"Because" (in the original quote) is about causality. Your inequality implies nothing causal without a lot of assumptions.
Yes, naturally. I suppose I should have made myself a little clearer there; I was not making any reference to the original quote, but rather to Jiro's comment, which makes no mention of causation, only Bayesian updates.
I don't understand what your setup is for increasing belief about a causal link based on an observed correlation (not saying it is impossible, but I think it would be helpful to be precise here).
Because P(causation|correlation) > P(causation|~correlation). That is, it's more likely that a causal link exists if you see a correlation than if you don't see a correlation.
As for your second paragraph, Jiro himself/herself has come to clarify, so I don't think it's necessary (for me) to continue that particular discussion.
Because P(causation|correlation) > P(causation|~correlation). That is, it's more likely that a causal link exists if you see a correlation than if you don't see a correlation.
Where are you getting this? What are the numerical values of those probabilities?
You can have presence or absence of a correlation between A and B, coexisting with presence or absence of a causal arrow between A and B. All four combinations occur in ordinary, everyday phenomena.
I cannot see how to define, let alone measure, probabilities P(causation|correlation) and P(causation|...
Another month, another rationality quotes thread. The rules are: