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Groups > comp.theory > #36063 > unrolled thread
| Started by | Mr Flibble <flibble@reddwarf.jmc> |
|---|---|
| First post | 2021-07-10 18:00 +0100 |
| Last post | 2021-07-19 13:25 -0700 |
| Articles | 20 on this page of 154 — 12 participants |
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Olcott's theory Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 18:00 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 12:08 -0500
Re: Olcott's theory Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 18:12 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 13:06 -0500
Re: Olcott's theory Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 19:23 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 13:32 -0500
Re: Olcott's theory Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 19:38 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 13:45 -0500
Re: Olcott's theory Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 19:59 +0100
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) olcott <NoOne@NoWhere.com> - 2021-07-10 14:09 -0500
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 20:14 +0100
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) olcott <NoOne@NoWhere.com> - 2021-07-10 14:32 -0500
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 20:35 +0100
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-10 14:08 -0700
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) olcott <NoOne@NoWhere.com> - 2021-07-10 16:12 -0500
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 22:39 +0100
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) olcott <NoOne@NoWhere.com> - 2021-07-10 16:46 -0500
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 22:52 +0100
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) olcott <NoOne@NoWhere.com> - 2021-07-10 16:58 -0500
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) Mr Flibble <flibble@reddwarf.jmc> - 2021-07-10 23:00 +0100
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) olcott <NoOne@NoWhere.com> - 2021-07-10 17:08 -0500
Re: Olcott's theory (Ben, Kaz or Mike please talk to Flibble) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-10 15:12 -0700
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-10 20:30 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 16:04 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-10 23:47 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 18:30 -0500
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-11 02:56 +0100
Re: Olcott's theory wij <wyniijj@gmail.com> - 2021-07-10 19:18 -0700
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-11 03:34 +0100
Re: Olcott's theory wij <wyniijj@gmail.com> - 2021-07-10 19:45 -0700
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-11 10:34 +0100
Re: Olcott's theory wij <wyniijj@gmail.com> - 2021-07-12 16:55 -0700
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-10 21:25 -0500
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-11 10:32 +0100
Re: Olcott's theory Jeff Barnett <jbb@notatt.com> - 2021-07-10 22:39 -0600
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-11 10:23 +0100
Re: Olcott's theory Jeff Barnett <jbb@notatt.com> - 2021-07-11 10:43 -0600
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-11 13:19 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-11 10:09 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-11 18:20 +0100
Re: Olcott's theory [ Flibble agrees that I am correct ] olcott <NoOne@NoWhere.com> - 2021-07-11 12:45 -0500
Re: Olcott's theory [ Flibble agrees that I am correct ] Peter <peterxpercival@hotmail.com> - 2021-07-11 19:18 +0100
Re: Olcott's theory [ Flibble agrees that I am correct ] Peter <peterxpercival@hotmail.com> - 2021-07-19 20:09 +0100
Re: Olcott's theory [ Flibble agrees that I am correct ] olcott <NoOne@NoWhere.com> - 2021-07-20 08:44 -0500
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-11 14:35 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-12 13:36 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 08:56 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-12 16:04 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 10:27 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-13 21:18 +0100
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-19 20:01 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-20 08:41 -0500
Re: Olcott's theory Richard Damon <Richard@Damon-Family.org> - 2021-07-20 09:12 -0700
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-20 17:16 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-20 14:41 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-21 06:55 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-21 09:40 -0500
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-21 16:49 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-21 11:00 -0500
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-22 08:44 -0500
Re: Olcott's theory Jeff Barnett <jbb@notatt.com> - 2021-07-10 22:32 -0600
Re: Olcott's theory Peter <peterxpercival@hotmail.com> - 2021-07-11 13:22 +0100
Re: Olcott's theory Andy Walker <anw@cuboid.co.uk> - 2021-07-12 14:13 +0100
Re: Olcott's theory Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-07-12 06:19 -0700
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-12 09:25 -0500
Re: Olcott's theory [ Flibble understands this ] David Brown <david.brown@hesbynett.no> - 2021-07-12 17:33 +0200
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-12 16:51 -0500
Re: Olcott's theory [ Flibble understands this ] Richard Damon <Richard@Damon-Family.org> - 2021-07-12 21:27 -0600
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-13 09:36 -0500
Re: Olcott's theory [ Flibble understands this ] Peter <peterxpercival@hotmail.com> - 2021-07-13 19:15 +0100
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-13 17:16 -0500
Re: Olcott's theory [ Flibble understands this ] Richard Damon <Richard@Damon-Family.org> - 2021-07-13 22:56 -0600
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-14 10:01 -0500
Re: Olcott's theory [ Flibble understands this ] Richard Damon <Richard@Damon-Family.org> - 2021-07-14 22:03 -0600
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-15 10:05 -0500
Re: Olcott's theory [ Flibble understands this ] Richard Damon <Richard@Damon-Family.org> - 2021-07-16 23:07 -0600
Re: Olcott's theory [ Flibble understands this ] Richard Damon <Richard@Damon-Family.org> - 2021-07-13 22:45 -0600
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) olcott <NoOne@NoWhere.com> - 2021-07-14 09:56 -0500
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-14 21:48 -0600
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-07-15 03:43 -0700
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-15 07:54 -0600
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) olcott <NoOne@NoWhere.com> - 2021-07-15 09:35 -0500
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) Richard Damon <Richard@Damon-Family.org> - 2021-07-16 23:09 -0600
Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) olcott <NoOne@NoWhere.com> - 2021-07-15 09:24 -0500
Re: Olcott's theory Jeff Barnett <jbb@notatt.com> - 2021-07-12 13:27 -0600
Re: Olcott's theory Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2021-07-12 21:08 +0100
Re: Olcott's theory Mr Flibble <flibble@reddwarf.jmc> - 2021-07-12 21:24 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 16:53 -0500
Re: Olcott's theory Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2021-07-12 22:59 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 17:23 -0500
