XPost: sci.math, comp.theory   
   From: chris.m.thomasson.1@gmail.com   
      
   On 11/25/2025 8:55 PM, dart200 wrote:   
   > 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,   
      
   When shall your body on Earth halt?   
      
     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   
   >   
      
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