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OnTheOtherHandle comments on Harry Potter and the Methods of Rationality discussion thread, part 25, chapter 96 - Less Wrong Discussion
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The first definition of "falsifiable" means that it's easy to fake - if a Patronus is falsifiable under this definition, you don't get much information when you see a Patronus, since it could easily be something else and you couldn't tell the difference.
The second definition of "falsifiable" means that it's easy to prove that it's not fake - if a Patronus is falsifiable under this definition, you get a lot of information when you see a Patronus, since it is very difficult for something that looks like a Patronus to actually be a fake.
Because the two defintions are pretty much opposites, between them they cover everything - the ones that are easily fakeable and the ones that are not easily fakeable.
Aha! Thank you!
My mistake was that I kept thinking about "false" as in "false theory" instead of "false" as in "false money".