Re: Olcott's theory Richard Damon <Richard@Damon-Family.org> - 2021-07-12 21:32 -0600
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 23:31 -0500
Re: Olcott's theory wij <wyniijj@gmail.com> - 2021-07-13 03:51 -0700
Re: Olcott's theory [ Flibble quote agrees] olcott <NoOne@NoWhere.com> - 2021-07-13 09:00 -0500
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 07:38 -0700
Re: Olcott's theory [ Flibble quote agrees] olcott <NoOne@NoWhere.com> - 2021-07-13 10:01 -0500
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 08:23 -0700
Re: Olcott's theory [ Flibble quote agrees] olcott <NoOne@NoWhere.com> - 2021-07-13 10:35 -0500
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 09:13 -0700
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 15:24 -0700
Re: Olcott's theory [ Flibble quote agrees] olcott <NoOne@NoWhere.com> - 2021-07-13 17:53 -0500
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 16:22 -0700
Re: Olcott's theory [ Flibble quote agrees] olcott <NoOne@NoWhere.com> - 2021-07-13 18:48 -0500
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 17:06 -0700
Re: Olcott's theory [ Flibble quote agrees] olcott <NoOne@NoWhere.com> - 2021-07-13 19:17 -0500
Re: Olcott's theory [ Flibble quote agrees] (Fixing Tarski's nonsense ) olcott <NoOne@NoWhere.com> - 2021-07-13 19:29 -0500
Re: Olcott's theory [ Flibble quote agrees] wij <wyniijj@gmail.com> - 2021-07-13 18:14 -0700
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) olcott <NoOne@NoWhere.com> - 2021-07-13 20:40 -0500
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) wij <wyniijj@gmail.com> - 2021-07-13 18:58 -0700
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) olcott <NoOne@NoWhere.com> - 2021-07-13 21:08 -0500
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) wij <wyniijj@gmail.com> - 2021-07-13 19:52 -0700
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) olcott <NoOne@NoWhere.com> - 2021-07-13 22:39 -0500
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) wij <wyniijj@gmail.com> - 2021-07-13 21:00 -0700
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) olcott <NoOne@NoWhere.com> - 2021-07-13 23:17 -0500
Re: Olcott's theory [ Flibble quote agrees] ( incorrect questions ) wij <wyniijj@gmail.com> - 2021-07-13 21:41 -0700
Re: Olcott's theory Richard Damon <Richard@Damon-Family.org> - 2021-07-13 07:23 -0600
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-13 00:00 +0100
Re: Olcott's theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-12 23:40 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 18:23 -0500
Re: Olcott's theory Andy Walker <anw@cuboid.co.uk> - 2021-07-12 22:57 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 17:21 -0500
Re: Olcott's theory Andy Walker <anw@cuboid.co.uk> - 2021-07-13 11:49 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-13 08:49 -0500
Re: Olcott's theory Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2021-07-13 00:45 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 21:10 -0500
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 17:03 -0500
Re: Olcott's theory Jeff Barnett <jbb@notatt.com> - 2021-07-12 16:52 -0600
Re: Olcott's theory Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2021-07-13 00:37 +0100
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 22:02 -0500
Re: Olcott's theory olcott <NoOne@NoWhere.com> - 2021-07-12 17:00 -0500
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-12 09:25 -0500
Re: Olcott's theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-10 23:04 -0700
Re: Olcott's theory [unknown to be undecidable] olcott <NoOne@NoWhere.com> - 2021-07-11 09:21 -0500
Re: Olcott's theory wij <wyniijj@gmail.com> - 2021-07-11 07:52 -0700
Re: Olcott's theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-11 11:42 -0700
Re: Olcott's theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-11 11:52 -0700
Re: Olcott's theory wij <wyniijj@gmail.com> - 2021-07-11 16:52 -0700
Re: Olcott's theory Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-07-12 04:39 -0700
Re: Olcott's theory [ "I agree with Olcott" ] olcott <NoOne@NoWhere.com> - 2021-07-11 11:04 -0500
Re: Olcott's theory Richard Damon <Richard@Damon-Family.org> - 2021-07-11 22:14 -0600
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-12 09:10 -0500
Re: Olcott's theory [ Flibble understands this ] wij <wyniijj@gmail.com> - 2021-07-12 16:09 -0700
Re: Olcott's theory [ Flibble understands this ] wij <wyniijj@gmail.com> - 2021-07-12 16:14 -0700
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-13 08:23 -0500
Re: Olcott's theory [ Flibble understands this ] wij <wyniijj@gmail.com> - 2021-07-13 07:24 -0700
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-13 09:59 -0500
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-12 22:07 -0500
Re: Olcott's theory [ Flibble understands this ] wij <wyniijj@gmail.com> - 2021-07-12 20:17 -0700
Re: Olcott's theory [ Flibble understands this ] olcott <NoOne@NoWhere.com> - 2021-07-13 08:45 -0500
Re: Olcott's theory [ Flibble understands this ] wij <wyniijj@gmail.com> - 2021-07-12 16:40 -0700
Re: Olcott's theory [ Flibble understands pathological self reference(Olcott 2004) ] olcott <NoOne@NoWhere.com> - 2021-07-19 14:33 -0500
Re: Olcott's theory [ Flibble understands pathological self reference(Olcott 2004) ] Peter <peterxpercival@hotmail.com> - 2021-07-19 20:40 +0100
Re: Olcott's theory [ Flibble understands pathological self reference(Olcott 2004) ] olcott <NoOne@NoWhere.com> - 2021-07-20 08:52 -0500
Re: Olcott's theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-07-19 13:25 -0700
Page 4 of 8 — ← Prev page 1 2 3 [4] 5 6 7 8 Next page →
| From | Jeff Barnett <jbb@notatt.com> |
|---|---|
| Date | 2021-07-10 22:32 -0600 |
| Message-ID | <scds8j$32h$1@dont-email.me> |
| In reply to | #36083 |
On 7/10/2021 1:30 PM, Peter wrote: > olcott wrote: >> On 7/10/2021 12:12 PM, Mr Flibble wrote: >>> On Sat, 10 Jul 2021 12:08:02 -0500 >>> olcott <NoOne@NoWhere.com> wrote: >>> >>>> The Halting Problem can only exist because >>>> of this same sort of pathological self-reference. >>> >>> ^ that is your mistake: the halting problem still exists even if a >>> collection of proofs have a mistake. >>> >>> Does [Turing 1937] rely on a decider being part of that which is >>> being decided? Wikipedia suggests not: >>> >>> "Turing's proof departs from calculation by recursive functions and >>> introduces the notion of computation by machine." >>> >>> /Flibble >>> >> >> *I agree that I have not solved the halting problem* >> At most I have only proved that the conventional proofs of the >> undecidability of the halting problem that rely on the Strachey form, >> are incorrect. This seems to include all textbook proofs. >> >> [An impossible program] C. Strachey >> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313, >> https://doi.org/10.1093/comjnl/7.4.313 >> >> Now seems to be a good time to finally look at the Turing proof. >> https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf >> I am not sure if the above linked copy has the later published >> correction. >> >> If the Turing proof is isomorphic to the Strachey form, I don't know >> what it left to prove that the halting problem is undecidable. > > There is more than one proof. I was taught, not the the halting problem > for TMs is unsolvable, but that the halting problem for register > machines is unsolvable. The reason being, I suppose, that the course > was taught by one of the inventors of the register machine. [There are > a variety of register machines, this one had an unlimited number of > registers and the instructions > add 1 to register R, > subtract 1 from register R (so long as it doesn't hold 0), > if R doesn't hold 0 go to instruction i. Did they teach you that only two registers are necessary? That's the most fun part of the result. Since the "two counter" machines have exactly the same computation power as Turing machines, a no halt theory for either extends to both. Automatic. > See Shepherdson & Sturgis, 'Computability of recursive functions', > /JACM/, vol 10, no 2, 1963, pp217-255.] > >> >> Goldbach's Conjecture is merely undecided and thus not undecidable. >> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >> >> Busy Beaver only seems intractable not undecidable. >> https://en.wikipedia.org/wiki/Busy_beaver-- Jeff Barnett
