A proof done with conditional probability. Definition 1 correlation : c Definition 2 causation : a Definition 3 not everything correlates : P(c) < 1 Definition 4 causation give correlation: P(c|a) = 1 P(a|c) : evidence for causation = P(c|a) P(a) / P(c) : Bayesian inference = 1 P(a) / P(c) : definition 4 > P(a) : definition 3 Conclusion: P(a|c) > P(a) : Correlation is evidence of causation. Q.e.d. This proof is quite simple. You may notice that I did not include proper definitions of correlation or causation. Correlation is easy, since it is clearly defined as matrix math. Causation however, is worse. I did not find any definition in my statistics books, and Googling it gave meagre results. It found mainly claims that correlation is not causation, without explaining what either is. Since my proof is for people discussing like that, I decided to drop the explanations too, since they are not necessary, and fewer would understand them anyway. It is only necessary to know that causation give correlation. Same goes for Wikipedia, such as its Post_hoc_ergo_proper_hoc page. http://en.wikipedia.org/wiki/Post_hoc_ergo_propter_hoc Its main subjects are again correlation and causation, but without defining them usefully. Or one can accept all the similar articles as dealing in boolean logic, and that explains their use of words quite nicely, but boolean logic is not science, while Bayesian inference is, because it deals in probabilities. This, and other logical "fallacies", are just _logical_ fallacies. When translated into probabilities, they are often true. So, what are they? Where do they come from? Are they some kind of fallout after a war between philosophers and scientists, or what? Kim0+ (I originally made a proof with a definition of causation, but the more I studied, the more vague it became, until I ended up with evidence as a mathematical synonym for causation, and 4D edgy integrals of 3D simplex pieces of probability space, giving a proof that the correlation of A and B is evidence that A is evidence of B. But this went too far away from the original goal, so I dropped it.) Quote from Daniel Dvorkin: The correlation between ignorance of statistics and using "correlation is not causatison" as an argument is close to 1.