XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 12/9/2025 6:42 AM, Richard Damon wrote:   
   > On 12/8/25 11:51 PM, polcott wrote:   
   >> On 12/8/2025 10:20 PM, Richard Damon wrote:   
   >>> On 12/8/25 11:00 PM, polcott wrote:   
   >>>> On 12/8/2025 9:38 PM, dart200 wrote:   
   >>>>   
   >>>> *You have support for this in high places*   
   >>>>   
   >>>> The Halting Paradox   
   >>>> Bill Stoddart   
   >>>>   
   >>>> 6 Conclusions   
   >>>> The idea of a universal halting test seems reasonable,   
   >>>> but cannot be formalised as a consistent specification.   
   >>>> It has no model and does not exist as a conceptual object.   
   >>>> Assuming its conceptual existence leads to a paradox.   
   >>>>   
   >>>> https://arxiv.org/pdf/1906.05340   
   >>>>   
   >>>   
   >>> Which doesn't prove anything, as there IS a consistant specification   
   >>> for the test.   
   >>>   
   >>> The problem is you (and Bill) just don't understand it.   
   >>>   
   >>> Part of the problem is Bill doesn't understand the nature of Turing   
   >>> Complete systems. In particular, he assume there is a UNIQUE encoding   
   >>> for every program, which is a false assumption in Turing Complete   
   >>> systems.   
   >>   
   >> With the text of each program P we associate a   
   >> unique number ⌈P⌉, known as the program’s encoding,   
   >> which will stand for the program when we want to   
   >> use that program as data, e.g. when passing one   
   >> program to another as an argument.   
   >>   
   >> You are just terribly inaccurate in paraphrasing.   
   >> Perhaps speaking to no one at all is better than   
   >> talking to you.   
   >>   
   >   
   > Except there are many texts that create the equivalent program, and thus   
   > many numbers for that program.   
   >   
      
   He is doing this like Gödel numbers, thus a unique   
   identifier is needed. And again this is merely nit-picky   
   his point is that the foundations of computer science   
   are incorrect and I have shown that two different ways.   
      
   > Yes, we can convert a program into data, but there are many data values   
   > that all represent the same program.   
   >   
      
   No there are not you are just not being precise enough   
   in your choice of words. And yet again this is an   
   irrelevant nit-picky detail.   
      
   > This means that Program H can't use a "unique" value of its   
   > representation to detect the input using it, as the pathological program   
   > can just use an equivalent variation not in the finite list of values   
   > that H tests for.   
      
   If the finite strings are not identical then the   
   inputs are not identical.   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)