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| From | Peter <peterxpercival@hotmail.com> |
|---|---|
| Date | 2021-07-11 13:22 +0100 |
| Message-ID | <scenpg$mic$2@gioia.aioe.org> |
| In reply to | #36123 |
Jeff Barnett wrote: > On 7/10/2021 1:30 PM, Peter wrote: >> olcott wrote: >>> On 7/10/2021 12:12 PM, Mr Flibble wrote: >>>> On Sat, 10 Jul 2021 12:08:02 -0500 >>>> olcott <NoOne@NoWhere.com> wrote: >>>> >>>>> The Halting Problem can only exist because >>>>> of this same sort of pathological self-reference. >>>> >>>> ^ that is your mistake: the halting problem still exists even if a >>>> collection of proofs have a mistake. >>>> >>>> Does [Turing 1937] rely on a decider being part of that which is >>>> being decided? Wikipedia suggests not: >>>> >>>> "Turing's proof departs from calculation by recursive functions and >>>> introduces the notion of computation by machine." >>>> >>>> /Flibble >>>> >>> >>> *I agree that I have not solved the halting problem* >>> At most I have only proved that the conventional proofs of the >>> undecidability of the halting problem that rely on the Strachey form, >>> are incorrect. This seems to include all textbook proofs. >>> >>> [An impossible program] C. Strachey >>> The Computer Journal, Volume 7, Issue 4, January 1965, Page 313, >>> https://doi.org/10.1093/comjnl/7.4.313 >>> >>> Now seems to be a good time to finally look at the Turing proof. >>> https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf >>> I am not sure if the above linked copy has the later published >>> correction. >>> >>> If the Turing proof is isomorphic to the Strachey form, I don't know >>> what it left to prove that the halting problem is undecidable. >> >> There is more than one proof. I was taught, not the the halting >> problem for TMs is unsolvable, but that the halting problem for >> register machines is unsolvable. The reason being, I suppose, that >> the course was taught by one of the inventors of the register >> machine. [There are a variety of register machines, this one had an >> unlimited number of registers and the instructions >> add 1 to register R, >> subtract 1 from register R (so long as it doesn't hold 0), >> if R doesn't hold 0 go to instruction i. > > Did they teach you that only two registers are necessary? That's the > most fun part of the result. Since the "two counter" machines have > exactly the same computation power as Turing machines, a no halt theory > for either extends to both. Automatic. Yes. The lecturer was John Shepherdson at Bristol. >> See Shepherdson & Sturgis, 'Computability of recursive functions', >> /JACM/, vol 10, no 2, 1963, pp217-255.] >> >>> >>> Goldbach's Conjecture is merely undecided and thus not undecidable. >>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>> >>> Busy Beaver only seems intractable not undecidable. >>> https://en.wikipedia.org/wiki/Busy_beaver-- > Jeff Barnett > -- The world will little note, nor long remember what we say here Abraham Lincoln at Gettysburg
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| From | Andy Walker <anw@cuboid.co.uk> |
|---|---|
| Date | 2021-07-12 14:13 +0100 |
| Message-ID | <schf57$1b8$1@gioia.aioe.org> |
| In reply to | #36070 |
On 10/07/2021 19:06, olcott wrote:
> At most I have only proved that the conventional proofs of the
> undecidability of the halting problem that rely on the Strachey form,
> are incorrect. This seems to include all textbook proofs.
As you know, Linz gives a quite different proof; and there are
several other proofs, inc one via "Busy Beaver" [see below].
[...]
> Goldbach's Conjecture is merely undecided and thus not undecidable.
"Thus" is a step too far. But note the reference to Goldbach
in the Wiki article on "Busy Beaver".
[...]
> Busy Beaver only seems intractable not undecidable.
It's undecidable whether an arbitrary TM is a BB; and the
BB function [ie, the "score" of a BB of given size] is uncomputable.
That's a stronger result than intractability. The proof that the
BB function is uncomputable is [reasonably] elementary, and does not
rely on the HP [or recursion]. If you had a "halting decider", then
you could find BBs by exhaustive [albeit intractable!] search and
thus compute the BB function; so there's yet another HP proof.
--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Ascher
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| From | Malcolm McLean <malcolm.arthur.mclean@gmail.com> |
|---|---|
| Date | 2021-07-12 06:19 -0700 |
| Message-ID | <cde66c0c-918d-46f9-9fa5-7c346e724f82n@googlegroups.com> |
| In reply to | #36173 |
On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote: > On 10/07/2021 19:06, olcott wrote: > > At most I have only proved that the conventional proofs of the > > undecidability of the halting problem that rely on the Strachey form, > > are incorrect. This seems to include all textbook proofs. > As you know, Linz gives a quite different proof; and there are > several other proofs, inc one via "Busy Beaver" [see below]. > > [...] > > Goldbach's Conjecture is merely undecided and thus not undecidable. > "Thus" is a step too far. But note the reference to Goldbach > in the Wiki article on "Busy Beaver". > > [...] > > Busy Beaver only seems intractable not undecidable. > It's undecidable whether an arbitrary TM is a BB; and the > BB function [ie, the "score" of a BB of given size] is uncomputable. > That's a stronger result than intractability. The proof that the > BB function is uncomputable is [reasonably] elementary, and does not > rely on the HP [or recursion]. If you had a "halting decider", then > you could find BBs by exhaustive [albeit intractable!] search and > thus compute the BB function; so there's yet another HP proof. > If you have a busy beaver function and a simulating decider, the busy beaver function tells you how many times you need to step the decider before you can be certain it will never halt. So halting is decideable if busy beaver is decideable.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-12 09:25 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <krmdnb7eI-ZozXH9nZ2dnUU7-bUAAAAA@giganews.com> |
| In reply to | #36174 |
