Here is something odd to consider. If no consistent system can be proved complete, then no outside system can prove this as fact. No system can prove that another cannot be proved complete or incomplete.

No system, then, is complete because it cannot be proved so, but this assertion, too, cannot be proved true. Therefore, nothing can be proved, perhaps.

Furthermore, a consistent system is one that never contradicts itself, but all systems contradict themselves if attempted to be proved complete. So, it follows that no system is ultimately consistent, either, because it must be proved complete to be so.

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