I've been trained to conduct sessions in root cause analysis. People have a tendency to pin down "the" cause, but in actuality there are many causes for anything. An example is an incident following a party where beer bottles fall off a plate during clean-up and shatter on the floor. Was the cause the use of glass beer bottles, a paper plate to carry them, wooden rather than carpeted floors, inconsiderate guests who refused to clean up, or the fact that there was a party to begin with?
Yep.
Obviously, I don't think I'm underplaying Popper. My impression from reading about in philosophy of science is that most are utterly unconvinced by his approach.
I think that misrepresents the history of it. An army of people led by Peirce tried to "prove" the scientific method. After many years of failing Popper precipitated the, "Ah nuts, maybe we can't prove it," movement. That his alternative has its flaws in no way invalidates the change in attitudes he effected.
Since I don't do philosophy of any kind ...
That's a very bold (and honestly, very naive sounding) statement. It belies a philosophy of its own.
I'm not going to present a philosophical defense of scientists' conviction that corroborated theories are more likely to be true than uncorroborated ones. Do note, though, that "correlation does not imply causation" is rarely intended to imply that we can't ever determine causation; it means that just seeing a correlation isn't adequate to conclude causation. Finding a mechanism that explains how one causes the other is really helpful.
I didn't ask for a philosophical defense, but a theoretical basis. All your statements are leaning on intuition, not a codified justification. Since you didn't respond to Sober, I assume we have not discussed him before. FYI, he has spent most of his career trying to establish that correlation is causation for evolution, and he's not being very widely accepted as successful. If a smart guy like him can't do it, I'm skeptical it's going to happen any time soon.
As I've said too many times to count, my experiences in mechanics led me to a similar, "Ah nuts," conclusion about using correlation to establish causation. It works most of the time, and when it doesn't you go back and try again ... but that's hardly something one proudly trumpets as a "method". It's little better than guess and try.
In discussing such with my engineering colleagues, most agreed with the statement that research involves a lot of guessing. What distinguishes the professional engineer from the amateur is serendipity - an ability to know what guesses not to make and that when a good solution comes along, the trained engineer is better equipped to recognize it, capture/codify it, and send it back out to the world in a manner that can be replicated.