Why did Hume think we couldn't perceive causation? Because we only see the constant conjunction and not the underlying cause? Hume assumed that if there is such thing as causation, it had to be something unperceived. — Marchesk
One thing not being mentioned is that causation - out there in the world - is heavily contextual. Things happen in predictable fashion because the world is organised in some way that constrains what is possible. And that history accumulates over multiple spatiotemporal scales.
So the car crash couldn't have happened at that junction unless 100 years ago the road hadn't been built. Or if two seconds earlier, the driver hadn't been distracted by the phone ringing.
But physics of course is a reductionist modelling of causality that plays the useful trick of imagining timeless laws animated by instantaneous measurements. So when it comes to conceiving and perceiving the causes of events through this lens, it leads to the Humean situation where the perceived event seems to take up no time and thus have no causal history, nor future. We imagine the event to be punctate and contain no information apart from some number that gives it an instantaneous value - like a momentum or inertial velocity.
So everyone was reacting to Newtonian mechanics - a new metaphysics that broke the world apart in this particular fashion. And if you took it literally, perception became identified with acts of measurement. It was imagined that events had punctate value that could be abstracted away from all the surrounding context. Causality became bound up in a property like momentum that a mass possessed. These values could be plugged into rules - the equations - that were like Platonic ideas.
Thus causality was pushed out of sight. It either became hidden in timeless laws. Or it was concealed within the value assigned as the identity of some timeless event. Causation was reduced to correlation as an act of the abstracting scientific imagination. Real things got replaced by the numbers that stood for them within a new system of sign.
If that's the way we find best to model causation, then it makes it quite legitimate just to count events and treat a regularity of conjunction - a matching of theory and prediction - as "seeing causality at work". The damn thing - Newtonian mechanics - works. The philosophical error is then to pretend to be confused - to start claiming an epistemic crisis like Hume, and even Kant.
Logic itself is the same trick - the abstraction to the timelessness of a syntax of rules and variables. A system of pure sign that leaves its semantics outside of it as something to be determined in some other "informal" fashion. Someone has to decide the meaning of the words in a proposition, just as they have to decide what counts as properly measuring some event in the world with sufficient care.
So it should be clear to us - as the inventors - that we have developed a powerful modelling trick (one that takes modelling itself to its formal extremes). And the world "in itself" is exactly what had to be left out so that we could choose precisely what then to include back in as the abstracted elements of a formalised and timeless approach.
Hence events became perceived as contextless, memoryless and historyless as the way to assign them some punctate value (like some weight of motion in a direction). And from there it became difficult to see why one thing leads to another except that we have constructed some laws as an act of conception. The events themselves - due to the way we measure them - can no longer give us a necessary connection to some actual lived past that is the world "in itself". We no longer seem to see (at a scientifically modelled level) what we in fact do feel we see (at a regular biological Bayesian brain level) with our own eyes.
The animal brain is evolved to reason inductively. It works by taking a guess and predicting its future states, and that creates a context in which the suprising can stand out. The unexpected - the breaks with expectable causality - is what is being looked for. The lack of Humean continguity is the feature, not the bug, as it is the failures of causal reasoning which are the teachable moments for the critter.
But philosophy turns nature on its head with this new language-based trick of deductive thought. It flips us into the timeless view of the world where causes are eternal ideals - like laws - or essentialist properties, like the numbers assigned as the values of instantaneously measured events.
And now there is no connection that can be seen between one instant and the next. But that is just the way our formalisms operate - the timeless view we have imposed so as to make time itself an abstraction within the modelling.