I'm linking to this because it summarizes what was the main argument of my Master's Thesis. "Scientific knowledge relies heavily on models and analogies, and the theorems that drive any model are necessarily simplified compared with real-world scenarios." If you understand that models and generalizations are created via a mechanism of subtraction, and not inductive extrapolation, you explain both the mystery of their derivation and the nature or their application. But it requires that you change your perspective on things like scientific principles and rules of logic and mathematics. They are not things that are necessarily true; they are things that are conditionally variable.
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