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   sci.logic      Logic -- math, philosophy & computationa      262,912 messages   

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   Message 261,862 of 262,912   
   polcott to All   
   Re: on mathematical ghosts (2/2)   
   13 Dec 25 07:15:48   
   
   [continued from previous message]   
      
   >>>>>>> see, if you can compute the BB number for any N-state machines,   
   >>>>>>> then for any N-state machine u can just run the N-state machine   
   >>>>>>> until BB number of steps. any machine that halts on or before   
   >>>>>>> BB(N) steps halts, any that run past must be nonhalting   
   >>>>>>   
   >>>>>> No, if we could establish an upper limit for BB(n) for all n, then   
   >>>>>> we could solve the hatling problem, as we have an upper limit for   
   >>>>>> the number of steps we need to simulate the machine.   
   >>>>>>   
   >>>>>> BB(n) has a value, but for sufficiently large values of n, we   
   >>>>>> don't have an upper bound for BB(n).   
   >>>>>>   
   >>>>>>>   
   >>>>>>> and the problem with allowing for partial decidability is that BB   
   >>>>>>> can run continually run more and more deciders in parallel, on   
   >>>>>>> every N- state machine, until one comes back with an halting   
   >>>>>>> answer, for every N-state machine, which then it can the use to   
   >>>>>>> decide what the BB number is for any N ...   
   >>>>>>   
   >>>>>> So, what BB are you running? Or are you misusing "running" to try   
   >>>>>> to mean somehow trying to calculate?   
   >>>>>>>   
   >>>>>>> contradicting the concept it must have a limit L, where some L-   
   >>>>>>> state machine cannot be decidable by *any* partial decider on the   
   >>>>>>> matter,   
   >>>>>>   
   >>>>>> No, it can have a limit, just not a KNOWN limit.   
   >>>>>   
   >>>>> consensus is there can a known limit L to the BB function, and   
   >>>>> proofs have been put out in regards to this   
   >>>>>   
   >>>>>>   
   >>>>>>>   
   >>>>>>> so no richard, partial decidability does not work if BB is to   
   >>>>>>> have a limit   
   >>>>>>>   
   >>>>>>   
   >>>>>> You only have the problem is BB has a KNOWN limit. Again, you trip   
   >>>>>> up on assuming you can know any answer you want.   
   >>>>>>   
   >>>>>> That some things are not knowable breaks your logic.   
   >>>>>   
   >>>>   
   >>>> I just glanced at your paper and skipped to the conclusion.   
   >>>> Why do we care about the undecidability of the halting problem?   
   >>>> Because undecidability in general (if it is correct) shows   
   >>>> that truth itself is broken. Truth itself cannot be broken.   
   >>>> This is the only reason why I have worked on these things   
   >>>> for 28 years.   
   >>>   
   >>> because it makes us suck as developing and maintaining software, and   
   >>> as a 35 year old burnt out SWE, i'm tired of living in a world   
   >>> running off sucky software. it really is limiting our potential, and   
   >>> i want my soon to be born son to have a far better experience with   
   >>> this shit than i did.   
   >>>   
   >>> a consequence of accepting the halting problem is then necessarily   
   >>> accepting proof against *all* semantic deciders, barring us from   
   >>> agreeing on what such general deciders might be   
   >>>   
   >>   
   >> Exactly: Tarski even "proved" that we can't even directly   
   >> compute what is true. This lets dangerous liars get away   
   >> with their dangerous lies.   
   >>   
   >>> this has lead to not only an unnecessary explosion in complexity of   
   >>> software engineering, because we can't generally compute semantic   
   >>> (turing) equivalence,   
   >>>   
   >>> but the general trend in deploying software that doesn't have   
   >>> computed semantic proofs guaranteeing they actually do what we want   
   >>> them to do.   
   >>   
   >> Yes without computing halting total proof of   
   >> correctness is impossible.   
   >>   
   >>> "testing" is poor substitute for doing so, but that's the most we can   
   >>> agree upon due to the current theory of computing.   
   >>>   
   >>> i think my ideas might contribute to dealing with incompleteness in   
   >>> fundamental math more generally ... like producing more refined   
   >>> limits to it's philosophical impact. tho idk if it can be gotten rid   
   >>> of completely, anymore than we can get rid of the words "this   
   >>> statement is false"   
   >>>   
   >>   
   >> I don't think that there actually are any limits   
   >> except for expressions requiring infinite proofs.   
   >>   
   >>> but i am currently focused on the theory of computing and not   
   >>> anything more generally. the fundamental objects comprising the   
   >>> theory of computing (machines) are far more constrained in their   
   >>> definitions than what set theory needs to encompass, and within those   
   >>> constraints i think i can twist the consensus into some contradiction   
   >>> that are just entirely ignorant of atm   
   >>>   
   >>   
   >> I have explored all of the key areas. None of them   
   >> can be made as 100% perfectly concrete and unequivocal   
   >> as computing.   
   >>   
   >>> that's the slam dunk left that i need. i have a means to rectify   
   >>> whatever contradiction we find thru the use of RTMs, but i'm still   
   >>> teasing out the contradiction that will *force* others to notice   
   >>>   
   >>   
   >> I do have my refutation of the halting problem itself   
   >> boiled down to a rough draft of two first principles.   
   >>   
   >> When the halting problem requires a halt decider   
   >> to report on the behavior of a Turing machine this   
   >> is always a category error because Turing machines   
   >> only take finite string inputs.   
   >>   
   >> The corrected halting problem requires a Turing   
   >> machine decider to report in the behavior that its   
   >> actual finite string input actually specifies.   
   >>   
   >>   
   >   
   > polcott, i'm working on making the halting problem complete and   
   > consistent in regards to a subset of the improved "reflective turing   
   > machines" that encompasses all useful computations   
   >   
   > i'm sorry, but not about trying to reaffirm the halting function as   
   > still uncomputable by calling it a category error   
   >   
      
   I do compute the halting function correctly.   
   I have been doing this for more than three years.   
   We probably should not be spamming alt.buddha.short.fat.guy   
      
   int sum(int x, int y){return x + y;}   
   sum(3,2) should return 5 and it is incorrect   
   to require sum(3,2) to return the sum of 5+6.   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning expressed in language"   
   reliably 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)   

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