The people, scientists or "laypersons", who conclude that they can know causality from correlation are in error already [1], but those who engage in an observational study, though there are inherent hearsay components when it comes to communication between the scientific observers and to the public, and think that their experiences are what show that a causal link between two things/events is possible thoroughly misunderstand possibility. Only one thing in itself dictates what is possible: consistency with logical necessities like axioms. Since axioms cannot be false [2], they must be true, and so anything that does not contradict them is either true or possible, while anything that does exclude them can only be false.
Does the artificial sweetener aspartame potentially cause cancer? Does that new medication have a potential risk of triggering heart palpitations? Of course they possibly have these effects, as all of this is a matter of simply not contradicting logical axioms or other necessary truths, and no one needs sensory experience to realize this. Still, a certain kind of idiot believes that an empirical study, which is incapable of ever epistemologically proving a metaphysical causal link to begin with, though it can reveal degrees of probability, is necessary to realize this. There would be nothing pointing to a particular correlation between events and thus probability of causation apart from empirical observation, which has no guarantee of not being illusory; all truths and possibilities are still a matter of logical necessity and consistency.
It only takes recognition of what does or does not logically follow from something, in this case consistency with axioms, and a moment or two of reflection on this topic to realize that possibility of a causal connection is not metaphysically determined or epistemologically revealed by a study, much less by hearsay afterward presented to the public about a study. Of course, since sources make claims inconsistent as it is, and new research can support or point away from a previously proclaimed scientific "certainty" or probability, the person who believes that something is possible because of a study is not just stupid, but he or she is also going to, if consistent, shift between believing something is possible or impossible as often as some source they subjectively find persuasive says so.
Any concept can immediately be known with absolute certainty to be possible or impossible through the aforementioned criterion. With phenomena in the natural world (by natural I mean physical here, so any artificial substance like aspartame would still be part of this), everything is by necessity constrained/governed by the separate laws of logic, and while possibility does not mean that a given correlation or causation is true of nature, whether something could or could not be true is knowable without going out to see what perceptions of events are reported by the senses. This is just as true of receiving hearsay, which has its own epistemological deficiencies, that in turn reports what someone else experienced.
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