What Does It Mean for One Thing to Cause Another?

Here’s a strange thing philosophers noticed. Suppose you want to know whether smoking causes lung cancer. You can’t just look at whether every smoker gets lung cancer—they don’t. Some smokers stay healthy, and some non-smokers get lung cancer anyway. So the connection isn’t a simple “if this, then always that.”

But that doesn’t mean there’s no connection. Smokers are more likely to get lung cancer than non-smokers. That’s a different kind of relationship. A cause doesn’t have to guarantee its effect. It just has to change the probability.

This observation led to an entire branch of philosophy: trying to understand causation in terms of probability. The idea is seductive, because probability is something we can measure and calculate with. If we can figure out the mathematical rules connecting causes to probabilities, we might be able to solve some puzzles that have bothered philosophers for centuries.

The Basic Idea: Causes Raise Probability

The simplest version of the idea goes like this: a cause raises the probability of its effect. Formally, if C causes E, then the probability that E happens, given that C happens, is higher than the probability that E happens given that C doesn’t happen.

This sounds straightforward, but it immediately runs into problems.

Problem 1: Spurious correlations. Imagine a drop in atmospheric pressure. This causes both a drop in the mercury in a barometer and a storm. Now suppose you look at the barometer and see the mercury drop. You’d predict a storm is coming. And you’d be right—the barometer reading and the storm are correlated. But the barometer reading doesn’t cause the storm. They just share a common cause (the pressure drop). The correlation is “spurious”—it’s real, but it doesn’t indicate a causal connection.

So if all we do is check whether C raises the probability of E, we’ll mistakenly think the barometer reading causes the storm. We need a way to distinguish real causes from things that are just correlated because of a shared cause.

Problem 2: The direction problem. Probability raising is symmetric. If C raises the probability of E, then E also raises the probability of C. (Try it mathematically if you like—the numbers work out that way.) But causation isn’t symmetric. Smoking causes lung cancer, but lung cancer doesn’t cause smoking. So we need something more than just probability raising to tell us which direction the causation runs.

Problem 3: Mixed effects. What if a cause raises probability in most situations but lowers it in a few? Suppose there’s a rare gene that makes smoking actually prevent lung cancer in people who have it. Then does smoking “cause” lung cancer? It does for most people, but not for everyone. Should we say it’s a cause overall, or not?

Screening Off and Common Causes

Hans Reichenbach, a philosopher and physicist who worked on these problems in the 1950s, introduced a useful concept. He noticed that when you have a chain of causation (A causes C, which causes E), the middle cause C “screens off” A from E. That means: once you know whether C happened, knowing about A gives you no extra information about E.

For example: unprotected sex causes HIV infection, which causes AIDS. Once you know someone is infected with HIV, it doesn’t matter how they got it—their probability of developing AIDS is the same. The HIV infection screens off the unprotected sex from the AIDS.

But here’s the twist: common causes also screen off their effects. If the drop in atmospheric pressure causes both the barometer reading and the storm, then once you know about the pressure drop, the barometer reading gives you no extra information about the storm.

So screening off can happen in two different situations: chains of causation and common causes. Reichenbach thought we could use this to solve the problem of spurious correlations. If C and E are correlated, we check whether there’s some earlier event that screens them off. If there is, maybe the correlation is spurious—they share a common cause. If there isn’t, maybe C really does cause E.

Reichenbach also proposed a “Common Cause Principle”: any time two events are correlated and neither causes the other, there must be some common cause that explains the correlation. This principle is controversial. Physicists have shown that in quantum mechanics, there are correlations that seem to have no common cause. But for everyday-sized objects, it seems to hold pretty well.

The Problem of Background Contexts

Nancy Cartwright, a philosopher working in the 1970s, noticed another problem. Sometimes a cause can actually lower the probability of its effect overall, even though it raises the probability in every specific situation. This is a version of something called Simpson’s Paradox.

