XPost: sci.math, comp.theory   
   From: user7160@newsgrouper.org.invalid   
      
   On 11/25/25 6:40 PM, Python wrote:   
   > Le 26/11/2025 à 03:38, dart200 a écrit :   
   >> On 11/25/25 5:19 PM, Python wrote:   
   >>> Le 26/11/2025 à 02:09, dart200 a écrit :   
   >>>> On 11/25/25 4:31 PM, Python wrote:   
   >>>>> Le 26/11/2025 à 01:29, dart200 a écrit :   
   >>> ..   
   >>>>> Encoding Gödel’s proof inside Gödel numbers doesn’t defeat the   
   >>>>> theorem —   
   >>>>> that is the theorem.   
   >>>>   
   >>>> sorry, i mean if u encode literally godel's paper into godel's   
   >>>> numbers...   
   >>>>   
   >>>> doesn't that produce a proof within the system, for the statement   
   >>>> that has no proof within the system? ? ?   
   >>>   
   >>> No — encoding Gödel’s paper as Gödel numbers does not produce a proof   
   >>> inside the system, and it cannot possibly do so.   
   >>>   
   >>> you get just a big natural number, representing these syntactic strings.   
   >>>   
   >>> But the theory (PA, ZFC, whatever formal system) does not   
   >>> automatically recognize that number as a proof.   
   >>>   
   >>> Because for a number to count as a proof inside the system, it must be:   
   >>>   
   >>> ✔ A well-formed derivation   
   >>> ✔ From axioms, using inference rules   
   >>> ✔ Such that each step is checkable arithmetically   
   >>>   
   >>> Gödel proves (in meta-math) that the system cannot prove G if it is   
   >>> consistent.   
   >>> Nothing in the system can know why Gödel outside the system can see   
   >>> that.   
   >>>   
   >>> Encoding Gödel’s meta-reasoning into a massive integer doesn’t   
   >>> activate the meta-reasoning inside the system.   
   >>>   
   >>> The formal system looks at the number and sees:   
   >>>   
   >>> just a number, with no significance unless it matches the definition   
   >>> of a proof.   
   >>>   
   >>> It does not read the argument.   
   >>> It does not interpret his English/German sentences.   
   >>> It does not adopt his epistemic insight.   
   >>>   
   >>> Meta-reasoning ≠ internal derivation.   
   >>>   
   >>> Gödel numbering is like ZIP-compressing a PDF.   
   >>> Feeding it into PA doesn't make PA understand the PDF.   
   >>>   
   >>> Gödel’s construction is self-referential, but the system remains   
   >>> blind to the meta-narrative explaining that construction. The blind   
   >>> spot is exactly why incompleteness holds.   
   >>   
   >> what if we could put a hard limit to the degree of incompeletness   
   >> found within a formal system?   
   >   
   > You can cap incompleteness only by capping expressiveness.   
   > You don’t get rid of Gödel — you get rid of arithmetic.   
      
   i tried to improve the fundamentals of computing by adding a reflection   
   mechanism to turing machines to rid computing of godel, and that i think   
   failed in the most strict sense...   
      
   but out of that exploration i think i managed to limit the problem of   
   godel's incompleteness (where self-referencing computations ask the   
   unanswerable) to a set of machines that cannot /effectively compute/   
   more than the set of machines then not subject to the problem of   
   incompleteness   
      
   i'm capping the expressiveness of the decidable set of machine, in a   
   very specific manner that that should not limit the /computational   
   effectiveness/ of the system, beyond *just* not expressing the various   
   undecidable liar's paradoxes that we find within computing ... which   
   aren't useful machines   
      
   i don't know how this would effect more formal math theory, i'm   
   interested very specifically in the fundamentals of computing atm rather   
   than math more generally   
      
    > cause the way we built out computing is just utterly ungodly   
    >   
    > #god   
      
   i think a lot of engineers out there would agree that the complexity   
   found with modern applied computing is just ... absolute fucking lunacy,   
   even if they wouldn't agree with me that idiocy stems from a fundamental   
   mistake in accepting semantic paradoxes (like the halting problem) as a   
   fundamental limitation to the /computational effectiveness/ of computing   
   as a whole   
      
   they probably blame management structures, profit motive, etc, etc ...   
   and there not wholly wrong there. capitalism has indeed run wild with   
   complexity in a mad dash to accumulate more wealth in their systems than   
   has ever before been possible,   
      
   but there is a more fundamental issue in computing theory being unable   
   to rectify this due to perceived limitations on computing as a whole.   
      
   --   
   a burnt out swe investigating into why our tooling doesn't involve   
   basic semantic proofs like halting analysis   
      
   please excuse my pseudo-pyscript,   
      
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)