The basic idea has been around for centuries.
We often use this saying when we encounter gullible creationists making extraordinary claims. For example, a few weeks ago Vincent Torley claimed that back in the 1600s a monk named St. Cupertino was routinely seen to fly through the air on numerous occasions [see What counts as "evidence"?].
Vincent Torley has returned to the topic in a recent post on Uncommon Descent: Good and bad skepticism: Carl Sagan on extraordinary claims.
If my friend Tom tells me that he saw a UFO land in his backyard last night, then I would naturally suspect that he was pulling my leg. But if several members of his family, as well as some friends of his whom I knew to be fine and upstanding people, swore on a stack of Bibles that they had seen the same thing, then I would have to believe that they weren’t lying, and that their claim was a genuine one. I would be irrationally obstinate, if I didn’t accept this fact at the outset of my investigation. The standard of evidence that would need to be satisfied here is what lawyers refer to as proof beyond reasonable doubt.That's a pretty good example. Most of us will strongly suspect that the claim is false and a UFO did not land in the backyard.
Let's see how Vincent Torley deals with the extraordinary claim ...
I would then proceed to consider naturalistic explanations for the sighting. The first question I’d need to answer is whether it had a subjective or an objective explanation. Could the witnesses have been hallucinating? If I were able to rule out known possible causes of mass hallucinations, such as alcohol, drugs or mass hysteria, I’d have to move on to the next question, which is whether the witnesses had experienced an optical illusion of some sort – perhaps caused by poor lighting, or freak atmospheric phenomena known to cause mirages. Physical traces left in the backyard after the sighting (e.g. burn marks on the ground) would rule out the possibility of an illusion or mirage. The third question I’d ask is whether any known physical phenomenon could account for the sighting – perhaps ball lightning, or a meteorite, for instance. But if witnesses’ accounts of the object’s appearance or pattern of descent proved incompatible with these phenomena, then I’d have to reject a physical explanation and look for an artifactual one. The fourth question I’d have to consider is whether any man-made artifact could explain the sighting – perhaps a child’s radio-controlled toy UFO, or some falling debris from a plane or satellite flying overhead, or for that matter, a top-secret military aircraft. It would be difficult to rule out all of these hypotheses, but I can certainly think of evidence that would convince me that the object seen was extra-terrestrial in origin: traces on the ground of elements not naturally found on Earth, or a star-map left behind by the visitors which contained detailed information, unknown to our astronomers. This would indeed be extraordinary evidence, and in order to satisfy myself that it was satisfactory evidence, I’d have to establish that the probability of such evidence having a human or natural source was vanishingly low.That sounds reasonable to me. When it comes to extraordinary claims, you need to come up with extraordinary evidence.
A similar failure of logic can be seen in biochemist Larry Moran’s dismissive comments regarding the massive amount of documentary evidence that thousands of people in the seventeenth century claimed to have witnessed a man levitating above the ground, often for hours, and on thousands of different occasions. Moran asks: "is it more reasonable to assume that thousands of people saw St. Cupertio fly or is it more reasonable to assume that they all just imagined it, or that the second-hand reports are untrue? (italics mine – VJT)" As I showed here and here, there are thirteen volumes of of eyewitness reports. Moran is happy to suppose that these may have been forged, rather than believing in a miracle. But here, he is confusing the question of whether people claimed to have seen a man levitate with the question of whether the man they claimed to have seen levitate actually did. As we have seen, a very high degree of skepticism is warranted only with regard to the second question. Proof beyond reasonable doubt suffices for the first.Extraordinary!!!