Here’s an example. Imagine that smoking is more common among people who live in the country. Now suppose that city pollution is an extremely strong cause of lung cancer—much stronger than smoking. It could turn out that smokers are less likely to get lung cancer than non-smokers overall, because non-smokers are more likely to live in polluted cities. But if you look just at people who live in the country, smokers are more likely to get lung cancer than non-smokers. And if you look just at people who live in the city, the same thing holds: smokers are more likely to get lung cancer.

So smoking raises the probability of lung cancer in every “background context” (country or city), but it lowers the probability overall. If we just check the overall probability, we’ll miss the real causal relationship.

Cartwright’s solution: a cause must raise the probability of its effect in every background context. But this creates a new problem. What counts as a “background context”? How do we know which factors to hold fixed? The answer turns out to involve knowing what other causes are at work—which means we can’t define causation in terms of probability alone without already having some causal knowledge.

Causal Models: A New Approach

In the 1990s and 2000s, computer scientist Judea Pearl and philosophers Peter Spirtes, Clark Glymour, and Richard Scheines developed a more sophisticated approach. Instead of trying to define causation in terms of probability, they built models that represent causal relationships and then asked what probabilities those models predict.

Here’s the basic setup. You have a set of variables (things that can take different values, like “whether the person smokes” or “whether they get lung cancer”). You draw a diagram with arrows showing which variables directly cause which others. This is called a “causal graph.” Then you add probabilities—for each variable, you specify the probability it will take each possible value, given the values of its causes.

The key insight is the “Markov Condition.” It says that once you know the values of a variable’s direct causes (its “parents” in the graph), knowing anything else about the system gives you no extra information about that variable. Your parents screen you off from everything outside your family.

This condition is powerful. It means you can calculate the probability of any combination of events just by multiplying together the probabilities of each variable given its parents. And it means that certain patterns of probability dependence and independence can tell you about the structure of the causal graph.

For example, imagine three variables: X, Y, and Z. Suppose X and Z are independent of each other (knowing X tells you nothing about Z), but they become dependent when you know Y (knowing Y makes X and Z relevant to each other). This pattern—independence when alone, dependence when conditioned on Y—is the signature of a “collider”: Y is caused by both X and Z. The graph looks like X → Y ← Z.

This is important because it gives us a way to figure out causal direction. In the simple probability-raising approach, causes and effects looked symmetric. But colliders create a distinctive pattern of conditional probabilities that can tell us which way the arrows point.

Actual Causation: What Actually Happened

So far, we’ve been talking about “general” causation: whether smoking in general causes lung cancer. But philosophers also care about “actual” causation: did this particular person’s smoking cause their lung cancer?

These can come apart. Imagine Billy and Suzy both throw rocks at a bottle. Suzy’s rock hits and breaks it. Billy’s rock misses. Billy’s throw definitely increased the probability that the bottle would break—it was a second rock heading toward the bottle. But Billy’s throw didn’t actually cause the bottle to break. Suzy’s did.

This is the problem of “fizzlers”: events that have the potential to cause something but don’t actually do it. A good theory of actual causation needs to distinguish the real cause (Suzy’s throw) from the fizzler (Billy’s throw).

One approach comes from David Lewis, who used counterfactuals. Suzy’s throw caused the bottle to break, he argued, because if she hadn’t thrown, the bottle wouldn’t have broken (or would have been much less likely to break). Billy’s throw didn’t cause the break, because even if he hadn’t thrown, the bottle would still have broken (Suzy’s rock was on its way).

But counterfactuals can get complicated. What if Billy would have thrown only if Suzy didn’t? Then Suzy’s throw actually prevented Billy from throwing—she lowered the probability of the bottle breaking by substituting her less accurate throw for his more accurate one. Yet her throw still caused the break. This is the problem of “preemption.”

More recent approaches use causal models to handle these cases. The basic idea is to look at what happens when you intervene to change a variable while holding other things fixed. Suzy’s throw causes the break because, holding fixed that Billy didn’t throw, setting Suzy to “throw” gives a much higher probability of breakage than setting her to “don’t throw.” Billy’s throw fails as a cause because, holding fixed that Billy’s rock missed, setting Billy to “throw” doesn’t change the probability of breakage compared to setting him to “don’t throw.”

