XPost: sci.math, comp.theory   
   From: chris.m.thomasson.1@gmail.com   
      
   On 11/25/2025 8:21 PM, Python wrote:   
   > Le 26/11/2025 à 05:18, olcott a écrit :   
   >> On 11/25/2025 9:58 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.   
   >>>   
   >>>   
   >>   
   >> The entire body of atomic facts of the world   
   >> is a finite set that can be syntactically   
   >> formalized as Rudolf Carnap Meaning Postulates.   
   >>   
   >> Every verbalized thought than anyone has ever   
   >> had or ever will have before the dying Sun   
   >> consumes the Earth is also a finite set.   
   >   
   > So no eternal life in Heaven then?   
   >   
   >   
      
   ^D Interesting comment. PO's body on earth will eventually die (like   
   all of us containers), but even after destruction of his body/container,   
   body, on earth. He will still post to USENET? ;^o   
      
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