In 1919, an writer named Charles Fort released The Book of the Damned, a collection of observations of anomalous phenomena that he had gathered from newspaper archives.

The power that has said to all these things that they are damned, is Dogmatic Science.

But they'll march.

Fort was specifically looking at supposedly "impossible" things, which science would deny - but by carefully tracking and collecting references to such things, Fort was making the case that "impossible" things actually happened, and the error was in a scientific vision that was too narrow and rigid to acknowledge phenomena they could not explain. Fort gave his name to this kind of phenomena, which became known as "Fortean" - and he enjoyed some considerable success in subsequent books and some decades later a magazine called The Fortean Times, which is still published today.

The right-hand view of Forteana is that science should keep an open mind - "There are more things in heaven and Earth, Horatio, Than are dreamt of in your philosophy." - and the left-hand is that "Extraordinary claims require extraordinary evidence." Lots of things are happening all the time; some small percentage of them are going to be statistically odd - and over time, the oddities are going to build up, if you keep records.

Fort noted this and collated some of the data, usually presenting them in a suggestive rather than a definitive matter - instead of claiming the answer, he arranged the data to suggest an answer, usually taking a swing at how a close-minded scientist or editor dismissed some element of the event or phenomena as impossible when given an explanation. It isn't exactly a scientific methodology, but it is suggestive for a lay audience - which was Fort's audience. On the plus side, Fort tried to discourage incredulity and promote critical thinking. On the minus side, he implicitly encourage pseudoscience, pseudohistory, and other "disciplines" which thrive on having an organized academic opponent to contrast, ridicule, and present themselves as credible alternatives to.

What it comes down to is burden of proof: how much evidence, and of what kind, is sufficient to say "this thing happened?" (Or more likely "this thing may plausibly have happened.") For historical events, that can be very difficult, especially if there is no surviving physical evidence (the province of archaeology, usually) or records from that period. You have to comb your sources, compile your evidence, examine it carefully, and present your arguments.

Sometimes, you can even perform experiments - like Thor Heyerdahl's famous Kon Tiki expedition in 1947, where he crossed the Pacific Ocean in a ship built using the materials and technology available to Native Americans before Colombus, to show that it was possible for trans-oceanic contact between South America and Polynesians. This was, essentially, "experimental archaeology" - proving that such a feat was possible did not establish that it had actually happened, but it went a long way forward to convince folks that it could have been done.

With scientifically anomalous phenomena, its gets more difficult. You have to have a good grounding in the sciences to realize what is and is not really possible; you have to examine the records with an eye for observations that are questionable or could have been skewed by witness bias, editors, lazy recorders, or bad translation; and in many cases experimental replication is not possible, at least not at scale - history, unlike other disciplines, is not one where you can re-run the same scenario with different variables.

In many practical cases, "overruling" doesn't happen - but scientific and historical consensus can be challenged, and changed, if the weight of evidence and argument is sufficient. Some sources that might help in this regard:

• The Logic and Methodology of Science and Pseudoscience by Fred Wilson

• Invented knowledge: false history, fake science and pseudo-religions by Ronald H Fritze