Why This Still Matters

Philosophers still argue about all of this. Nobody has produced a theory of causation that handles every tricky case without problems. But the work on probabilistic causation has real-world applications.

The methods Pearl and others developed are used in artificial intelligence, epidemiology, economics, and other fields. When a drug company wants to know whether a new treatment works, they use randomized trials that depend on the same logic: if you randomly assign people to treatment and control groups, you break the influence of common causes, and any remaining probability difference tells you about causation. When social scientists want to know whether a policy caused a change, they use techniques that trace back to these philosophical debates about screening off, colliders, and interventions.

The questions are deep and hard: What does it mean for one thing to make another happen? Can we ever really know what causes what? And if causation is just about probabilities, what makes it different from mere correlation?

Nobody has fully answered these questions. But the attempt to answer them has given us powerful tools for thinking about the world—and a healthy reminder that even our most basic concepts can turn out to be much stranger than they first appear.

Key Terms

Term	What it does in this debate
Probability raising	The basic idea that causes make their effects more likely, even if they don’t guarantee them
Screening off	When knowing one variable makes another variable irrelevant—this can happen in chains of causation or with common causes
Common cause	A factor that causes two things at once, creating a correlation that isn’t itself a causal connection
Spurious correlation	A correlation that doesn’t indicate a causal relationship, because both things share a common cause
Background context	The set of other relevant factors that need to be held fixed to see whether a cause really raises probability
Markov Condition	The principle that once you know a variable’s direct causes, nothing else about the system gives you extra information about it
Collider	A variable that is caused by two other variables, creating a distinctive pattern of probability dependence
Actual causation	Whether a particular event (not just a type) actually made another particular event happen
Intervention	Forcing a variable to take a particular value, overriding its normal causes—used to test what would happen
Causal model	A mathematical representation of a system using variables, arrows, and probabilities

Key People

Hans Reichenbach — A philosopher and physicist who pioneered the probabilistic approach to causation and introduced the concept of screening off.
Nancy Cartwright — A philosopher who pointed out that causes can lower probability overall while raising it in every specific situation (Simpson’s Paradox).
David Lewis — A philosopher who developed counterfactual theories of causation, including a probabilistic version that uses “what would have happened if” reasoning.
Judea Pearl — A computer scientist who developed causal models and the “do-calculus” for reasoning about interventions, now widely used in AI and statistics.
Peter Spirtes, Clark Glymour, and Richard Scheines — Philosophers and computer scientists who developed algorithms for inferring causal structure from probability data.

Things to Think About

If two things are correlated, when should you assume one causes the other, and when should you look for a common cause? How do you decide which possibility is more likely?
The barometer example shows that a perfect predictor (the mercury drop) isn’t necessarily a cause. Can you think of other examples where something predicts an outcome but doesn’t cause it?
When scientists say “smoking causes cancer,” they don’t mean every smoker gets cancer. What kind of evidence would actually prove that smoking causes cancer rather than just being correlated with it?
The distinction between “general causation” (smoking causes cancer) and “actual causation” (Joe’s smoking caused his cancer) matters in court cases. What kind of evidence would you need to prove that someone’s specific actions caused a specific harm?

Where This Shows Up

Medicine and public health: When researchers say a drug works or a behavior is risky, they’re making causal claims based on probability data. Understanding the logic helps you evaluate their claims.
Legal reasoning: Courts have to decide whether someone’s actions actually caused a harm. The debate about fizzlers and preemption maps onto real legal cases about responsibility.
Machine learning and AI: Many AI systems use causal models to make predictions and plan actions. The math Pearl developed is used in self-driving cars, medical diagnosis systems, and recommendation algorithms.
Sports and games: When a player “makes a play that changed the game,” we’re making a causal judgment. The difference between being statistically good and actually making the key play is the difference between general and actual causation.