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Decius comments on Falsifiable and non-Falsifiable Ideas - Less Wrong Discussion
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In the future, I hope you notice this sort of situation and respond by getting curious and engaging with the other person, rather than attempting to win the argument.
In fact, it's rather worse :) The negation of an unfalsifiable belief is also unfalsifiable - you unfalsifiably believe that Carl's garage does not have an immaterial dragon in it. Even if you make an observation, e.g. you throw a ball to measure the gravitational acceleration, you have an unfalsifiable belief that you have not just hallucinated the whole thing.
At some point you devolve into declaring all beliefs unfalsifiable, because of the unfalsifiable belief that you exist (what different observations would you expect to you didn't exist?) and the complementary unfalsifiable belief that you don't exist (suppose you existed; what observations would be different?)