There's an interesting article on Slate by someone miffed at all those 'correlation doesn't impy causation' slams common in retorts. He makes the good point that, while not proof, correlation is suggestive, and consistent with causation. If you want to be a pedant nothing non-tautological can be proven (see Hume's problem of induction). It reminds me of the saying 'absence of evidence is not evidence of absence.' This is wrong. It's not proof of absence, but from a bayesian perspective, it should increase one's belief in absence.
you've probably already read this (given that you mentioned bayesianism), but just in case not, you might like fallacies as weak bayesian evidence
"...from a bayesian perspective, it should increase one's belief in absence..."
That's perfectly valid only if you have some additional information about the expected background incidence of observation. For example, suppose I live in a swamp and every evening I slap at mosquitoes as a normal thing because that's just always the way I have always lived. Then one day not a single mosquito turns up, all night, not a single one, then I'd be thinking something weird is going on.
If I live in a desert and there's no open water for 50 miles in every direction and I've never even seen a mosquito in all my life, then I go all night and still don't see any mosquitoes, then that's just a normal night. I might even be tempted to think the whole idea of insects living in water was pretty far fetched.
In a way, you are right that all empirical science is nothing more than a framework for explaining correlated observations, but actually there's a little bit more to it. I build an experimental rig, then flip a coin and set a variable one way on head and another way on tail. Then I repeatedly run the experiment and I note some output variable is correlated with the coin toss. Well, I have to believe that the output of the experiment can't go back in time and adjust the coin toss.
See also: the importance of the control group; so you have something to contrast against (Feynman used to bang on about this).
The alt text for that image is:
"Correlation doesn't imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing 'look over there'."
so i guess it insinuates causation…
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