If propositional calculus (simpler than it sounds is a good way of describing causality in the territory, I very much doubt there is a fourth option. If I’m doing logic right:
A problem, or a strength, depending on the context, with this sort of argument is that it does not depend on the meaning of the phrase “X is caused by Y”. Logically, any binary relation forms chains that are either infinite, lead to a cycle, or stop. If the words “X is caused by Y” indeed define a binary relation, then the argument tells you this fact about that relation.
If the concept being groped for with the words is vague, ill-defined, or confused, then the argument will be working from a wrong ontology, and the precision and soundness of the argument may distract from noticing that. Hume denied causation, in favour of correlation; Pearl asserts causation as distinct but as far as I can see takes it as unproblematic enough for his purposes to leave undefined. The discussion here suggests the concept of causation is still unclear. Or if there is a clear concept, people are still unclear what it is.
A problem, or a strength, depending on the context, with this sort of argument is that it does not depend on the meaning of the phrase “X is caused by Y”. Logically, any binary relation forms chains that are either infinite, lead to a cycle, or stop. If the words “X is caused by Y” indeed define a binary relation, then the argument tells you this fact about that relation.
If the concept being groped for with the words is vague, ill-defined, or confused, then the argument will be working from a wrong ontology, and the precision and soundness of the argument may distract from noticing that. Hume denied causation, in favour of correlation; Pearl asserts causation as distinct but as far as I can see takes it as unproblematic enough for his purposes to leave undefined. The discussion here suggests the concept of causation is still unclear. Or if there is a clear concept, people are still unclear what it is.