XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-19, dart200  wrote:   
   > On 11/19/25 10:48 AM, Kaz Kylheku wrote:   
   >> On 2025-11-19, dart200  wrote:   
   >>> On 11/19/25 9:17 AM, Tristan Wibberley wrote:   
   >>>> On 19/11/2025 01:40, dart200 wrote:   
   >>>>   
   >>>>> i'm currently a bit stumped on dealing with a possible a halting paradox   
   >>>>> constructed within RTMs, using an RTM simulating a TM simulating an RTM.   
   >>>>> this chain similarly mechanically cuts off the required information to   
   >>>>> avoid a paradox, kinda like a TM alone. not fully confident it's a   
   >>>>> problem or not   
   >>>>   
   >>>> It sounds equivalent to problems of security wrt. leaky sandboxes.   
   >>>> Interesting stuff. Maybe valuable too.   
   >>>   
   >>> i'm actually pretty distraught over this rn. who's gunna care if all i   
   >>> did was reframe the halting problem?? i'm stuck on quite literally a   
   >>> liar's paradox, with emphasis on a clear lie taking place   
   >>>   
   >>> specifically: the simulated TM simulating an RTM is lying about the true   
   >>> runtime context, bamboozling reflection's ability to prevent paradox   
   >>> construction   
   >>   
   >> Don't you have mechanisms to prevent the procedures from being   
   >> able to manipulate the environment?   
   >>   
   >>> und = () -> {   
   >>>     simTM {   
   >>>       if ( simRTM{halts(und)} )   
   >>>         loop_forever()   
   >>>       else   
   >>>         return   
   >>>     }   
   >>> }   
   >>   
   >> So in ths above construction, simTM creates a contour around a new   
   >> context, which is empty?   
   >   
   > essentially yes. simTM does not support REFLECT, so simulations within   
   > the simulation have no method of accessing the runtime context, creating   
   > the illusion (or lie) of an null context   
      
   In a computational system with context, functions do not have a halting   
   status that depends only on their arguments, but on their arguments plus   
   context.   
      
   Therefore, the question "does this function halt when applied to these   
   arguments" isn't right in this domain; it needs to be "does this function,   
   in a context with such and such content, and these arguments, halt".   
      
   Then, to have a diagonal case whch opposes the decider, that diagonal   
   case has to be sure to be using that same context, otherwise it   
   is not diagonal; i.e.   
      
     in_context C { // <-- but but construct is banned!   
      
        // D, in context C "behaves opposite" to the decision   
        // produced by H regarding D in context C:   
      
        D() {   
          if (H(D, C))   
            loop();   
        }   
     }   
      
   Or:   
      
     D() {   
       let C = getParentContext(); // likewise banned?   
      
       if (H(D, C))   
         loop();   
     }   
      
      
      
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