> "No Correlation does imply non-causation" You're wrong. Random variables can be uncorrelated but not independent [1]. In general, you can't apply "algebra"

> "No Correlation does imply non-causation" You're wrong. Random variables can be uncorrelated but not independent [1]. In general, you can't apply "algebra" to logic as you attempted above and explained below. Logic is very precise. To "prove" that `A => B` is equivalent `~B => ~A`, you use truth tables: | A | B | A => B | ~B => ~A | +---+---+--------+----------+ | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 1 | 1 | 1 | Your statements above aren't equivalent; the first is a tautology (it's always true), whereas the second is standard implication, which can be false. [1] http://en.wikipedia.org/wiki/Normally_distributed_and_uncorrelated_does_not_imply_independent http://en.wikipedia.org/wiki/Normally_distributed_and_uncorr...