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?