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Undecideable arithmetic →
The most severe implications are philosophical. The result means that the rules we use to manipulate numbers cannot be assumed to represent the pure and perfect truth. Rather, they are something more akin to a scientific theory such as the “standard model” that particle physicists use to predict the workings of particles and forces: our best approximation to reality, well supported by experimental data, but at the same time manifestly incomplete and subject to continuous and possibly radical reappraisal as fresh information comes in.
