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|    comp.ai.philosophy    |    Perhaps we should ask SkyNet about this    |    59,235 messages    |
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|    Message 58,846 of 59,235    |
|    olcott to Richard Damon    |
|    Re: Proof that the halting problem is in    |
|    27 Dec 25 16:45:57    |
      [continued from previous message]              >>>>> It can not handle most systems with a countably infinite domain of       >>>>> regard, so not Natural Numbers, not Finite Strings, not Turing       >>>>> Complete Systems.       >>>>>       >>>>       >>>> It can handle them at least to the same extent       >>>> as humans minds. Algorithmic compression.       >>>       >>> NOPE, As if it could handle Natural Numbers, then we could create the       >>> G for the system, and it couldn't prove it.       >>>       >>       >> It is merely that diagonalization hides the semantic       >> incoherence that reject's G.       >       > Nope. It seems you don't understand that G is just a statement that no       > number statisfies a specific (complicated) Primitive Recursive       > Relationship. A Relationship that can ALWAYS, for ANY number, be       > evaluated in finite time.       >              "that no number satisfies a specific (complicated) Primitive       Recursive Relationship" How is this shown?              > There is no "diagonalization" in G. You are confusing different proof.       >       > The question of G is a pure mathematical question, either a number does       > or does not satisfy it.       >       > In other words, your "logic" says some questions with factual answers       > are just wrong.       >       > In other words, your logic is proven to be self-inconsistant, as       > statements provably true are considered to be illogical.       >              You know that the Liar Paradox: "This sentence is not true"       is not a truth bearer. None-the-less when we add one level       of indirect reference       This sentence is not true: "This sentence is not true"       it becomes true.                     --       Copyright 2025 Olcott |
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