What you describe sounds like Hilbert's Program. Unfortunately, Godel's Incompleteness Theorem states that we can never find an all encompassing axiomatic system which is able to prove all mathematical truths, but no falsehoods.

*In reply to* **Re^2: What do you know, and how do you know that you know it?**
*by* **bunnyman**
*in thread* **What do you know, and how do you know that you know it?**
*by* **tilly**

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