This principle, says McLatchie, “has led many skeptics to push the bar of demonstration so unreasonably high that it cannot possibly be cleared by any amount of testimonial evidence”:
The problem with the word “extraordinary” here is that it is rarely clearly defined. The mantra that I would adopt instead is that all claims require sufficient evidence. What counts as sufficient evidence will depend upon the relevant prior probability. And, indeed, the only relevance that the fact that a given event is supernatural has epistemically is that it suppresses the prior. However, even prior probabilities that are extremely small (but non-zero) can, in principle, be overcome if adequate evidence is forthcoming. This failure on the part of atheists to define what they mean by “extraordinary” in this context leads to them setting the bar of evidence so unreasonably high that the burden of proof cannot possibly be met.
What is the problem with the word “extraordinary”? If by that word we simply mean an event that is highly improbable or unique, then any event can be defined with sufficient specificity to meet that criteria. For example, consider Joe’s marriage to Sally. Joe being married to someone with the specific traits and characteristics of Sally is enormously improbable — especially when one considers the numerous other couples who had to meet, and the specific sperm cells that had to meet specific egg cells, all the way back to the dawn of humanity, in order for Joe and Sally to both be living at the same time. And yet Joe would be able to offer sufficient evidence that he is in fact married to Sally – adequate evidence to overcome a low prior probability. Is the fact that Joe married Sally an extraordinary event? Well, it depends on what you mean by “extraordinary.”
The point I am trying to make here is that you cannot simply define an extraordinary event as an occurrence that is highly improbable or unique (i.e. that it is something that lies outside of what normally happens), since that takes us into the realm where we can show that lots of events are very improbable or unique, if they are defined with enough specificity. Instead, the argument here is going to need to be more sophisticated…Jonathan McLatchie, “Do Extraordinary Claims Require Extraordinary Evidence? Assessing Carl Sagan’s Dictum” at Writing
But then many atheists have no difficulty believing in extraterrestrial aliens even though we have no evidence for their existence. See:
Why do people who believe in extraterrestrials dismiss ghosts? The talk about extraordinary claims requiring extraordinary evidence—or otherwise—misses the point. There is no evidence. People who have a fully naturalist worldview can believe that there are extraterrestrials but not ghosts. That’s worldview, not evidence as such.