>The smoking → tar causation is a red herring here. It's presumed it's not controversial.

You have to mention this explicitly. Because it's also presumed not controversial that genetics can predispose someone to cancer. Additionally if you restrict your universe to two hypothesis but then suddenly I can pick up adhoc "red herrings"/assumptions like this anywhere seems inconsistent with your point.

>But the point is the universe of plausible hypotheses is not infinite, either. Scientists in the real world are not dealing with the set of logically possible statements consistent with raw sensory experience. They're building models of the world, and testing and challenging a few of their beliefs at a time, to gradually come closer to the truth.

This is factually wrong. We don't know whether plausible hypothesis are finite or infinite. This is the very reason why nothing can actually be proven. The entire reason why nothing can be proven with science is because we can't specify a range and domain for the universe because we simply don't know.

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.

I can bring it back to the world of axioms and theorems so . Imagine the real world as a model where there the domain and range is infinite in size and entity types. The only thing that can be assumed is probability and logic. That is what the scientific method is operating in. Therefore your methods have to account for an infinite amount of hypothesis rendering your assumptions and deductions impossible without caveating your conclusion with a limiting assumption.

In the logical model above the best you can do to establish causality it by placing yourself into the system. Any other method requires assumptions (which is commonly done).

>When they can conduct randomized controlled trials, that's great. But it's not always feasible or even possible, yet it's still often possible in those cases to test competing causal hypotheses via observation. The Eddington experiment tested the (causal) theory of General Relativity against the (causal) theory of Newtonian gravity, but there was no intervention. The discovery of iridium in a giant crater off the coast of Mexico was a key confirmation for the (causal) dinosaur meteor extinction theory, but there was no intervention there either. These were causal hypotheses tested by observation.

Of course. I'm saying we have limited tools so we tend to jump to conclusions and make assumptions based off of our intuition and understanding of probable outcomes. But this does not discount the fact that these assumptions were made.

I am saying that the ONLY way to determine causality to a degree in a universe where the domain and codomain is unknowable is by placing your self into the system and making yourself the causal factor. But this is not how we operate in practice. Clearly many scientists assume causality based only off of correlating evidence do in no part to, like you said, how hard it is to actually create these experiments.

>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.

All of our science is founded off of a few foundational axioms/assumptions. The recursive assumption that logic is true, the assumption probability is true and maybe a few more intuitive adhoc foundational assumptions that the random number generator is random and that influencing the causal event does not produce side effects. The scientific method is foundational because it operates within these foundational assumptions and so does determining causality by placing yourself into the system.

The "RCT" thing you introduced is not foundational because you must create new assumptions outside of the foundational ones we use for all of science. You make up stuff. Which is fine, but it's no different then using correlation to imply causality. It's the same type of "assumption." We're so against the term correlation does not imply causation but these and similar leaps of assumptions are common place, often done and allow us to come to conclusions without actually proving anything.