Nonsense, if we view proving as providing evidence for, then absolutely we can prove a negative. We have our priors, we accumulate evidence, we generate a posterior. At some point we are sufficiently convinced. Don't get hung up on the narrow mathematical definition of prove (c.f. the exception[al case] that proves [tests] the rule), and we're just dandy.

I like to think that what the “can’t prove a negative” phrase originated from was someone grasping at the difference between Pi_1 and Sigma_1 statements . For a Pi_1 statement, one needs only a single counterexample to refute it, but to verify it by considering individual cases, one has to consider all of them and show that they all work (which, if there are infinitely many, it is impossible to handle them all individually, and if there are just a lot, it may still be infeasible) . Conversely, for a Sigma_1 statement, a single example is sufficient to verify the claim, but refuting it by checking individual cases would require checking every case.

Mathematics and scientific proof of negatives are different kinds of proofs.

> Impossible standard. You cannot prove a negative

It's also a deep incumbency advantage. Of course the guys selling the existing stuff are going to dispute the safety of a competitor.

And when a chemical goes off patent protection and you have a new patented chemical ready to go, it's advantageous to suddenly dis the now public domain entity.