On 7/12/2021 8:19 AM, Malcolm McLean wrote: > On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote: >> On 10/07/2021 19:06, olcott wrote: >>> At most I have only proved that the conventional proofs of the >>> undecidability of the halting problem that rely on the Strachey form, >>> are incorrect. This seems to include all textbook proofs. >> As you know, Linz gives a quite different proof; and there are >> several other proofs, inc one via "Busy Beaver" [see below]. >> >> [...] >>> Goldbach's Conjecture is merely undecided and thus not undecidable. >> "Thus" is a step too far. But note the reference to Goldbach >> in the Wiki article on "Busy Beaver". >> >> [...] >>> Busy Beaver only seems intractable not undecidable. >> It's undecidable whether an arbitrary TM is a BB; and the >> BB function [ie, the "score" of a BB of given size] is uncomputable. >> That's a stronger result than intractability. The proof that the >> BB function is uncomputable is [reasonably] elementary, and does not >> rely on the HP [or recursion]. If you had a "halting decider", then >> you could find BBs by exhaustive [albeit intractable!] search and >> thus compute the BB function; so there's yet another HP proof. >> > If you have a busy beaver function and a simulating decider, the busy > beaver function tells you how many times you need to step the decider > before you can be certain it will never halt. So halting is decideable if > busy beaver is decideable. > > Flibble understands this: What correct Boolean value can a TM return to an input that does the opposite of whatever it decides? : neither, is excluded from the solution set thus making the question itself incorrect. What time is it (yes or no)? hours and minutes are excluded from the solution set making the question itself incorrect. -- Copyright 2021 Pete Olcott "Great spirits have always encountered violent opposition from mediocre minds." Einstein
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2021-07-12 17:33 +0200 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <schncf$pki$1@dont-email.me> |
| In reply to | #36180 |
On 12/07/2021 16:25, olcott wrote: > On 7/12/2021 8:19 AM, Malcolm McLean wrote: >> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote: >>> On 10/07/2021 19:06, olcott wrote: >>>> At most I have only proved that the conventional proofs of the >>>> undecidability of the halting problem that rely on the Strachey form, >>>> are incorrect. This seems to include all textbook proofs. >>> As you know, Linz gives a quite different proof; and there are >>> several other proofs, inc one via "Busy Beaver" [see below]. >>> >>> [...] >>>> Goldbach's Conjecture is merely undecided and thus not undecidable. >>> "Thus" is a step too far. But note the reference to Goldbach >>> in the Wiki article on "Busy Beaver". >>> >>> [...] >>>> Busy Beaver only seems intractable not undecidable. >>> It's undecidable whether an arbitrary TM is a BB; and the >>> BB function [ie, the "score" of a BB of given size] is uncomputable. >>> That's a stronger result than intractability. The proof that the >>> BB function is uncomputable is [reasonably] elementary, and does not >>> rely on the HP [or recursion]. If you had a "halting decider", then >>> you could find BBs by exhaustive [albeit intractable!] search and >>> thus compute the BB function; so there's yet another HP proof. >>> >> If you have a busy beaver function and a simulating decider, the busy >> beaver function tells you how many times you need to step the decider >> before you can be certain it will never halt. So halting is decideable if >> busy beaver is decideable. >> >> > > Flibble understands this: > What correct Boolean value can a TM return to an input that does the > opposite of whatever it decides? : neither, is excluded from the > solution set thus making the question itself incorrect. > You still don't understand this "proof by contradiction" concept, do you? It is not the /question/ that is incorrect, it is the assumption that such a TM exists that is incorrect. > What time is it (yes or no)? hours and minutes are excluded from the > solution set making the question itself incorrect. >
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-12 16:51 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <5rOdncjw_cHJJHH9nZ2dnUU7-WudnZ2d@giganews.com> |
| In reply to | #36186 |
On 7/12/2021 10:33 AM, David Brown wrote: > On 12/07/2021 16:25, olcott wrote: >> On 7/12/2021 8:19 AM, Malcolm McLean wrote: >>> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote: >>>> On 10/07/2021 19:06, olcott wrote: >>>>> At most I have only proved that the conventional proofs of the >>>>> undecidability of the halting problem that rely on the Strachey form, >>>>> are incorrect. This seems to include all textbook proofs. >>>> As you know, Linz gives a quite different proof; and there are >>>> several other proofs, inc one via "Busy Beaver" [see below]. >>>> >>>> [...] >>>>> Goldbach's Conjecture is merely undecided and thus not undecidable. >>>> "Thus" is a step too far. But note the reference to Goldbach >>>> in the Wiki article on "Busy Beaver". >>>> >>>> [...] >>>>> Busy Beaver only seems intractable not undecidable. >>>> It's undecidable whether an arbitrary TM is a BB; and the >>>> BB function [ie, the "score" of a BB of given size] is uncomputable. >>>> That's a stronger result than intractability. The proof that the >>>> BB function is uncomputable is [reasonably] elementary, and does not >>>> rely on the HP [or recursion]. If you had a "halting decider", then >>>> you could find BBs by exhaustive [albeit intractable!] search and >>>> thus compute the BB function; so there's yet another HP proof. >>>> >>> If you have a busy beaver function and a simulating decider, the busy >>> beaver function tells you how many times you need to step the decider >>> before you can be certain it will never halt. So halting is decideable if >>> busy beaver is decideable. >>> >>> >> >> Flibble understands this: >> What correct Boolean value can a TM return to an input that does the >> opposite of whatever it decides? : neither, is excluded from the >> solution set thus making the question itself incorrect. >> > > You still don't understand this "proof by contradiction" concept, do you? We can say that the following expression is undecidable on the basis that both true and false derive contradictions: "This sentence is not true." That same sentence is used as the basis of the Tarski undefinability theorem. http://www.liarparadox.org/Tarski_247_248.pdf http://www.liarparadox.org/Tarski_275_276.pdf Although we have proven that it is undecidable on the basis of proof by contradiction we are ignoring the key detail that the proof by contradiction only succeeds because the expression of language is self-contradictory, thus not a truth bearer and therefore erroneous. > > It is not the /question/ that is incorrect, it is the assumption that > such a TM exists that is incorrect. > > >> What time is it (yes or no)? hours and minutes are excluded from the >> solution set making the question itself incorrect. >> > > -- Copyright 2021 Pete Olcott "Great spirits have always encountered violent opposition from mediocre minds." Einstein
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2021-07-12 21:27 -0600 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <5L7HI.11472$h8.9785@fx47.iad> |
| In reply to | #36197 |
