Suppose you observe data from some Bernoulli distribution and want to test whether the mean is 0.2 or 0.5 (hypothesis testing). If and you observe 463 tails and 537 heads, this is evidence against the mean being 0.2. Moreover, the precise amount of evidence it is in favor of 0.5 is quantifiable.
This is perhaps obvious to statisticians but is a fairly deep point. And the reason it’s deep is because this only works because of the artificial assumptions we’ve introduced into our statistical model. The real-world does not work this way. todo
We are wondering whether all swans are white, and we observe white swan after white swan. Does this mean there is mounting evidence against the hypothesis that there are black swans?