XPost: sci.math, comp.theory   
   From: user7160@newsgrouper.org.invalid   
      
   On 11/25/25 7:58 PM, Python wrote:   
   > BTW you should think about what Ben Bacarisse once wrote:   
   >   
   > The set of all functions from ℕ to ℕ is uncountable (as large as the   
   > real numbers), while the set of all finite programs is only countable,   
   > so there are far more possible functions than there are programs to   
   > compute them; this guarantees that most functions are uncomputable and,   
   > more generally, that no finite formal system or algorithmic procedure   
   > can cover “all” functions, all truths, or all behaviors describable over   
   > the naturals—so whenever someone claims to have a universal decider, a   
   > complete semantic engine, or a single system that captures all “objects   
   > of thought,” they are implicitly pretending that countably many programs   
   > can represent uncountably many functions, which is mathematically   
   > impossible.   
   >   
   > The "halting problem" is actually only a way to confirm this with a   
   > specific case.   
      
   u don't need undecidable machines (that are actually hypothetical) to   
   confirm uncomputable functions   
      
   that is also something i stumbled upon in my musings   
      
   --   
   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)