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>Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability

not really. You can consider positive proof as an experiment confirming your theory and the negative proof and counter examples as an experiment falsifying your theory.

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Yes, really. "Positive proof" opposes the concept of falsification. You can only have it within a system formal logic, and science can contain those, but isn't one.

>"Positive proof" opposes the concept of falsification.

no. Positive proofs have nothing to do with falsification. They just tell you that there is no point in spending effort on searching for negative proofs and counter examples. They don't prevent nor prohibit you from spending that effort. They just advise you that that effort will be wasted.

It is like nobody prevents from experiments to turn lead into gold. Of from searching for a right angled triangle violating Pythagoras.

... within a system formal logic.

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