If you are in a maze with no exit, no matter how much you wander around, no matter how many different ways you try, you will never find the exit because there is no exit
Mathematics is an abstract universe with infinite and unexplored lands that the human mind builds using logic and intuition, inspired by both the outer world and its own inner structure.
Gödel's theorems are a profound discovery of the limits of human knowledge. He showed us that a final and perfect math. system cannot exist for which we can prove everything. This is not a failure, but rather the tremendous success of the human mind in understanding its limits.
Would you buy (shares of) a company worth 50 million dollar, knowing it had no debt and 200+ million in treasury?
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These experiences are "native" characteristics that cannot be reduced to scientific measurements, but only experienced by the individual himself. Qualia is seen as the basic building blocks of subjective experience.