[qmalzp]

As a former mathematican, I was at first a little offended and dismissive of his claim. But, perhaps what one can say is that mathematicians don't seem to distinguish "causation" with "implication". After all, if the barometer goes down, that does imply a storm is coming (perhaps with some increased probability), but it still doesn't cause the storm to come (even with increased probability).

In a simplified closed system, where all you have are barometers and storms, maybe there is no difference between implication and causation; all you know is these variables are correlated. Perhaps once you take every atom in the universe into account, the two start to look the same.

[goatlover]

That can't be right, because you can take the barometers out of the closed system, and it will still storm. Correlation isn't causation, and for good reasons.

[ordu]

> In a simplified closed system, where all you have are barometers and storms, maybe there is no difference between implication and causation; all you know is these variables are correlated. Perhaps once you take every atom in the universe into account, the two start to look the same.

Implication it is a very mathematical thing. It is like you know, that y=f(x), and then you write x=g(x), where g is inverse of f. It works both ways, there are no cause, no effect, just link between two variables. If you use math to reason about causal links in reality, you need to use some implicit knowledge which is not represented in formula. It doesn't means that math is bad. Geometry likes euclidian space while we know from Einstein that our space is not euclidian one -- it doesn't mean that geometry is bad. Euclidian geometry just solves some specific problems and doesn't solve others.

Causal link reflects ability to change dependant variable by changing independant one. It is not something like "fundamental property of the Universe", it is our subjective way to structure information about the reality. It seems to me, that physicists believe the other way, that causation is the inherent property of reality. Maybe they are right in their field, but it doesn't work in everyday life. Causal link is an abstraction that helps us to know what we can do to change outcomes.

In this sense there are no causal link between barometer readings and a storm: if you change barometer readings to reflect a fine weather the storm will come anyway. Maybe there is causal link between atmosphetic pressure and a storm? I do not know it, because I see no way to change atmospheric pressure and I'm not educated well enough to understand scientific weather models. Though it is relatively safe for me to believe that low atmospheric pressure causes storm: causational link or correlational one -- it will not change my behaviour, because I cannot change atmospheric pressure. If I'll find a way, than it would be cruicial to figure out the kind of the link, because I'll be able to break something if I'm wrong. But I said that it is relatively safe, because if I suppose that link is causational, I would use that link differently while reasoning about the weather, it will change my other beliefs and probably it will change my behaviour somehow.

So, the main idea is: causation is just our way to structure reality. We are free to choose which links are causal, it is all up to us. If we think it will help us to reason about reality, then we should speak about casuality. And the most important difference between causation and correlation is the ability to change dependant variable by changing independant. If we can change dependant variable that way, than we should mark link as causational. If we cannot, that we should think about that link as about correlational. Implication just do not draw this difference.