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A French farmer brought a rock to the French Academy and told the scientists that it had fallen from the sky. For years and years the claim that rocks could fall from the sky was ridiculed and called an extraordinary claim that contradicted everything that was know about astronomy. Eventually, astronomers realized that there WERE rocks floating around in space, and that from time to time they DO fall into the atmosphere and either burn up or partially burn before hitting the ground.
At the time the claim was made, the unstated assumption was that rocks in space were impossible. Therefore the claim was called extraordinary not based on on having been falsified, but based on an unstated assumption about the way things are.
The same with continental drift. It was an extraordinary claim, not because it had been falsified, but because it contradicted an unproven, unquestioned assumption that continents don't move around. Then plate t4ectonics was discovered, and we learned that continents actually FLOAT on top of a semi-liquid mantle.
Another example, which HAS NOT YET BEEN SETTLED, is the claim of ESP. There is a lot of tantalizing research, but no real proof, one way or the other. The claim is called extraordinary simply because the unquestioned assumption of materialism is that it is not possible. This assumption is made without explaining WHY it is not possible, only that it violates an unquestioned assumption. ESP may well prove to be false, but until it is established one way or the other, it is an extraordinary claim ONLY if you grant the underlying assumptions of materialism. Well, as a philosophy, materialism has the basic, founding assumption that ONLY matter/energy is real. So naturally, anything which is neither matter nor energy MUST be false. Not provably false, but ASSUMED false by the fundamental axiom of materialism.
Now if any of the other underlying philosophical positions (such as idealism, or dualism) is assumed, the claim of ESP is no longer extraordinary under the assumptions of those philosophies.
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