.g., studying more after a disappointing grade;[14]). When they engage in upward counterfactual thinking, people are able to imagine alternatives with better positive outcomes. The outcome seems worse when compared to positive alternative outcomes. This realization motivates them to take positive action in order to meet their goal in the future.[16][17]

Markman et al. (1993) identified the repeatability of an event as an important factor in determining what function will be used. For events that happen repeatedly (e.g., sport games) there is an increased motivation to imagine alternative antecedents in order to prepare for a better future outcome. For one-time events, however, the opportunity to improve future performance does not exist, so it is more likely that the person will try to alleviate disappointment by imagining how things could have been worse. The direction of the counterfactual statement is also indicative of which function may be used. Upward counterfactuals have a greater preparative function and focus on future improvement, while downward counterfactuals are used as a coping mechanism in an affective function (1993). Furthermore, additive counterfactuals have shown greater potential to induce behavioral intentions of improving performance.[14] Hence, counterfactual thinking motivates individuals into making goal-oriented actions in order to attain their (failed) goal in the future. Collective action

Main article: Collective action

On the other hand, at a group level, counterfactual thinking can lead to collective action. According to Milesi and Catellani (2011), political activists exhibit group commitment and are more likely to re-engage in collective action following a collective defeat and show when they are engage in counterfactual thinking. Unlike the cognitive processes involved at individual level, abstract counterfactuals lead to an increase in group identification, which is positively correlated with collective action intention. The increase in group identification impacts on people’s affect. Abstract counterfactuals also lead to an increase in group efficacy. Increase in group efficacy translates to belief that the group has the ability to change outcomes in situations. This in turn motivates group members to make group-based actions to attain their goal in the future.[16][18] Benefits and consequences

When thinking of downward counterfactual thinking, or ways that the situation could have turned out worse, people tend to feel a sense of relief. For example, if after getting into a car accident somebody thinks “At least I wasn’t speeding, then my car would have been totaled.” This allows for the positives of the situation to be accounted for, rather than the negatives. In the case of upward counterfactual thinking, people tend to feel more guilty or negatively about the situation. When thinking in this manner, people are focusing on ways that the situation could have turned out more positively. For example, “If only I had studied more, then I wouldn’t have failed my test.” This kind of thinking results in feeling guilty and have a lower sense of self-esteem. “[14]""