I am supported in this by
Judea Pearl [1] when he stresses that probability is about "association" not "causality" (which is, in a sense, the reverse of randomness): An associational concept is any relationship that can be defined in terms of a joint distribution of observed variables, and a causal concept is any relationship that cannot be defined from the distribution alone. Examples of associational concepts are: correlation, regression, dependence, conditional independence, like-lihood, collapsibility, propensity score, risk ratio, odds ratio, marginalization, conditionalization, “controlling for,” and so on. Examples of causal concepts are:randomization, influence, effect, confounding, “holding constant,” disturbance, spurious correlation, faithfulness/stability, instrumental variables, intervention, explanation, attribution, and so on. The former can, while the latter cannot be defined in term of distribution functions." He also writes: " Every claim invoking causal concepts must rely onsome premises that invoke such concepts; it cannot be inferred from, or even defined in terms statistical associations alone."