I think we're close to an impasse, partially due to a language barrier, so I may give up soon, but let me give this another try.

I don't think you've understood my example. We may have philosophical disagreements left over even once you've understood my example. But so far you still don't seem to understand it. For example, you say:

You have to mention [that the smoking → tar causation is presumed not controversial] explicitly. Because it's also presumed not controversial that genetics can predispose someone to cancer.

Right, of course it's not controversial that genetics can predispose someone to cancer. That's the whole point. That's why it's among the two hypotheses being tested. It is ruled out (under the assumptions of the causal super-graph, which includes that hypothesis and an alternative hypothesis as the world of possibilities) by the statistical data. Please try to understand this point and acknowledge that it is the case.

You may question the usefulness of this model of science. But so far you don't seem to understand what I'm even saying with this.

This is factually wrong. We don't know whether plausible hypothesis are finite or infinite.

"Plausible", as I'm using it, is a partially subjective term: plausible in the view of subject matter experts. As you're using it, it appears to be an objective term, meaning something akin to "logically possible", perhaps with some ill-defined notion of probability (but what are your priors?). I'm talking about real scientists in the real world. You seem to be talking about some idealized scientist which doesn't, and can't, exist. General Relativity was not plausible in the 17th century. It was not even conceived of then. It became plausible in the 20th century. What's the plausible (as judged by actual scientists, not in some hypothetical abstract logic) alternative hypothesis to the meteor killing the dinosaurs? There is none, so far as I know. The set of hypotheses under consideration changes over time due to the imagination and skepticism of real flesh and blood scientists, not due to some Platonic logic which no scientist can follow.

Formally in the scientific world your method is flawed. This is what I'm saying. In the mathematical world your assumptions and logic can hold but not in science. I get that your toy example was used for illustration purposes but it's failure to be applicable to the real world is also an illustration of the flaw behind the method itself.

… The only thing that can be assumed is probability and logic. That is what the scientific method is operating in.

To be quite frank, I think it is your model which fails to be applicable to the real world. You'll be hard-pressed to find a single practicing scientist who sees themself as a logic/probability machine. In the real world we need to operate, provisionally, with certain assumptions about how the world works, or else we can understand nothing. Those assumptions can always be challenged. But they are held, provisionally, so that we can make progress in our understanding.

>The point is RCTs are a special case of a more general causal logic. RCTs work because they sever the statistical link to confounders, but only provided your assumptions about the RCTs are correct.

Ok we're probably on the same page then. This is exactly what I'm saying.

No, my whole point is that RCTs are just one special case of the more general theory of causal inference, and that more general theory can be applied elsewhere too. The assumptions underlying an RCT are not exceptional, and like everything else in science, they can be challenged.

If you have a population of 1000 people come in and take pills A or B, as determined by a random number generator, and then the ones who took pill A survive and the ones who took pill B die, the RCT says B killed them. But perhaps unbeknownst to you, there was a source of gamma rays due to an experiment in the next room which was simultaneously flipping bits on your random number generator and also irradiating your subjects with lethal doses. The gamma rays would then be the confounder.

"Science" does not rule out this possibility in theory. But in practice, it may be implausible to the experts. (Remember: plausibility is partially subjective, a function of the current state of scientific understanding! It can change over time!) So they are not worried about it when interpreting the results of the RCT.

Similarly, the universe of logically possible causal explanations consists mostly of hypotheses that no scientist currently takes seriously (i.e. considers plausible). Of the ones on the table, so to speak, the predictions can be tested to leave only one causal explanation (for the time being) standing.