> Godel showed us there are true things that can't be represented by a formal system. This is stretching things a bit. Specifically, it defines truth as 'does

> Godel showed us there are true things that can't be represented by a formal system. This is stretching things a bit. Specifically, it defines truth as 'does not lead to a contradiction in (some formal system that extends) Peano arithmetic'. Then, as there are statements that are 'true' in this sense in such a system A but not probable by that system, there are 'unproveable truths'. But is that satisfactory as a definition of truth? It used to be because we had hope for a complete and consistent formal system, which feel very truthy. When Godel proved that cannot exist, perhaps the conclusion is that formal systems aren't the 'base' for truth.