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It is generally accepted that the main characteristic of any science, which distinguishes it from other forms of knowledge, is falsifiability. For any scientific theory it must be possible to make predictions that can be tested.
Unfortunately, this requirement means that any non-trivial mathematical system cannot be part of science. Kurt Godel proved that any mathematical system that was worth having had to include statements whose truth or falsehood could not be proven without appealing to a more sophisticated system. But then that system contained statements whose truth value could not be ascertained ... and so on.
Rubye Mante
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