Oh alright, but it's not really as interesting as all that. False implications in the logical context are commonly referred to as logical fallacies. Wikipedia has a (non-exhaustive) list of those. One of the more famous false implications is interesting in that it maps between types of implication.
A is correlated with B implies that A implies (causal) B or B implies (causal) A (note that this is false, with a plethora of different types of counter example). This is probably the most commonly exploited false implication by hucksters, and, perhaps more importantly, is a very common source of false beliefs with no malicious intent at all.
It is easy to leverage this false belief into new false beliefs with true facts. If I want to sell coffee for example, I must convince someone of the buying coffee implies (causal) utility fact. All I must convince them of is that coffee is correlated with a thing that implies (causal) utility. Say for instance, that people with heart conditions have those conditions exacerbated negatively by taking coffee or drinking stimulants, and therefore don't. It follows then that drinking coffee is probably correlated with much better heart health. I phrase my findings as "People who drink coffee tend to have much better cardiac calcium scores", and just watch as people draw the incorrect conclusion about the utility of coffee from this fact, plus their fallacy (plus the additional assumption that better cardiac calcium scores probably don't cause coffee consumption).
I should note that It could very well be that coffee does have utility to you. So as a fact it might still be "true". So it turns out that what really ends up mattering, is not the facts, but the chains of implications that lead you to them.
