>>13880504Forget ZFC and just consider formal systems in general
Nicholas of Cuza believed in three levels of mind:
1. Sensorium: this was the lowest, and is the level that allows for physical objects that is causing sense perceptions in our mind.
2. Reason: This is identical to formal systems, or theories in science. The intelligible reason why things are happening, not identical to sense perception. Reason is generally self contained.
3. Intuition: This is the highest level, and is the drive that makes people agree such things as sets, numbers, ideas exist and can describe the world. Intuition is supra-rational, you have to appeal to things like Beauty and "it just feels right".
>How do you know ZFC can be identical to real truths?Because for any formal system F, I can define an identical formal system F' that is identical to F, but changed a truth value for one proposition in the system. As long as it is logically consistent, I can do it. This is why you need to appeal to supra-rational truths when talking about these things. Truth is not found in purely mechanical formal systems only.
