Hmm, this seems to assume that we only have access to collected data (e.g. epidemiological studies) rather than being able to generate the data ourselves (many other types of scientific studies).
There is a key difference. A million surveys of smokers and cancer patients will never definitively prove causality. But if we could (legally and ethically) construct a randomized experiment in which we assigned a random half of the participants to smoke, we could easily conclude with very high confidence that smoking causes cancer.
(If this is not self-evident to you, the reason is straightforward probability. Suppose smoking does not cause cancer. Then when you take any given person and have them start smoking, their probability of getting cancer does not go up. Then the rates of cancer in the smoking group are exactly what they would have been had they not smoked. Then, since the people were placed in groups at random, with very high probability the rate of cancer in the smoking group will be almost the same as in the nonsmoking group. So if we find in our experiment that the rates of cancer are much higher in the smoking group, we must reject the hypothesis that smoking does not cause cancer.)
Agreed, this is also a problem in economics (though even in economics there are some limited experiments that can be done). I think a key issue people overlook in this debate is the presence of a theory that makes sense. If you just plot data until you spot something that looks like a trend, or fit models until your F-test comes back significant or your R^2 is big enough, then yeah, you can't even make a good case for causation. But if you start with a reasonable theory that fits with existing knowledge, then you can at least make a case.
There is a key difference. A million surveys of smokers and cancer patients will never definitively prove causality. But if we could (legally and ethically) construct a randomized experiment in which we assigned a random half of the participants to smoke, we could easily conclude with very high confidence that smoking causes cancer.
(If this is not self-evident to you, the reason is straightforward probability. Suppose smoking does not cause cancer. Then when you take any given person and have them start smoking, their probability of getting cancer does not go up. Then the rates of cancer in the smoking group are exactly what they would have been had they not smoked. Then, since the people were placed in groups at random, with very high probability the rate of cancer in the smoking group will be almost the same as in the nonsmoking group. So if we find in our experiment that the rates of cancer are much higher in the smoking group, we must reject the hypothesis that smoking does not cause cancer.)