idea

The triangle: checkable, complete, true

There is one special system that is complete and fully true: take every true statement about numbers as an axiom. It exists, but nobody can write it down or check it, so it is useless as a rulebook.

Gödel says no system can have all three. Pure randomness gives up checkability and truth, and only gets completeness by luck.

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Sources

  1. Wikipedia: True arithmetic
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