# How to demonstrate causation if correlation isn't sufficient?

It is widely known that correlation does not necessarily imply causation. However, after recognizing that the correlation alone doesn't prove causation, what needs to happen in order to evaluate whether the causation exists? What's the missing ingredient that make some subset of correlations indicative of actual causation.

The following videos discuss the issue, mostly about why you can't infer causation for correlation, but also touch on what's missing:

Both videos state the basic idea that in order to infer causation from correlation, you need to know the causal mechanism. You have to know how the one item caused the other.

This strikes me as incorrect. I would say that in order to distinguish spurious correlation from causative ones you have to investigate which hypotheses generate accurate predictions. I can postulate seemingly plausible mechanisms for many spurious correlations, and I don't need to know the underlying mechanism to infer the existence of a correlation. The only thing that really matters in establishing a hypothesis is the track record of predictions.

Am I on base here? Or is my understanding of the scientific method flawed?

• I was going to ask this too! Something like: Given that scientific method can only ever demonstrate a repeatable experiment, isn't it the case that all you can ever do is establish a correlation between events x and y ? I'd suggest that it boils down to the interactions at a molecular level, which is still only observed. I guess my question would have been very similar but ended up asking whether causality is unprovable, just demonstrable statistically. – user2808054 Feb 19 '15 at 9:51

One can have quantitative predictions only if a hypothesis is well formulated within a background theory, which de facto will make of the hypothesis some sort of "mechanism". Also note that track records is not the only thing that matters in establishing a hypothesis, there is also: compatibility with other accepted theories, with common knowledge and auxilliary assumptions, with methodological principles, simplicity of the hypothesis, etc. For these reasons, an hypothetical causal relation between two types of phenomena will generally rely on (or take the form of) a hypothetical mechanism, framed in a background theory, which explains and predicts the observed correlation.

As noted in an other answer, different hypotheses (one in which you have a spurious correlation between two effects of a common cause, another with a direct causal relation) can make the same predictions. Track records won't be sufficient in this case.

One way to distinguish causation and spurious correlations is through interventions. If changing a factor produces an observational change then you have a causal relation. One can also vary the experimental setup to force two hypothesis to make different predictions in certain circumstances, which is also a form of intervention.

You can read this for more ways to distinguish correlation and causation: http://people.hss.caltech.edu/~fde/papers/Eberhardt_PhilComp.pdf

Causation has been an open question in philosophy at least as far back as Hume's problematization of causation in An Enquiry concerning Human Understanding. As such, there's no one universally accepted, uncontroversial understanding of causation in the philosophical world.

The specific problem with your proposal is that there can easily be multiple theories that do match a given set of data, including ones that call A a cause of B, when in reality A and B are independent consequences of C. This problem is sharpened in the case where you legitimize attribution of causation without explanation of the underlying mechanism.

The short answer to how you demonstrate causation is that you don't. Any explanation covers a lot of stuff you don't and can't observe (e.g. - what's happening in the core of the sun). There are also more basic logical reasons why you can't demonstrate causation, or anything else. To create knowledge, you make guesses about what is happening in reality, and then you test the guesses by critical argument and experiment. Guesses that survive tests may be true.

If your theory predicts some particular correlation between X and Y, and you find the correlation, then your theory has passed that test and it may not be false. That's all a correlation can tell you.

You say you don't need to know the underlying mechanism, but you're wrong. For a start, if you don't know the underlying mechanism, you can't tell what will count as a test. For example, if I want to trap atoms in a magnetic field, then unless I know how the magnetic field traps the atoms, I won't know if I've set it up correctly, how long I should wait for the atoms to be trapped and stuff like that. Another problem is that if you don't know the underlying mechanism it is difficult to test whether an apparent failure is a result of the theory being wrong. If you know the mechanism you can test whether your experiment is working properly by doing related experiments that test different parts of the experiment, e.g. - look at currents in magnetic field producing coils.

