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Gödel's Incompleteness Theorem: It Is About the Medium, Not the Facts
When I first approached Gödel’s incompleteness theorems, I came through the standard route: Gödel numbering, the diagonal lemma, self-referential sentences that encode their own unprovability. The machinery is genuinely impressive, and by the time the theorem emerges from it, it feels like a conjuring trick — something uncanny conjured from symbol manipulation. I came away thinking that something was fundamentally lost, that arithmetic inexplicably leaves a statement in genuine limbo, ambiguous in truth value, neither true nor false.
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