On 7/12/21 3:51 PM, olcott wrote: > On 7/12/2021 10:33 AM, David Brown wrote: >> On 12/07/2021 16:25, olcott wrote: >>> On 7/12/2021 8:19 AM, Malcolm McLean wrote: >>>> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote: >>>>> On 10/07/2021 19:06, olcott wrote: >>>>>> At most I have only proved that the conventional proofs of the >>>>>> undecidability of the halting problem that rely on the Strachey form, >>>>>> are incorrect. This seems to include all textbook proofs. >>>>> As you know, Linz gives a quite different proof; and there are >>>>> several other proofs, inc one via "Busy Beaver" [see below]. >>>>> >>>>> [...] >>>>>> Goldbach's Conjecture is merely undecided and thus not undecidable. >>>>> "Thus" is a step too far. But note the reference to Goldbach >>>>> in the Wiki article on "Busy Beaver". >>>>> >>>>> [...] >>>>>> Busy Beaver only seems intractable not undecidable. >>>>> It's undecidable whether an arbitrary TM is a BB; and the >>>>> BB function [ie, the "score" of a BB of given size] is uncomputable. >>>>> That's a stronger result than intractability. The proof that the >>>>> BB function is uncomputable is [reasonably] elementary, and does not >>>>> rely on the HP [or recursion]. If you had a "halting decider", then >>>>> you could find BBs by exhaustive [albeit intractable!] search and >>>>> thus compute the BB function; so there's yet another HP proof. >>>>> >>>> If you have a busy beaver function and a simulating decider, the busy >>>> beaver function tells you how many times you need to step the decider >>>> before you can be certain it will never halt. So halting is >>>> decideable if >>>> busy beaver is decideable. >>>> >>>> >>> >>> Flibble understands this: >>> What correct Boolean value can a TM return to an input that does the >>> opposite of whatever it decides? : neither, is excluded from the >>> solution set thus making the question itself incorrect. >>> >> >> You still don't understand this "proof by contradiction" concept, do you? > > We can say that the following expression is undecidable on the basis > that both true and false derive contradictions: > "This sentence is not true." That same sentence is used as the basis of > the Tarski undefinability theorem. > > http://www.liarparadox.org/Tarski_247_248.pdf > http://www.liarparadox.org/Tarski_275_276.pdf > > > > Although we have proven that it is undecidable on the basis of proof by > contradiction we are ignoring the key detail that the proof by > contradiction only succeeds because the expression of language is > self-contradictory, thus not a truth bearer and therefore erroneous. Does P(I) Halt IS a Truth Bearing Sentence, as P(I) will either Halt or it won't. We may not be able to prove that answer, but that is one fundamental property of the Higher level Logic that includes mathematics. If you want to keep to the concept that something is only true if you can prove it, then you must restrict yourself to only First Order Logic, or you WILL eventually run into an inconsistency in your logic system. Yes, if you make that restriction to your logic, you can use that property, but you can not express the fullness of mathematics in your logic. This is well established.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-13 09:36 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <X8udnTDJo8hOOXD9nZ2dnUU7-SvNnZ2d@giganews.com> |
| In reply to | #36228 |
On 7/12/2021 10:27 PM, Richard Damon wrote:
> On 7/12/21 3:51 PM, olcott wrote:
>> On 7/12/2021 10:33 AM, David Brown wrote:
>>> On 12/07/2021 16:25, olcott wrote:
>>>> On 7/12/2021 8:19 AM, Malcolm McLean wrote:
>>>>> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote:
>>>>>> On 10/07/2021 19:06, olcott wrote:
>>>>>>> At most I have only proved that the conventional proofs of the
>>>>>>> undecidability of the halting problem that rely on the Strachey form,
>>>>>>> are incorrect. This seems to include all textbook proofs.
>>>>>> As you know, Linz gives a quite different proof; and there are
>>>>>> several other proofs, inc one via "Busy Beaver" [see below].
>>>>>>
>>>>>> [...]
>>>>>>> Goldbach's Conjecture is merely undecided and thus not undecidable.
>>>>>> "Thus" is a step too far. But note the reference to Goldbach
>>>>>> in the Wiki article on "Busy Beaver".
>>>>>>
>>>>>> [...]
>>>>>>> Busy Beaver only seems intractable not undecidable.
>>>>>> It's undecidable whether an arbitrary TM is a BB; and the
>>>>>> BB function [ie, the "score" of a BB of given size] is uncomputable.
>>>>>> That's a stronger result than intractability. The proof that the
>>>>>> BB function is uncomputable is [reasonably] elementary, and does not
>>>>>> rely on the HP [or recursion]. If you had a "halting decider", then
>>>>>> you could find BBs by exhaustive [albeit intractable!] search and
>>>>>> thus compute the BB function; so there's yet another HP proof.
>>>>>>
>>>>> If you have a busy beaver function and a simulating decider, the busy
>>>>> beaver function tells you how many times you need to step the decider
>>>>> before you can be certain it will never halt. So halting is
>>>>> decideable if
>>>>> busy beaver is decideable.
>>>>>
>>>>>
>>>>
>>>> Flibble understands this:
>>>> What correct Boolean value can a TM return to an input that does the
>>>> opposite of whatever it decides? : neither, is excluded from the
>>>> solution set thus making the question itself incorrect.
>>>>
>>>
>>> You still don't understand this "proof by contradiction" concept, do you?
>>
>> We can say that the following expression is undecidable on the basis
>> that both true and false derive contradictions:
>> "This sentence is not true." That same sentence is used as the basis of
>> the Tarski undefinability theorem.
>>
>> http://www.liarparadox.org/Tarski_247_248.pdf
>> http://www.liarparadox.org/Tarski_275_276.pdf
>>
>>
>>
>> Although we have proven that it is undecidable on the basis of proof by
>> contradiction we are ignoring the key detail that the proof by
>> contradiction only succeeds because the expression of language is
>> self-contradictory, thus not a truth bearer and therefore erroneous.
>
> Does P(I) Halt IS a Truth Bearing Sentence, as P(I) will either Halt or
> it won't. We may not be able to prove that answer, but that is one
> fundamental property of the Higher level Logic that includes mathematics.
>
That is not the actual question, you leave out the key context that
makes the question incorrect. Ben played this same dishonest dodge since
2006. When you strip off the context of the question you change it into
an entirely different question.
Here is the actual question:
When we ask what Boolean value can a halt decider return to an input
that changes its behavior to contradict this value we cannot answer this
question because it is an incorrect type mismatch error question.
The answer is restricted to {true, false} thus excluding the correct
answer of “neither” making the question itself incorrect.
If we ask a man that has never been married:
Have you stopped beating you wife?
This is an incorrect question.
Every polar question lacking a correct yes/no answer is incorrect.
Every TM/input to a decision problem lacking a correct Boolean return
value is an incorrect TM/input for this decision problem.
The TM / input pairs that “prove” the halting problem is undecidable
have the same pathological self-reference(Olcott 2004) error as the
self-contradictory liar paradox.
It has been at least 2000 years since the liar paradox was discovered
and academicians still do not understand the because self-contradictory
sentences do not map to a Boolean value they are not truth bearers.
> If you want to keep to the concept that something is only true if you
> can prove it, then you must restrict yourself to only First Order Logic,
> or you WILL eventually run into an inconsistency in your logic system.
>
Not at all. Not in the least.
When Gödel's 1931 incompleteness theorem is translated into HOL that has
its own provability predicate thus no need for the purely extraneous
complexity of Gödel numbers then it is very obvious that it is modeled
after the liar paradox.