To generate accurate predictions, is a basic demand from scientific hypotheses. But it has no specific relation to causation. Therefore it does not relate to the question, as to the gap between causation and correlation.

It isn't clear whether an "underlying mechanism" is the best way to fill the gap between correlation and causation. What could such a mechanism be? For one thing, it cannot be a causal mechanism, for this would just push the question back instead of answering it. Anyway, the consideration of accurate prediction is unrelated to this issue.

• I don't really understand. Isn't the point of a scientific hypothesis to postulate causation? – Winston Ewert Feb 19 '15 at 2:44
• @WinstonEwert Newton faced this issue. His theory of gravity gave a mathematical description of how we observed bodies falling; but he supplied no underlying mechanism. He was famously challenged on this point and said: *I frame no hypotheses." The entire quote is well worth reading. en.wikipedia.org/wiki/Hypotheses_non_fingo Newton understood what so many people still don't understand today: that science is ultimately descriptive and not necessarily explanatory. Even if we have an "explanation" we never have an ultimate explanation. In the end, science can only describe. – user4894 Feb 19 '15 at 3:01
• @user4894, it seems to me that Newton was postulating a causative relationship between massive bodies and falling. He didn't know anything about the causal mechanism, and wisely refused to guess at it. But he was still able to infer the same sort of cause and effect relationship existed. – Winston Ewert Feb 19 '15 at 3:07
• @user4894 Newton's statement that he "frames no hypothesis" is widely recognized to be false. For example the principle of inertia is not falsifiable since no inertial system exists in reality, and masses and forces are free parameters that he could not deduce from pure observation, without hypothesis on the form of his laws. Newton's mechanics is explanatory. – Quentin Ruyant Feb 19 '15 at 6:28
• @user4894 the project of reducing scientific theories to pure phenomenal descriptions was pursued by the logical empiricists, and notoriously failed. Importantly, one aspect of this failure is the fact that physical properties are generally dispositional (i.e. causal), and dispositions do not reduce to regularity descriptions. – Quentin Ruyant Feb 19 '15 at 6:33

I think in a purely theoretical world, the only time correlation could imply causation is if you invoke ceteris parabus to the max. Ceteris parabus is when you ensure all variables are the same. If every single variable apart from your dependent and independent are kept identical, I think it would be a fair assumption that correlation implies causation.

The scientific method is not perfect, because it 'affirms the consequent'.

Consider the example of hooke's law: Our hypothesis is that extension is proportional to the attached load. Experimentally, we see that this is the case.So we assume our hypothesis is correct.

We are basically saying:

If P, then Q

Q occurs, therefore P occurs

This is flawed logic. What if something else caused Q

Take a clearly false example:

If it rains, the grass is wet

The grass is wet, therefore it has rained

What if I was watering the garden?

Hope this helps.

You are absolutely right.

As Hume's famous "problem of induction" suggests, the difference between correlation and causation may be purely numerical. Attributions of "causation" simply assume that the "past resembles the present" and "the future resembles the present," and that what happened "before" is our best Bayesian prediction of what will happen in the future.

That really is our best scientific consensus. Each "guess" gets stronger the longer it survives and thus becomes a surviving "prediction." We predict the sun will rise tomorrow, because it has risen for millions of tomorrows. We have no better application to certainty. Certainty is only a reduction of possibility.

However, this is why modern "causation" is, in many people's view, a very suspect concept, and Aristotelean causation may be making a comeback, I really don't know. We now see ideas like "overdetermination" or "strange attractors" or "statistical states" or various other mediums of change introduced into even physical science in the place of old "billiard-ball"causation.

It might be better now to say that "causation" is a subset of "correlations." As you suggest. What limits it to this subset would seem to be that it happened "before" the effect. Before and after. Which leads us, unwillingly and miserably, into theories of time, which are the most difficult and unsettled regions of philosophy and science.