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The sentence that we cannot draw causal conclusions from correlations is heard several times in many scientific courses, especially in statistics, but also in philosophy. Here this consideration is known as logical fallacy under the Latin term "cum hoc ergo propter hoc". In short, this refers to the inability to derive a cause-effect relationship between two events or variables solely on the basis of an observed association or correlation between them.
Now, it is foreseeable that philosophers themselves will argue about this, and even statisticians admit that, yes, causal inference is not ruled out per se, and the correlation of two events or variables is a good indication of just such causal inference. Nevertheless, very scary - and completely wrong - false conclusions (pseudo-correlations) can occur, which is why one prefers to consider the correlation only as an indication of a possible causal conclusion.
In doing so, philosophers can first deal in detail with what causality is in the first place. The Scottish empiricist David Hume has worked out a remarkable position on this. He argues that we cannot conceive of any other connection between cause and effect simply because there is no other impression to which our conception can be traced. This certainty is all that remains. For Hume, the necessary connection that causality produces is nothing other than this certainty.
A correlation may be statistically demonstrable, but for an empiricist it does not exist in human experience because the empiricist simply has no sense of it. The human being sees the one billiard ball bump another one, so that this one moves on, but the forces which cause this remain invisible for the direct observation. It may be simply because of the human being that we like to draw causalities from correlations. It would be so beautiful to understand simply and to make descriptive.
Exactly therefore we find this false conclusion probably also so often with politicians who want to produce a mood. Here, too, two observations are often - and erroneously - mentioned together in such a way that the listeners automatically form a causal conclusion (as with Hume's empiricism), even if this conclusion is not even formulated. This might sound like this: Population group X has a higher proportion of characteristic Y compared to the total population. So much for the facts. However, the causal conclusion that characteristic Y is more strongly represented in population group X because it is precisely this population group is by no means true, even if this is suggested simply by showing statistics. The question why characteristic Y is more strongly represented is not even discussed. The shortcut about the reverse conclusion as causality seems to be easier to grasp and to spread than an actual research about the circumstances of the connection. And that is what is actually scary about the subject.
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