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Hume showed that one cannot infer cause & effect in nature by induction alone. We only notice that when event A occurs then so does event B.
If event A always occurs before event B we are still not entitled to say that event A causes event B. For night always follows day and we do not say that day causes night, but that it is caused by the spinning of the earth whilst orbiting the sun.
Is there any theoretical consideration that effectively distinguishes causality from regular occurance?
According to Kant, causality is a human way to interpret our sensory impressions: it may not be useful or meaningful to think of it as something that exists like a Ding an sich, an objective thing independent of human interpretation. The same applies to space and time. In that line of thought, one cannot in principle establish the truth of a causal relationship, and everything is just an ordering of our impressions.
There are at least some guidelines, but it's impossible to know for sure.
If there is a plausible line of causation, it increases the likelihood of causation. For example, making a hole in a water jug can plausibly be responsible for the water leaking out. Simplicity is useful here, as many complicated arguments can look plausible.
If we have multiple instances, not spaced according to pattern or long-term trend, that's more convincing. One example might be leaded gasoline and its effect on crime: apparently the introduction of leaded gasoline into countries eventually raised the crime rate, and removing it eventually lowered the crime rate. Going over numerous countries, this becomes more convincing.
As a special case, if we do A repeatedly, and get effect B reliably, it sure looks like causation. When I want my car to move forward, I put it in a D gear and release the brake, and that happens reliably.
The "correlation equals causation" fallacy says that one thing preceding another can't be used as a proof of causation. Consider the claim that "increased education spending leads to better outcomes for children." A simple correlation of spending on schools versus education outcomes would lead to a positive result; those that spent more also had better outcomes. We can control for confounding variables, such as income, at any given time, but current spending may not affect outcomes until later. The idea of Granger causality is if whenever there is a "surprise" in the explanatory variable that leads to a later increase in the outcome variable we call this variable "Granger causal."
In the education example, assume there were some places where education spending spiked to an unusual level some years while the confounders did not significantly change. If every time this spike happened there was a corresponding increase in performance in the future relative to when these spikes didn't happen, education spending "Granger causes" higher performance. This is not the only definition of causality but in many applications it is useful.
Wikipedia: Granger causality
PS: The notion of "suprise" is used elsewhere as well. For example, Conway uses the "surprise argument" quite entertainingly in lecture 6 (from time stamp 25:52 onwards) on the free will theorem. Note one of his initial remarks:
Now remember this is not a deductive logical argument.
