Godel & Turing Turning Turning Turning

 "Truth and provability are not the same thing."

Even in mathematics, the gem of man's reason, there are some truths which can not be proven.

A civilization may operate with a system for a thousand years, and then one day a contradiction finally arises proving the system had always been inconsistent.

No system can prove its own consistency, it is beyond the bounds of its scope.

Within systems like math, the best one can aim for is a consistent, yet incomplete system. The only problem, as stated before, is that the system has no way to know if it is consistent.

Attempting to add additional systems to remedy this will only create a larger cascade of incomplete and/or inconsistent systems.