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In every instance of A and B (A and B always occur when either occurs), A always comes before B.

In such cases, it can be inferred that A causes (predicts) B.

Does a single instance of B coming before A discredit this?

Consider the alleged theoretical reason against information traveling faster than the speed of light - causality. Consider that in every instance of A and B, that A comes before B, and then based on this you conclude that A causes B. That is, that A PREDICTS B. But if in one instance B happens before A, there IS a case where B comes before A. Is this sufficient to say that causality has not been established? If so, why is it necessary for A to always come before B in order to say A causes B? By what PROOF does A always have to precede B in every instance in order to establish causality? Is it sufficient to say that, in all instances of A and B, that A almost always has to come before B, to infer causality? Is it established that B can never come before A?

In terms of faster than light travel, A is the information about the launch, travelling at the speed of light, arriving at point X. B is the arrival of the space craft at X. The theory is that A HAS to occur before B, or the basic inviolate tenants of causality are breached. My ultimate question is, 'is there any proof in statistics that supports this'?

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closed as too broad by Richard Hardy, Peter Flom Aug 26 '17 at 11:48

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Every time I have danced at night, the sun came up the next day. What powers I must have over the heavens! $\endgroup$ – whuber Aug 25 '17 at 20:33
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    $\begingroup$ Consider the possibility that there is some other $N$ (which you may not even be aware exists!) that causes $A$ and then causes $B$. While $A$ and $B$ are not causally linked ($N$ just causes each in turn), $B$ always follows $A$. How will you rule out this scenario? Answering that question well will help bridge part of the gap here. [e.g. If I notice that if I see lots of people carrying umbrellas in the morning (even though it's not raining then) then it's almost certain to rain that day, I might imagine that it's at least partly causal, but actually it has no effect at all.] $\endgroup$ – Glen_b Aug 26 '17 at 1:06
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    $\begingroup$ Whole books (MANY books) have been written about this. Since you asked on a statistics website, I'd suggest Causality by Judea Pearl. But there's lots of others in statistics and also a bunch in philosophy. $\endgroup$ – Peter Flom Aug 26 '17 at 11:48
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    $\begingroup$ My point is that Granger causality is explicitly NOT the same thing as causality. So explaining something that you get with causality but you don't necessarily get with Granger causality would be showing how Granger "causality" is not in fact causality in the usual sense. Surely this is not remotely controversial. Granger causality is a useful concept, but we should not read more into the use of the word causality in the name than was really intended. $\endgroup$ – Glen_b Aug 28 '17 at 5:18
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    $\begingroup$ As far as I know, the idea that causality flows unidirectionally in time is taken as an axiom, it's not proven using statistics. Philosophers work on choosing the axioms. Statistics gives us tools to learn about particular causal relationships, when the axioms apply. If you are a time traveler, we shouldn't assume our methods work on you. :) We do know that causation can be simultaneous - e.g. the simultaneous transfer of information between entangled particles in quantum physics. So on the quantum scale, the statistical tools we use to learn about causation would no longer work. $\endgroup$ – Lizzie Silver Aug 28 '17 at 22:24
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Let $A$ be the event "a hurricane warning is issued", and $B$ "a hurricane arrives." In the past X years, $A$ has always preceded $B$, because the weather service is pretty good. Does $A$ cause $B$?

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    $\begingroup$ Yes, in the sense of Granger causality. $\endgroup$ – Aksakal Aug 25 '17 at 19:41
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    $\begingroup$ @Aksakal That merely serves to demonstrate that "Granger causality" is not causality, at least not in anything like the usual sense. If the weather service now attempted to prevent hurricanes by no longer predicting any, they'd fail, horribly -- while if it was causal in anything like the usual sense, it should succeed. Granger causality is a jargon term with an entirely different meaning to the usual thing "causality" is taken to mean. It's a useful concept in its intended application area, but we should be careful not to conflate it with causality in what seems to be the intended sense. $\endgroup$ – Glen_b Aug 26 '17 at 1:08
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    $\begingroup$ Without experiments it's impossible to establish causality based on solely observations. $\endgroup$ – Aksakal Aug 26 '17 at 1:12
  • $\begingroup$ Regarding Granger causality, what is the difference between 'predictability' and 'causality'? If A always predicts B, and always comes before B, then does the existence of A cause B? $\endgroup$ – Justin Thyme Aug 27 '17 at 0:18

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