XPost: comp.theory   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 12/12/2025 14:35, Richard Damon wrote:   
   > On 12/12/25 9:29 AM, olcott wrote:   
   >> On 12/12/2025 8:12 AM, Richard Damon wrote:   
   >>> On 12/11/25 11:01 PM, olcott wrote:   
   >>>> Principle 1: Turing machine deciders compute functions   
   >>>> from finite strings to {accept, reject} according to   
   >>>> whether the input has a syntactic property or specifies   
   >>>> a semantic property.   
   >>>>   
   >>>> The halting problem requires that a halt decider   
   >>>> report on the direct execution of a Turing machine,   
   >>>> thus category error.   
   >>>>   
   >>>   
   >>> Which is a semantic property of the string, assuming it is a   
   >>> representation of the machine in question,   
   >>   
   >> Principle 1: Turing machine deciders compute functions   
   >> from finite strings to {accept, reject} according to   
   >> whether the input has a syntactic property or specifies   
   >> a semantic property.   
   >>   
   >> Turing machine deciders only report on the behavior   
   >> of Turing machines indirectly through the proxy of   
   >> finite strings. *This key detail has been ignored*   
   >   
   > But, you seem to forget, that said finite string can fully contain the   
   > information needed to recreate that execution behavior, and thus that   
   > behavior is a valid target for a question to it.   
      
   No. The information required is:   
      
   1. the program (the finite string)   
   2. the reduction rules   
      
   The finite string only contains 1, because 2 is nonempty.   
      
   >>   
   >> Principle 2: We measure the semantic property that   
   >> the finite string specifies by a UTM-based halt   
   >> decider that simulates its input finite string   
   >> step-by-step and watches the execution trace of   
   >> this behavior.   
   >>   
   >>   
   >   
   > No, it is measured by the results created by an ACTUAL UTM.   
      
   no, it is measured by the results defined by the reduction rules. The   
   statement that it has anything to do directly with an actual UTM (or TM)   
   is a misconception. Any physical, ostensible TMs (OTMs?) are   
   approximations of their respective reduction rules that, statistically,   
   are unlikely to deviate.   
      
   The problem is about physical computers only in as much as it elaborates   
   on what will happen in the limit of the process of creating ever more   
   reliable TMs.   
      
      
   --   
   Tristan Wibberley   
      
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