XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-17, olcott  wrote:   
   > On 11/17/2025 5:38 PM, Alan Mackenzie wrote:   
   >> olcott  wrote:   
   >>   
   >> [ .... ]   
   >>   
   >>> *you cannot begin to understand the nuances that this entails*   
   >>   
   >> There's nothing particularly remarkable in what follows.   
   >>   
   >>> Turing machine deciders only compute a mapping from   
   >>> their [finite string] inputs to an accept or reject   
   >>> state on the basis that this [finite string] input   
   >>> specifies or fails to specify a semantic or syntactic   
   >>> property.   
   >>   
   >> Yes.  So what?  You can omit the redundant "on the basis that ... or   
   >> syntactic property" without any loss.  You could omit the redundant   
   >> "only", too.   
   >>   
   >>> *This one single point makes your whole view a compete failure*   
   >>   
   >> Perhaps you could elaborate just how that platitude makes my view a   
   >> failure.  It's certainly not clear from what you've written.   
   >>   
   >   
   > The above that I formed myself has key details that   
   > are simply assumed away from the conventional way   
   > this is stated:   
   >   
   > In computability theory, the halting problem is   
   > the problem of determining, from a description   
   > of an arbitrary computer program and an input,   
   > whether the program will finish running, or   
   > continue to run forever.   
   > https://en.wikipedia.org/wiki/Halting_problem   
   >   
   > Makes sure to not take into account that an input   
   > that calls its own decider specifies a different   
   > sequence of steps than this same input to a decider   
   > that it does not call.   
      
   The input D does not "call its own decider".   
      
   It incorporates an implementation of a particular decider algorithm,   
   appiles it on itself, and then behaves contrary to its output.   
      
   > You can disbelieve that DD simulated by HHH does not   
   > specify recursive simulation the same way that you   
   > can disbelieve that 2 + 3 = 5.   
      
   It does! But (it has been shown with code, even, using   
   your own framework!) that a recursive simulation can consist   
   of a regenerating progression of /terminating/ simulations.   
      
   It is possible that generation of new simulations never stops;   
   but the simulations themselves terminate.  (It's also possible that they   
   don't terminate.)   
      
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