> You can even do so in a sophisticated way such that your defined system is internally coherent Rest assured, any mathematical or logical system capable of ex

> You can even do so in a sophisticated way such that your defined system is internally coherent Rest assured, any mathematical or logical system capable of expressing arithmetic is incoherent, if only trying to prove so using it's own rules. (You can shift the burden of proof to an external system you trust, but that external system would suffer from the same problem if a similar proof was attempted) https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_th... https://en.wikipedia.org/wiki/Gentzen's_consistency_proof https://en.wikipedia.org/wiki/Gentzen's_consistency_proof