Further to David Deming’s observation that is often misused, Laszlo Bencze offers this thought: reminds us that he reflected a while back on the whole business of extraordinary claims requiring extraordinary evidence.
As to Carl Sagan’s “Extraordinary claims demand extraordinary evidence,“ well, my goodness, there’s a flaw here. The person making the demand is always the one to judge the sufficiency of how “extraordinary” is extraordinary enough. The extraordinary evidence demanded may be a mite too extraordinary. By these standards, we might still be stuck with ancient animistic notions of how the world works because no evidence extraordinary enough could ever be found to dislodge them.
But what’s wrong with “ordinary” evidence such as we usually get in the world of science? After all most great scientific insights are the result of thinking about quite ordinary events. Galileo’s swinging chandelier in the cathedral of Pisa comes readily to mind. What could be more ordinary? Yet it led to the extraordinary understanding that the time period to swing through a complete cycle is independent of the amplitude of the swing.
As Karl Popper points out, refutations of theories can be ordinary. A single contradictory fact is quite sufficient to upset a theory nor must the fact be spectacular. It can even be quite subtle. Certainly a single refutation of a popular theory will be viewed with a great deal of skepticism and will be examined rigorously. Nonetheless, if the example is sound then one is all that is needed. It does not have to be extraordinary (whatever that might mean).
The Michaelson-Morley experiment which showed that the speed of light did not vary according to the movement of the earth was unspectacular. It involved no pyrotechnics, no explosions. In many ways it was subtle and difficult to understand. Yet it pretty much laid to rest the notion that light traveled in a rarified medium called “ether.” I’m not sure that it received much popular notice at the time. But it did set the stage for a new physics that Einstein proposed about a decade later.
So I think it is better to use the phrase “An extraordinary claim demands ordinary, sound evidence.” Or more technically, “A single refutation upsets the theory.”
See also: David Deming: “Extraordinary claims require extraordinary evidence” misused due to ambiguity
and
The Materialist “Extraordinary Claims” Double Standard (Barry Arrington)
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