In Response to Popular Demand: Causality and Inference: Back to Basics

Consider conditions X, A, and B.

We have observed conditions A and B.

We suspect condition X but we have not observed or studied it.

We have observed -- but only to the extent that we have observed -- that A almost invariably follows B. We have also observed that A rarely or never occurs when B does not occur (whether before A or after A).

In the absence of further observations, can we view B as a pretty good or excellent indicator of A?

In the absence of further observations, can we presume that B is a cause of A?

Can we say "yes" to the former question if we are unwilling to say "yes" to the latter?

Now suppose that A is "motorcycle trashing"; and that B is "motorcycle tattoo on forearm."

We might well think that it would be unwise to try to do away with motorcycle trashing A by doing away with motorcycle tattoos on forearms B. We might be so inclined to think because even though we have seen (thus far) that motorcycle trashing A always or almost happens when motorcycle tattoos on forearms B (of the eventual culprits) are present, we might have strong doubts that motorcycle tattoos on forearms B cause motorcycle trashing A. We might instead suspect that some third factor (e.g., X, which happens to be "gang membership") causes both motorcycle tattoos on forearms B and motorcycle trashing A.

But, if we suspect that factor X is lurking in the background, perhaps causing both B and A, and, if we believe that X, if present, may expose B as a spurious cause of A -- we may believe this, perhaps, because we may believe that further investigation will show (we suspect) that if a potential culprit is a gang member, this factor of gang membership makes the probability of motorcycle trashing high and, furthermore, that any added information about a tattoo on the potential culprit's forearm would add nothing to the probability that the potential culprit trashed a motorcycle -- if, in short, (we strongly suspect) the following pattern of causal influence obtains

 

 

		X
	/		\
A				B

 

If we suspect that this pattern of causal influence obtains -- or if we suspect that it just cannot be that motorcycle tattoos on forearms increase the frequency of motor trashing or makes motorcycle trashing more probable -- does it follow that we should forego the use of B as evidence of A -- if, for example, (i) we have not made any observations in the past to confirm our suspicion about the causal potency of X (or some other factor); or -- alternatively -- (ii) we have made such observations about X but in this case we happen not to know if X -- gang membership -- is or is not present?

Note: In situation #(ii) the occurrence of B may be a good indicator of the (prior) existence of X. If so, the failure to observe X directly may be immaterial. So focus on scenario #(i) in the question directly above.

In the absence of something like causation -- or, if you prefer, in the absence of some "natural stability" in the phenomena that we may observe --, it may turn out that the observed connection (in the past) between A and B is just an accident, a coincidence and, thus, cannot be trusted to recur. This thought is what gives the belief in the importance of causality for inference its power! But ..., again, does it follow that human beings should abandon reliance on all "mere associations" when they are bereft of an articulable causal theory (or when they have no evidence to support whatever choate or inchoate causal theory they may happen to entertain)? But, by the same token, it really is true, isn't it, that mere association is not enough? The world is full of coincidences -- and you can find them (easily! everywhere!) -- you can find meaningless coincidences all around you -- if you just look for them.