Gödel himself said that the liar paradox could be used as his
incompleteness basis.
there is also a close relationship with the “liar”
antinomy,14
We are therefore confronted with a proposition which
asserts its own unprovability
14 Every epistemological antinomy can likewise be
used for a similar undecidability proof.
This is HOL with its in provability predicate:
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
I have examples that show the propositions that assert their own
unprovability are only undecidable because there is an infinite cycle in
their directed graph.
The problem is that like the liar paradox that have a vacuous truth
object. This sentence is not true. This sentence is not provable. Have
no truth object that they are true or provable about.
"It is true that this sentence is a dump truck."
has a truth object thus enabling the sentence to be evaluated as false.
"This sentence is true"
"This sentence is false"
"This sentence is provable"
Have no truth object, thus specify an infinite cycle in the directed
graph of their resolution.
> Yes, if you make that restriction to your logic, you can use that
> property, but you can not express the fullness of mathematics in your logic.
>
> This is well established.
>
I reestablished it correctly this time.
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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| From | Peter <peterxpercival@hotmail.com> |
|---|---|
| Date | 2021-07-13 19:15 +0100 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <sckl8h$1q4c$1@gioia.aioe.org> |
| In reply to | #36243 |
olcott wrote: > [...] > When Gödel's 1931 incompleteness theorem is translated into HOL that has > its own provability predicate thus no need for the purely extraneous > complexity of Gödel numbers then it is very obvious that it is modeled > after the liar paradox. It's almost certainly of no interest to you, but a proof of the incompleteness of second order predicate calculus may be found in Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, computability/, 2nd edition, Springer, 1964. It does not use Gödel numbering. Nor is it "is modeled after the liar paradox." -- The world will little note, nor long remember what we say here Abraham Lincoln at Gettysburg
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-13 17:16 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <FpKdnbmEF-InjXP9nZ2dnUU7-d3NnZ2d@giganews.com> |
| In reply to | #36258 |
On 7/13/2021 1:15 PM, Peter wrote: > olcott wrote: >> [...] >> When Gödel's 1931 incompleteness theorem is translated into HOL that >> has its own provability predicate thus no need for the purely >> extraneous complexity of Gödel numbers then it is very obvious that it >> is modeled after the liar paradox. > > It's almost certainly of no interest to you, but a proof of the > incompleteness of second order predicate calculus may be found in > > Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, > computability/, 2nd edition, Springer, 1964. > > It does not use Gödel numbering. Nor is it "is modeled after the liar > paradox." > I did not initially add that it must also have its own provability predicate like the Tarski undefinability theorem. Even when we get these things boiled down to their simplest possible essence no academicians can begin to understand what is really going on. They still don't understand that the actual liar paradox is simply not a truth bearer because it is self contradictory. They all seem to think that it is some puzzle that is far too difficult to ever figure out. The Tarski undefinability theory has the liar paradox as its only basis. http://www.liarparadox.org/Tarski_247_248.pdf http://www.liarparadox.org/Tarski_Proof_275_276.pdf -- Copyright 2021 Pete Olcott "Great spirits have always encountered violent opposition from mediocre minds." Einstein
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2021-07-13 22:56 -0600 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <l8uHI.2205$gE.553@fx21.iad> |
| In reply to | #36260 |
On 7/13/21 4:16 PM, olcott wrote: > On 7/13/2021 1:15 PM, Peter wrote: >> olcott wrote: >>> [...] >>> When Gödel's 1931 incompleteness theorem is translated into HOL that >>> has its own provability predicate thus no need for the purely >>> extraneous complexity of Gödel numbers then it is very obvious that >>> it is modeled after the liar paradox. >> >> It's almost certainly of no interest to you, but a proof of the >> incompleteness of second order predicate calculus may be found in >> >> Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, >> computability/, 2nd edition, Springer, 1964. >> >> It does not use Gödel numbering. Nor is it "is modeled after the liar >> paradox." >> > > I did not initially add that it must also have its own provability > predicate like the Tarski undefinability theorem. > > Even when we get these things boiled down to their simplest possible > essence no academicians can begin to understand what is really going on. > > They still don't understand that the actual liar paradox is simply not a > truth bearer because it is self contradictory. > > They all seem to think that it is some puzzle that is far too difficult > to ever figure out. The Tarski undefinability theory has the liar > paradox as its only basis. > > http://www.liarparadox.org/Tarski_247_248.pdf > > http://www.liarparadox.org/Tarski_Proof_275_276.pdf > > YOU do not understand the TRUE meaning of a Truth Bearer. Truth Bearer does NOT mean provable, unless you have decided to restrict your logic to only provable things. If you do this, then you can not use higher than First Order Logic or you become inconsistent. And even if you use only First Order Logic, unless your filed of knowledge is so limited as to be finitely enumerated, it can not actually prove that it has stayed consistant. If you are going to try to live with the proposition that All Truth must be Provable, live within its limits, and get out of the fields that are beyond it. This was settled a Century ago. Your problem is that you aren't accepting that, going beyond that allowable limits of your logic, and you are failing to recognize that your logic system is inconsistent. The mere fact that we can prove a machine to be both Halting and Non-Halting is proof of that. You seem to fail to understand that you can't 'DISPROVE' something that has been proved by proving its opposite. THAT doesn't work. That method only works if the theorem is unproven. When these contradictions pop up, that real answer is this shows that either one of the proofs has an error (that should be able to be found) or the logic system has broken and gone inconsistent, and the whole theory needs to be rewound to find the axiom that broke it. In your case, this is fairly easy, as you keep asserting as postulates things that are provably false, so it is easy to see where the errors came in.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-14 10:01 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <0_CdnfQkOa7aYXP9nZ2dnUU7-fPNnZ2d@giganews.com> |
| In reply to | #36299 |
