In this piece, I first share a framework for causality put forth by Karl Popper; I then share how it differed from my initial intuitions about causality; and then I explain why Popper’s framework is better.
In The Logic of Scientific Discovery (§12), Karl Popper states that there are two elements of any causal explanation:
- a statement in the form of a universal law.
- a statement of initial conditions.
He gives the following example of a causal claim: a weight is placed on a thread and causes the thread to break. We have:
- [universal law] any thread made of cotton will tear when a weight greater than 2 kg is placed on it.
- [initial condition] this specific cotton thread has a weight of 5 kg placed on it.
The result is that the cotton thread breaks, and we say that the 5-kg weight caused it to do so.
At first, this formulation of causality came across as needlessly complicated to me. Why do we need all this stuff about ‘universal laws’ and ‘initial conditions’? If you want to talk about causality, you just need two things: an event A and an event B. We can say that A causes B, or A → B. I’ll call this the naive formulation of causality.
However, merely having two events A and B is insufficient to make a causal claim. A statement of causality needs more than the statement that one thing happened and then another thing happened. Example: imagine I walk outside (event A) and it immediately starts raining (event B). I can’t conclude here that A caused B. They just happened to occur one after the other.
Perhaps we could modify our naive definition a bit: to assert that A caused B, we need the condition that A happened and then B happened, and also that if A hadn’t happened, then B would not have happened. (This is a counterfactual.)
This definition is better, and we don’t need Popper’s ‘initial conditions’ or ‘universal laws’. Going back to the rain example: imagine again that I walk outside and it starts raining. We don’t say there’s a causal connection here, because we know (from our understanding of weather) that if I didn’t walk outside, it still would’ve rained.
However, this definition is still not sufficient. Consider this example: I walk outside (event A), and when I reach the next block, the sidewalk collapses and I fall into the sewage (event B). It’s true that if I had never walked outside, then I never would’ve fallen into the sewage. But does this mean that me walking outside caused me to fall into the sewage?
If this were our definition of causality, things would get very confusing. Imagine we agree that me walking outside caused me to fall, because if I hadn’t walked outside, I would not have fallen. Then we could also claim that me getting out of bed today caused me to fall: if I’d never gotten out of bed, then I never would’ve fallen. Or we could say that me moving to New York two years ago caused my fall. Or that me being born caused it. Or that the Big Bang itself caused me to fall into the sidewalk. This is absurd.
This is where the need for a universal claim comes in. What we need is not just an event A and an event B, but some kind of regularity L that asserts that whenever A happens, B happens.
Here’s a better causal explanation for why I fell: the sidewalk was not structurally sound and my bodyweight was sufficient to break it. This is a regularity: whenever an object with sufficient weight is placed onto a sidewalk that no longer has structural integrity, the sidewalk will collapse and that object will fall.
But those other absurd causal claims we made wouldn’t satisfy this definition. It’s not the case that anytime I get out of bed, I will fall into a sidewalk. Or that anytime I go outside I will fall into a sidewalk. These would be bad hypotheses for ‘regularities in nature’.
Anytime we make a causal claim we are implicitly pointing to a regularity. It could be the regularity that structures of a given material, when placed underneath a given weight, will collapse. It could be that if you throw a ball into the air, it will fall back to the ground (at the same velocity). It could be that if a certain viral particle enters your body, your immune system will have a particular reaction.
But there’s always some assertion of a regularity. And this assertion is conjectural: it could be wrong. Causes are always something we hypothesize. They are never something we assert with certainty.
To make a claim that an event A caused an event B is to state that if the same set of initial circumstances were to repeat, the same result would follow. And we can test this experimentally. And ideally, when we make such a causal claim, we should be as precise and detailed as we can about how those initial circumstances brought about the observed effect. This is the best way to think about causality.
- How do we distinguish between mere correlation and actual causation? My current view is that we can only do this tentatively. We don’t know with certainty that what we’re observing is a cause or a mere correlation. It helps to create detailed and hard-to-vary explanations so that we can test and corroborate them with experiments, giving us some “confidence” over time. (This is based on the work of Karl Popper and David Deutsch.)
- I’d like to read Judea Pearl’s work on causality (e.g. this paper or his book) but I have not done so yet.