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Thoughts on technology, engineering, and everything in between.
Cognitive Incompleteness IV: Beyond Gödel
Why this framework differs from Gödelian incompleteness, how latent reasoning in LLMs provides an empirical interface, and the open questions ahead.
Read more →Cognitive Incompleteness III: The Resonant Blind Morphism
Theorem 2 — when two incomplete cognitive systems couple, they don't cover each other's gaps. They co-create shared hallucinations that pass all internal verification.
Read more →Cognitive Incompleteness II: Perceptible Unknowability
Theorem 1 — a cognitive system can prove its self-representation is incomplete, yet cannot identify any specific element in the gap. You can feel the boundary; you cannot name what lies beyond it.
Read more →Cognitive Incompleteness I: The Metaphor and the Axioms
A category-theoretic framework for why minds cannot fully understand themselves — introducing the core axioms of Finite Generation, Self-Reference, and Categorical Rupture.
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