XPost: sci.math, comp.theory   
   From: user7160@newsgrouper.org.invalid   
      
   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?   
      
   --   
   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)