I won't challenge Hume; I'm referring only to the fact that a causal relation implies necessity: B can't happen unless A acted to cause it. Probability can't provide this insight, it can only encourage or discourage it. The agent must formulate a mental model of the relation in order to hypothecate the presence of necessity / causality between a pair of events. A model that lacks that ability (e.g. probability) can lead to all sorts of nonsense in interpreting events, like proposing causality. Or at least meaning by connecting a baseball pitcher's hat color with the weather on game day.

BTW, precision isn't necessary for relative time to have great value in a huge fraction of possible world events. Obviously all you need is relative temporal sequence to disprove causality - since the batter can't hit until the pitcher throws.

In a great many event pairs, a lot of temporal precision Is unnecessary. Often it's only approximate relative time that matters, since the mental task intuits all the temporal constraints needed for understanding event coupling, like knowing the parent child relation implies the relative ages of each and much more latent info that may or not be relevant to a given interpretive task at hand.

And what I am saying is that when you say A implies B you’re making a ton of assumptions. If those assumptions are violated (eg all swans are white, all men are taller than all women) then suddenly you have caveats and hedges.

So what you actually use is not Propositional Logic / Boolean Algebra but Bayes’ Theorem. You only use rules of inference because you make assumptions.

I am saying that may work sometimes but those models are not exact.