# Pearl et al. (2016) definition of cause: circular?; how to improve?

Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 26 provides the following definitions of direct cause and cause:

A variable $$X$$ is a direct cause of a variable $$Y$$ if $$X$$ appears in the function that assigns $$Y$$’s value. $$X$$ is a cause of $$Y$$ if it is a direct cause of $$Y$$, or of any cause of $$Y$$.

It seems to me the definition of cause is circular (and thus essentially invalid) as it refers back to itself within the definition. Am I misunderstanding it? If not, how could the definition be improved?

• I was suspecting something like that, but it is still hard to wrap my head around it... How do I verify whether $X$ is a cause of $Y$ in cases when it is not a direct cause? In such cases, I have to verify that $X$ is a direct cause of a cause of $Y$. But the definition of a cause is not explicit (it is recursive). Could you help me further? – Richard Hardy Mar 19 at 13:13