Quote from MAESTRO:
Although our intuition suggests that this abstract and self-contained world of science and mathematics could be as independent and complete as our real world the truth is that it is quite impossible.
This impossibility is based on two major logical discoveries:
1. Gödelâs incompleteness theorem. This theorem logically and self-evidently proves that any abstract, logically designed system can never be absolutely closed and self-contained â i.e. it can never possess in itself all possible theorems. In Wilderâs terms: "This demonstrates that in any system broad enough to contain all the formulas of any formalized theory, there exist theorems (formulas) that can be neither proved nor disproved within the system". This conclusion is in fact true for every
formally designed abstract system of beliefs.
2. Psychological impossibility. There is enough experimental evidence in modern cognitive psychology today that suggests that no productive system possible that uses the formal or abstract means only. If a system of beliefs contains all the definitions, axioms, theorems, proofs, etc. it needs the system will never work by itself in any productive manner.
Intuition therefore is our method of utilizing the abstract systems we created productively.