When wondering whether a phenomenon A causes a phenomenon B, people often ask whether phenomenon A is necessary and sufficient to produce the phenomenon B. That got me thinking whether a phenomenon A can ever be proven to be a necessary condition for phenomenon B.
According to modal logic, a proposition "p" is necessary if, and only if, not "p" is not possible. So, if we can demonstrate that in the absence of A, B is not possible, we would be demonstrating that A is necessary for the occurrence of B. My question is: Can it ever be proven that something is not possible? How?