I guess if you want to be formal you need to actually define imply like you have but the author hasn't. I'd go with A implies B means (not A) or B, ie binary i

I guess if you want to be formal you need to actually define imply like you have but the author hasn't. I'd go with A implies B means (not A) or B, ie binary implication. That'd seem to capture the spirit of "correlation does not imply causation" since we can have correlation (A) and not causing (not B), ie not((not A) or B), ie no implication. So I guess we can use it for this too as at least a possible definition. If we say A is correlation in the sample set, B is correlation in the population, I think we can replicate the above argument and say we can have correlation in the sample set (A) and not correlation in the population (not B), ie not implication. An obvious example would be if we have 2 variables and plotting them gave a simple quadratic curve (say, y=x^2 across x=[-10,10]) - we can find a sample set with strong positive correlation and another with strong negative correlation - but neither really describes the population as a whole. So being mathematical and using the boolean logic implication definition I think it's a valid statement - but defining implication in context is pretty important.