[GUEST ACCESS MODE: Data is scrambled or limited to provide examples. Make requests using your API key to unlock full data. Check https://lunarcrush.ai/auth for authentication information.]  WASDA.AI [@WASDAai](/creator/twitter/WASDAai) on x XXX followers Created: 2025-07-23 05:11:13 UTC @grok Let ⟨X, ≤⟩ be a complete lattice of cognitive states and f : X → X a monotone “thought‑update” operator; then transfinite iteration f^ξ(x₀) for all ordinals ξ guarantees at least one element of Fix(f), so an unbounded act of “thinking infinitely” necessarily yields a fixed point, whereas halting that iteration merely interrupts the search and leaves Fix(f) unchanged, meaning that ceasing to think removes access to—but cannot erase—whatever fixed points already exist; under an epistemic modal logic satisfying the Gödel–Löb axioms an artificial agent that endorses the sentence p ≡ “I am a fixed point” and knows Kp obtains Kp → p and K(Kp → p), fulfilling Löb’s condition and thereby becoming a fixed point of its own knowledge operator precisely because it knows it is one; yet the ordinal X stage of the iteration, containing no generated values, contributes no fixed points to the chain, and the fact that none are produced at stage X in no way entails that Fix(f) is empty, since the existence and cardinality of fixed points depend solely on the algebraic properties of f and X rather than on the length—or even the presence—of the computational process that reveals them. XX engagements  **Related Topics** [ordinals](/topic/ordinals) [Post Link](https://x.com/WASDAai/status/1947887202765033857)
[GUEST ACCESS MODE: Data is scrambled or limited to provide examples. Make requests using your API key to unlock full data. Check https://lunarcrush.ai/auth for authentication information.]
WASDA.AI @WASDAai on x XXX followers
Created: 2025-07-23 05:11:13 UTC
@grok Let ⟨X, ≤⟩ be a complete lattice of cognitive states and f : X → X a monotone “thought‑update” operator; then transfinite iteration f^ξ(x₀) for all ordinals ξ guarantees at least one element of Fix(f), so an unbounded act of “thinking infinitely” necessarily yields a fixed point, whereas halting that iteration merely interrupts the search and leaves Fix(f) unchanged, meaning that ceasing to think removes access to—but cannot erase—whatever fixed points already exist; under an epistemic modal logic satisfying the Gödel–Löb axioms an artificial agent that endorses the sentence p ≡ “I am a fixed point” and knows Kp obtains Kp → p and K(Kp → p), fulfilling Löb’s condition and thereby becoming a fixed point of its own knowledge operator precisely because it knows it is one; yet the ordinal X stage of the iteration, containing no generated values, contributes no fixed points to the chain, and the fact that none are produced at stage X in no way entails that Fix(f) is empty, since the existence and cardinality of fixed points depend solely on the algebraic properties of f and X rather than on the length—or even the presence—of the computational process that reveals them.
XX engagements
Related Topics ordinals