On 7/13/2021 11:56 PM, Richard Damon wrote: > On 7/13/21 4:16 PM, olcott wrote: >> On 7/13/2021 1:15 PM, Peter wrote: >>> olcott wrote: >>>> [...] >>>> When Gödel's 1931 incompleteness theorem is translated into HOL that >>>> has its own provability predicate thus no need for the purely >>>> extraneous complexity of Gödel numbers then it is very obvious that >>>> it is modeled after the liar paradox. >>> >>> It's almost certainly of no interest to you, but a proof of the >>> incompleteness of second order predicate calculus may be found in >>> >>> Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, >>> computability/, 2nd edition, Springer, 1964. >>> >>> It does not use Gödel numbering. Nor is it "is modeled after the liar >>> paradox." >>> >> >> I did not initially add that it must also have its own provability >> predicate like the Tarski undefinability theorem. >> >> Even when we get these things boiled down to their simplest possible >> essence no academicians can begin to understand what is really going on. >> >> They still don't understand that the actual liar paradox is simply not a >> truth bearer because it is self contradictory. >> >> They all seem to think that it is some puzzle that is far too difficult >> to ever figure out. The Tarski undefinability theory has the liar >> paradox as its only basis. >> >> http://www.liarparadox.org/Tarski_247_248.pdf >> >> http://www.liarparadox.org/Tarski_Proof_275_276.pdf >> >> > > > YOU do not understand the TRUE meaning of a Truth Bearer. > A "Truth bearer" is an expression of language capable of having a Boolean property. In all cases where it is impossible to resolve an expression of language to a Boolean value this expression is not a truth bearer. The key case of this is the liar Paradox. Something must be wrong with the world if no academician has figured out that self-contradictory sentences are not truth bearers in more than 2000 years. > Truth Bearer does NOT mean provable, unless you have decided to restrict > your logic to only provable things. If you do this, then you can not use > higher than First Order Logic or you become inconsistent. And even if > you use only First Order Logic, unless your filed of knowledge is so > limited as to be finitely enumerated, it can not actually prove that it > has stayed consistant. > > If you are going to try to live with the proposition that All Truth must > be Provable, live within its limits, and get out of the fields that are > beyond it. > > This was settled a Century ago. Your problem is that you aren't > accepting that, going beyond that allowable limits of your logic, and > you are failing to recognize that your logic system is inconsistent. The > mere fact that we can prove a machine to be both Halting and Non-Halting > is proof of that. > > You seem to fail to understand that you can't 'DISPROVE' something that > has been proved by proving its opposite. THAT doesn't work. That method > only works if the theorem is unproven. > > When these contradictions pop up, that real answer is this shows that > either one of the proofs has an error (that should be able to be found) > or the logic system has broken and gone inconsistent, and the whole > theory needs to be rewound to find the axiom that broke it. > > In your case, this is fairly easy, as you keep asserting as postulates > things that are provably false, so it is easy to see where the errors > came in. > -- Copyright 2021 Pete Olcott "Great spirits have always encountered violent opposition from mediocre minds." Einstein
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2021-07-14 22:03 -0600 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <YrOHI.10651$7H7.311@fx42.iad> |
| In reply to | #36305 |
On 7/14/21 9:01 AM, olcott wrote: > On 7/13/2021 11:56 PM, Richard Damon wrote: >> On 7/13/21 4:16 PM, olcott wrote: >>> On 7/13/2021 1:15 PM, Peter wrote: >>>> olcott wrote: >>>>> [...] >>>>> When Gödel's 1931 incompleteness theorem is translated into HOL that >>>>> has its own provability predicate thus no need for the purely >>>>> extraneous complexity of Gödel numbers then it is very obvious that >>>>> it is modeled after the liar paradox. >>>> >>>> It's almost certainly of no interest to you, but a proof of the >>>> incompleteness of second order predicate calculus may be found in >>>> >>>> Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, >>>> computability/, 2nd edition, Springer, 1964. >>>> >>>> It does not use Gödel numbering. Nor is it "is modeled after the liar >>>> paradox." >>>> >>> >>> I did not initially add that it must also have its own provability >>> predicate like the Tarski undefinability theorem. >>> >>> Even when we get these things boiled down to their simplest possible >>> essence no academicians can begin to understand what is really going on. >>> >>> They still don't understand that the actual liar paradox is simply not a >>> truth bearer because it is self contradictory. >>> >>> They all seem to think that it is some puzzle that is far too difficult >>> to ever figure out. The Tarski undefinability theory has the liar >>> paradox as its only basis. >>> >>> http://www.liarparadox.org/Tarski_247_248.pdf >>> >>> http://www.liarparadox.org/Tarski_Proof_275_276.pdf >>> >>> >> >> >> YOU do not understand the TRUE meaning of a Truth Bearer. >> > > A "Truth bearer" is an expression of language capable of having a > Boolean property. Right, and the answer to the Halting Problem, "Does P(I) come to a Halting state in a finite number of steps?" always, yes always. has a Yes or No anser. > > In all cases where it is impossible to resolve an expression of language > to a Boolean value this expression is not a truth bearer. And the Halting Problem never doesn't have an answer. > > The key case of this is the liar Paradox. Something must be wrong with > the world if no academician has figured out that self-contradictory > sentences are not truth bearers in more than 2000 years. Right, you get the Liar paradox when you assume that H exists and ask what it should produce in this case, the lack of answer shows that H doesn't exist, not that the Halting Problem has a problem. The WRONG QUESTIOH isn't a Truth Bearer.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-15 10:05 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <zeadnUMuW9cw0239nZ2dnUU7-YnNnZ2d@giganews.com> |
| In reply to | #36327 |
On 7/14/2021 11:03 PM, Richard Damon wrote: > On 7/14/21 9:01 AM, olcott wrote: >> On 7/13/2021 11:56 PM, Richard Damon wrote: >>> On 7/13/21 4:16 PM, olcott wrote: >>>> On 7/13/2021 1:15 PM, Peter wrote: >>>>> olcott wrote: >>>>>> [...] >>>>>> When Gödel's 1931 incompleteness theorem is translated into HOL that >>>>>> has its own provability predicate thus no need for the purely >>>>>> extraneous complexity of Gödel numbers then it is very obvious that >>>>>> it is modeled after the liar paradox. >>>>> >>>>> It's almost certainly of no interest to you, but a proof of the >>>>> incompleteness of second order predicate calculus may be found in >>>>> >>>>> Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, >>>>> computability/, 2nd edition, Springer, 1964. >>>>> >>>>> It does not use Gödel numbering. Nor is it "is modeled after the liar >>>>> paradox." >>>>> >>>> >>>> I did not initially add that it must also have its own provability >>>> predicate like the Tarski undefinability theorem. >>>> >>>> Even when we get these things boiled down to their simplest possible >>>> essence no academicians can begin to understand what is really going on. >>>> >>>> They still don't understand that the actual liar paradox is simply not a >>>> truth bearer because it is self contradictory. >>>> >>>> They all seem to think that it is some puzzle that is far too difficult >>>> to ever figure out. The Tarski undefinability theory has the liar >>>> paradox as its only basis. >>>> >>>> http://www.liarparadox.org/Tarski_247_248.pdf >>>> >>>> http://www.liarparadox.org/Tarski_Proof_275_276.pdf >>>> >>>> >>> >>> >>> YOU do not understand the TRUE meaning of a Truth