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응시, 원경의 지평
<Contemplative Contemplation - The Horizon in a distant view>
ENDLESS OPENNESS
According to the Gödel's Incompleteness Theorem
If F is a consistent formal system that is capable of expressing arithmetic,
then there exists a statement G such that:
This tells us that there are true statements G
that cannot be proven within the system F.
Let 𝕂 represent the body of knowledge within a formal system F.
Gödel's theorem implies:
This means there exists a true statement G
that is not provable within the system F.
ITERATIVE EXPANSION
As we expand our system F to a new system F' to include G, there will always be new statements G' that remain unprovable:
Each expansion leads to a new system where new true but unprovable statements exist, symbolizing the endless openness.
HIERARCHICAL SYSTEMS
The idea of an infinite hierarchy of systems emphasizes the ever-growing horizon of knowledge.
LIMIT OF KNOWLEDGE
As n approaches infinity, the union of all these systems still leaves some truths unprovable:
The conclusion that even the union of all these systems might not encompass complete knowledge reinforces the concept of "endless openness.”
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