Before you dismiss that is philosophical non-sense, causality is closely related to the "Arrow of Time" which is considered an unsolved problem in physics [0]. From what we've observed time appears to be the only asymmetric physical process, largely due to entropy (that is you can immediately tell if a video of a jar breaking is being played backwards because we don't expected a jar to "fall together"). There are Quantum processes, for example, that are time symmetric, that is playing a video of these processes would look the same reversed and forward.
That said, as someone who does a lot of statistics, in practice what we do is model the causal process with a directed acyclic graph and see how well our models behave under causal assumptions. These work okay for answering practical questions about does A cause B. By controlling for correlating variables we can see the impact on what we believe to be a causal variable when we condition on these other correlating factors.
Worth mention that nearly all of the work is done by linear models in practice.
