XPost: sci.math, comp.theory   
   From: user7160@newsgrouper.org.invalid   
      
   On 11/25/25 8:23 PM, Python wrote:   
   > Le 26/11/2025 à 05:22, dart200 a écrit :   
   >> 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   
   >   
   > So ?   
      
   the "halting problem" is not the only way to confirm a specific case of   
   an uncomputable function, and therefore it is not necessary for that   
   reasoning   
      
   in fact, the very first example of an uncomputable function was not an   
   undecidable paradox like the halting paradox, read the first couple   
   paragraphs of §8 from his 1936 paper   
      
   --   
   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)