Carl Sagan, as usual when it came to epistemology, was wrong. “Extraordinary claims require extraordinary evidence” is applicable when speaking of empirical, falsifiable claims. Fine when you’re dealing with the hard sciences, or if for some reason you’re a positivist (impossible to be one, so we won’t go there today), but achieving a functional navigation in the physical world requires an actor to be much more epistemically open. It’s not something we have to think about, since it’s achieved on autopilot. You wouldn’t be able to step out your front door without it.
Just Thomism approaches it differently:
The humdrum thing you point at (soot jiggling in a jar) might have no proportion to the magnitude of the thing it is evidence for (the composition of all bodies in the universe). So what are we to make of the claim that extraordinary claims require extraordinary evidence? This obviously isn’t true if evidence is just “what one points to to prove the case”: jiggling soot is hardly an extraordinary thing to point to, though a claim about the composition of the entire universe clearly is. So it must mean that an extraordinary claim requires an extraordinary story or argument in defense of it.
In other words: evidence is not and cannot be incontrovertible, undeniable, or “hard.” It requires an explanation, and bringing language into the argument’s existence drags it outright into the realm of the subjective.