A Possible "solution" to the Halting Problem
in [Theory]
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From: Peter Olcott on 18 Oct 2006 20:02 "Ben Bacarisse" <ben.usenet(a)bsb.me.uk> wrote in message news:87ac3t8b3g.fsf(a)bsb.me.uk... > "Peter Olcott" <NoSpam(a)SeeScreen.com> writes: > >> "Ben Bacarisse" <ben.usenet(a)bsb.me.uk> wrote in message >> news:87wt6x8yc2.fsf(a)bsb.me.uk... >>> "Peter Olcott" <NoSpam(a)SeeScreen.com> writes: >>> >>>> "Ben Bacarisse" <ben.usenet(a)bsb.me.uk> wrote in message >>>> news:87lkneqm4p.fsf(a)bsb.me.uk... >>>>> "Peter Olcott" <NoSpam(a)SeeScreen.com> writes: >>>>> >>> <big snip> >>>>>>>>>> >>>>>>>>>> http://www.cprogramming.com/tutorial/computersciencetheory/halting.html >>>> Explain this proof within the context of the model that I provided. >>> >>> No thanks. More formal methods are the only way to avoid these vague, >>> hand-waving arguments. >>> >> >> Or perhaps they are a way to make a model that only seems to >> correspond to the actuality, with slight errors of the precise >> mathematical mapping, thus creating the fallacy of equivocation. > > Perhaps. How will you ever know? When someone says something that > "sounds reasonable"? That was the point of my asking the questions you > did not answer. I am genuinely curious to know if you really think > your vague words will persuade anyone here to change his/her mind and what > kind of thing anyone here might say that would cause you to doubt your > arguments. I suspect that you don't really think anyone will be > persuaded and that you are just enjoying a good troll. > The mathematical mapping between the mathematical conclusions drawn from the HP, and the English language statements used to describe these conclusions is not precisely correct. Further still the degree of this error is great. > PS. Please stop quoting sigs. A biot of snipping would not go amiss > either. This is gibberish to me. > > -- > Ben.
From: Peter Olcott on 18 Oct 2006 20:23 "Patricia Shanahan" <pats(a)acm.org> wrote in message news:pUyZg.11247$Y24.7075(a)newsread4.news.pas.earthlink.net... > Peter Olcott wrote: >> "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message >> news:1161210790.800534.60930(a)h48g2000cwc.googlegroups.com... >>> Peter Olcott wrote: >>>> What is the >>>> official precise English language conclusion drawn from the results of the >>>> mathematical analysis of the Halting Problem? >>> Why not start by at least informing yourself of an exact mathematical >>> statement of the theorem and its proof? >>> >>> MoeBlee >>> >> >> That is not within my purpose. My purpose is to show that the Halting Problem >> is really nothing more than an ill-formed question. > > The whole Halting Problem? There are large classes of computations that > provably halt. Indeed, there are algorithms that are known to halt for > every input. On the other hand, there are computations that can be > proved to not halt. Not only is the question interesting and > well-formed, it is frequently answered. > > In between, there is a set of computations for which neither halting nor > not-halting has been proved. > > The non-decidability of the halting problem tells us that we can never > reduce that set to the empty set. That seems to be a very precise English language statement that is most typically used to describe the results of the HP. It is this statement that I refute. I may be wrong, I have been wrong before, but, it is still this specific statement that I refute. The HP can be decided, yet the answer can not be restricted to YES or NO because the question is not a YES or NO question. The true meaning of the HP goes straight to the essence of truth itself, and thus the true essence of reality, as opposed to and contrast with misconceptions and illusions. > > As far as I can tell, you agree with that conclusion. You don't seem to > have contributed anything interesting, such as an algorithm for deciding > whether a computation is one that can never be proved to halt or not-halt. > > Patricia
From: MoeBlee on 18 Oct 2006 20:29 Peter Olcott wrote: > I know that the UTM form mathematically maps to the form that I provided. Sure you do. MoeBlee
