Yes, these are generally called empirical laws or empirical principles, which do a good job of predicting your outcomes based on conditions and causes, but is totally lacking in explaining the underlying mechanism for the cause. They are numerous and is part of research. Perhaps the measurement problem of quantum mechanics fits here (QM is one of the most successful theory out there, but it is largely empirical in its explanation and often does not have any grasp of the underlying mechanism involved; check out the quantum bomb thought experiment if you’re interested in just how absurd it can all be and it’s empirically verified).
In contrast there are also laws that do a good job of explaining the underlying mechanism (causes), but suck at making predictions due to complexity, this is most famously perhaps evolution. We can explain species dynamics and everything with it, but we cannot predict things like “when will crows be dominantly white-feathered?”.
If you don’t know the mechanism then you have a correlation, it could be a great correlation but still you don’t know the cause. To establish causation you need to have a mechanism and an underlying theory that explains the phenomena, e.g. gravity for things falling. Even then causation is very hard to achieve, perhaps impossible, since at the end of the day it’s always a correlation of experimental observations.
Yes, absolutely! This is very common in medicine. We know antidepressants are effective in depression and anxiety without a robust theory of action. We also know psychotherapy is effective without really knowing why. Lots of competing theories for both but so far no principled or empirical path to a solution.
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