Do we really need an operational definition of causality?
Or of anything else for that matter
In Remarks on Colour, Wittgenstein writes (remark 171):
This piece of paper varies in lightness from place to place, but does it look grey to me in the darker places? The shadow that my hand casts is in part grey. I see the parts of the paper that are farther away from the light darker but still white, even though I would have to mix a grey to paint it. Isn’t this similar to the fact that we often see a distant object merely as distant and not as smaller? Thus we cannot say “I notice that it looks smaller, and I conclude from that that he is farther away”, but rather I notice that he is farther away, without being able to say how I notice it.
What is direct perception, exactly? This matters, because if science is an exercise in translation, we need to know which language we are translating to. When you say that to measure a certain quantity you need to do such-and-such and record the number that comes out, you have to stop at some point because you can’t break up the building blocks of such-and-such indefinitely into more and more elementary building blocks.
The point where you stop is the boundary between tacit knowledge and codified knowledge. You decide where to put that boundary on pragmatic grounds. For instance, in elementary physics and astronomy courses, we do not problematise the concept of distance. You just know what it means that something is farther away, and that’s all you need. So operational definitions help translating complex concepts into the outcome of sequences of concrete actions carried out by an agent, but this relies on the agent being able to carry out such actions. This requires knowledge that in part must be tacit, because it can’t be turtles operational definitions all the way down.
Coming to causality: what if “A causes B” could be treated as a basic building block in this fashion? If we could assume that you just know causality when you see it, perhaps there would be no need to define it operationally. This is in fact the naïve point of view of many people, who are genuinely surprised when they hear that we need to define causality at all.
As it turns out, the experimental psychologist Albert Michotte wrote a whole book about his experiments on how people perceive causal relations in response to visual stimuli –like two dots of light seemingly bumping into each other. And indeed he claims that causality is directly perceived, at least under certain circumstances:
These are the two Type-experiments of causality; we shall call them respectively the Launching Effect and the Entraining Effect. In the case of these two experiments the production of movement is thus directly experienced. There is no question of an interpretation, not of a significance superimposed on the impression of movement; in other words what is actually ‘given’ is not a mere representation of a symbol of causality. In the same way as stroboscopic movement is not, psychologically speaking, the ‘symbol’ of a movement, but is a phenomenal movement, so the causality perceived here is a phenomenal causality.
The relevance of this to our need for operational definitions of the concept of causal relation between statistical variables is however remote. To leverage the analogy with Wittgenstein’s remark once more, our ability to visually perceive distance in a direct fashion is no help if we want to talk about distance in the context of cosmology. Similarly, perceiving causality in videos of bouncing balls won’t let us do without causal discovery algorithms.
Still, one could maybe learn to eyeball causality by staring at a (possibly 3D) scatter plot?