From: Patricia Shanahan on 18 Oct 2006 20:57 Peter Olcott wrote: > "Patricia Shanahan" <pats(a)acm.org> wrote in message > news:pUyZg.11247$Y24.7075(a)newsread4.news.pas.earthlink.net... >> Peter Olcott wrote: >>> "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message >>> news:1161210790.800534.60930(a)h48g2000cwc.googlegroups.com... >>>> Peter Olcott wrote: >>>>> What is the >>>>> official precise English language conclusion drawn from the results of the >>>>> mathematical analysis of the Halting Problem? >>>> Why not start by at least informing yourself of an exact mathematical >>>> statement of the theorem and its proof? >>>> >>>> MoeBlee >>>> >>> That is not within my purpose. My purpose is to show that the Halting Problem >>> is really nothing more than an ill-formed question. >> The whole Halting Problem? There are large classes of computations that >> provably halt. Indeed, there are algorithms that are known to halt for >> every input. On the other hand, there are computations that can be >> proved to not halt. Not only is the question interesting and >> well-formed, it is frequently answered. >> >> In between, there is a set of computations for which neither halting nor >> not-halting has been proved. >> >> The non-decidability of the halting problem tells us that we can never >> reduce that set to the empty set. > > That seems to be a very precise English language statement that is most > typically used to describe the results of the HP. It is this statement that I > refute. I may be wrong, I have been wrong before, but, it is still this specific > statement that I refute. The HP can be decided, yet the answer can not be > restricted to YES or NO because the question is not a YES or NO question. > > The true meaning of the HP goes straight to the essence of truth itself, and > thus the true essence of reality, as opposed to and contrast with misconceptions > and illusions. > I'm not sure what you are disagreeing with. How does your statement differ from the idea that, for any claimed halting decision procedure, there are some computations for which it cannot provide a yes/no answer? Patricia
From: Peter Olcott on 18 Oct 2006 21:06
"Patricia Shanahan" <pats(a)acm.org> wrote in message news:S3AZg.15658$UG4.11496(a)newsread2.news.pas.earthlink.net... > Peter Olcott wrote: >> "Patricia Shanahan" <pats(a)acm.org> wrote in message >> news:pUyZg.11247$Y24.7075(a)newsread4.news.pas.earthlink.net... >>> Peter Olcott wrote: >>>> "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message >>>> news:1161210790.800534.60930(a)h48g2000cwc.googlegroups.com... >>>>> Peter Olcott wrote: >>>>>> What is the >>>>>> official precise English language conclusion drawn from the results of >>>>>> the >>>>>> mathematical analysis of the Halting Problem? >>>>> Why not start by at least informing yourself of an exact mathematical >>>>> statement of the theorem and its proof? >>>>> >>>>> MoeBlee >>>>> >>>> That is not within my purpose. My purpose is to show that the Halting >>>> Problem is really nothing more than an ill-formed question. >>> The whole Halting Problem? There are large classes of computations that >>> provably halt. Indeed, there are algorithms that are known to halt for >>> every input. On the other hand, there are computations that can be >>> proved to not halt. Not only is the question interesting and >>> well-formed, it is frequently answered. >>> >>> In between, there is a set of computations for which neither halting nor >>> not-halting has been proved. >>> >>> The non-decidability of the halting problem tells us that we can never >>> reduce that set to the empty set. >> >> That seems to be a very precise English language statement that is most >> typically used to describe the results of the HP. It is this statement that I >> refute. I may be wrong, I have been wrong before, but, it is still this >> specific statement that I refute. The HP can be decided, yet the answer can >> not be restricted to YES or NO because the question is not a YES or NO >> question. >> >> The true meaning of the HP goes straight to the essence of truth itself, and >> thus the true essence of reality, as opposed to and contrast with >> misconceptions and illusions. >> > > I'm not sure what you are disagreeing with. How does your statement > differ from the idea that, for any claimed halting decision procedure, > there are some computations for which it cannot provide a yes/no answer? > > Patricia What it boils down to is this, (at least within the scope of the HP) it is not that there exists some problems too difficult to be solved by computation, it is merely the case that some ill-formed questions have no correct answer. |