That depends what you mean by an “experiment.” If you divide a set of patients into a control group and a test group, and then have the test group smoke a pack of cigarettes per day, that is an “experiment” to me, one that is represented by an intervention (because we are forcing the test group to smoke regardless of what they would naturally want to do).
Observing that the test group is much more likely to develop cancer would lead me to conclude that the graph
smoking → cancer
is a causal graph rather than merely a statistical graph.
If we do not perform the above experiment due to ethical reasons, but instead use observational data on smokers, we have to worry about confounders, like Fisher did. We also have to worry, because we are implicitly linking that data with counterfactual situations (what would have happened if those guys we observed were forced to smoke). This linking isn’t “free,” there are assumptions operating in the background. Assumptions expressed in a language that can talk about counterfactual situations.
That depends what you mean by an “experiment.” If you divide a set of patients into a control group and a test group, and then have the test group smoke a pack of cigarettes per day, that is an “experiment” to me, one that is represented by an intervention (because we are forcing the test group to smoke regardless of what they would naturally want to do).
Observing that the test group is much more likely to develop cancer would lead me to conclude that the graph
smoking → cancer
is a causal graph rather than merely a statistical graph.
If we do not perform the above experiment due to ethical reasons, but instead use observational data on smokers, we have to worry about confounders, like Fisher did. We also have to worry, because we are implicitly linking that data with counterfactual situations (what would have happened if those guys we observed were forced to smoke). This linking isn’t “free,” there are assumptions operating in the background. Assumptions expressed in a language that can talk about counterfactual situations.