This isn't really true if you use Bayesian science. The idea you're stating is something like "It's not possible to prove hypothesis H1 if H1 is 'all swans are

This isn't really true if you use Bayesian science. The idea you're stating is something like "It's not possible to prove hypothesis H1 if H1 is 'all swans are white' by sampling swans and only getting white ones, but it's possible to disprove hypothesis H1 by finding a black swan." However, you can prove hypothesis H2 that "there exists a black swan" by finding such a swan. And you can't really disprove it for the same reason that you can't prove H1. Neither of theses hypotheses are proven/disproven in the mathematical sense of "proof" but finding sufficient evidence in favor or against a hypothesis is practically the same in the case of science. The Bayesian version of this is that the hypothesis is something like "the probability of a swan being white is P" and the value of P will by updated based on the strength of the evidence. It will never be exactly 0 or 1, but it will be close enough in many cases. Then you avoid the argument about whether a hypothesis is a binary "true" or "false" but discuss a continuous probability. E.g, the a hypothesis about the Earth being round has a probability close to one for most people while Russell's teapot and Sagan's invisible dragon have probabilities close to zero until evidence shows otherwise.