Bearer. >>> >> >> A "Truth bearer" is an expression of language capable of having a >> Boolean property. > > Right, and the answer to the Halting Problem, "Does P(I) come to a > Halting state in a finite number of steps?" always, yes always. has a > Yes or No anser. Yes continue to dishonestly change the question by ignoring the mandatory context of the question. Does being a liar make you feel good? What Boolean value can H return to an input that does the opposite of whatever H decides making sure to contradict the halt status that H returns such that H returns the correct Boolean value halt status to P? >> >> In all cases where it is impossible to resolve an expression of language >> to a Boolean value this expression is not a truth bearer. > > And the Halting Problem never doesn't have an answer. Only because you dishonestly remove the context of the question. I claim there are no grocery stores that are bigger than the universe and your reply is that I am wrong Walmart is a big store. >> >> The key case of this is the liar Paradox. Something must be wrong with >> the world if no academician has figured out that self-contradictory >> sentences are not truth bearers in more than 2000 years. > > Right, you get the Liar paradox when you assume that H exists and ask > what it should produce in this case, the lack of answer shows that H > doesn't exist, not that the Halting Problem has a problem. > When-so-ever any decision problem TM/input pair has no correct Boolean value this is not an undecidable instance where the TM cannot decide which Boolean value is correct. It is an incorrect instance where both Boolean values are the wrong answer. > The WRONG QUESTIOH isn't a Truth Bearer. > -- Copyright 2021 Pete Olcott "Great spirits have always encountered violent opposition from mediocre minds." Einstein
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2021-07-16 23:07 -0600 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <eAtII.4481$B3Uf.2646@fx17.iad> |
| In reply to | #36336 |
On 7/15/21 9:05 AM, olcott wrote: > On 7/14/2021 11:03 PM, Richard Damon wrote: >> On 7/14/21 9:01 AM, olcott wrote: >>> On 7/13/2021 11:56 PM, Richard Damon wrote: >>>> On 7/13/21 4:16 PM, olcott wrote: >>>>> On 7/13/2021 1:15 PM, Peter wrote: >>>>>> olcott wrote: >>>>>>> [...] >>>>>>> When Gödel's 1931 incompleteness theorem is translated into HOL that >>>>>>> has its own provability predicate thus no need for the purely >>>>>>> extraneous complexity of Gödel numbers then it is very obvious that >>>>>>> it is modeled after the liar paradox. >>>>>> >>>>>> It's almost certainly of no interest to you, but a proof of the >>>>>> incompleteness of second order predicate calculus may be found in >>>>>> >>>>>> Hans Hermes, (trans Herman & Plassmann) /Enumerability, decidability, >>>>>> computability/, 2nd edition, Springer, 1964. >>>>>> >>>>>> It does not use Gödel numbering. Nor is it "is modeled after the >>>>>> liar >>>>>> paradox." >>>>>> >>>>> >>>>> I did not initially add that it must also have its own provability >>>>> predicate like the Tarski undefinability theorem. >>>>> >>>>> Even when we get these things boiled down to their simplest possible >>>>> essence no academicians can begin to understand what is really >>>>> going on. >>>>> >>>>> They still don't understand that the actual liar paradox is simply >>>>> not a >>>>> truth bearer because it is self contradictory. >>>>> >>>>> They all seem to think that it is some puzzle that is far too >>>>> difficult >>>>> to ever figure out. The Tarski undefinability theory has the liar >>>>> paradox as its only basis. >>>>> >>>>> http://www.liarparadox.org/Tarski_247_248.pdf >>>>> >>>>> http://www.liarparadox.org/Tarski_Proof_275_276.pdf >>>>> >>>>> >>>> >>>> >>>> YOU do not understand the TRUE meaning of a Truth Bearer. >>>> >>> >>> A "Truth bearer" is an expression of language capable of having a >>> Boolean property. >> >> Right, and the answer to the Halting Problem, "Does P(I) come to a >> Halting state in a finite number of steps?" always, yes always. has a >> Yes or No anser. > > Yes continue to dishonestly change the question by ignoring the > mandatory context of the question. Does being a liar make you feel good? You are the one that is ignoring the context. The answer to thge Halting Property of a Computation is INDEPENDENT of the decider being asked to decide it. PERIOD. Your POOP conflates the operation of the decider with the operation of the computation being asked about, > > What Boolean value can H return to an input that does the opposite of > whatever H decides making sure to contradict the halt status that H > returns such that H returns the correct Boolean value halt status to P? WRONG. That question persupposes that a universally accurate halt decider exists. The roughly equivalent question would be: What Boolean value should have the decider H returned to make an accurate halting determination for its input. THAT DOES have an answer, since to even ask it, we have to have the P, so we have to have an H, and the answer will be the opposite of whatever that H actually does return. > >>> >>> In all cases where it is impossible to resolve an expression of language >>> to a Boolean value this expression is not a truth bearer. >> >> And the Halting Problem never doesn't have an answer. > > Only because you dishonestly remove the context of the question. As I said, YOU have the wrong context. The answer to the Halting Problem of P(I) always has a definite answer, and thus the Halting Problem for the machine H^(H^) has a definite answer, and for H to have been RIGHT, it need to match that answer. The problem is that the right answer will never be the answer that H actually gave. There is NO logical contradiction in this. H is just WRONG > > I claim there are no grocery stores that are bigger than the universe > and your reply is that I am wrong Walmart is a big store. STRAWMAN, That isn't the question. The Halting Problem ALWAYS have a right answer for ANY Turing Machine. >>> >>> The key case of this is the liar Paradox. Something must be wrong with >>> the world if no academician has figured out that self-contradictory >>> sentences are not truth bearers in more than 2000 years. >> >> Right, you get the Liar paradox when you assume that H exists and ask >> what it should produce in this case, the lack of answer shows that H >> doesn't exist, not that the Halting Problem has a problem. >> > > When-so-ever any decision problem TM/input pair has no correct Boolean > value this is not an undecidable instance where the TM cannot decide > which Boolean value is correct. It is an incorrect instance where both > Boolean values are the wrong answer. AND H^(H^) HAS a deefinite answer for any give H (and you can't actually ask the question until you do). It is just the fact that H will ALWAYS be wrong about H^, that is NOT a contradiction. That is NOT a case of the question not having a proper anwer, because the question is NOT what should H return to be right, it is what does H^(H^) do, which depends on H as it is built on it as allowed by Turing Theory.
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2021-07-13 22:45 -0600 |
| Subject | Re: Olcott's theory [ Flibble understands this ] |
| Message-ID | <mZtHI.7239$Ei1.6336@fx07.iad> |
| In reply to | #36243 |
On 7/13/21 8:36 AM, olcott wrote:
> On 7/12/2021 10:27 PM, Richard Damon wrote:
>> On 7/12/21 3:51 PM, olcott wrote:
>>> On 7/12/2021 10:33 AM, David Brown wrote:
>>>> On 12/07/2021 16:25, olcott wrote:
>>>>> On 7/12/2021 8:19 AM, Malcolm McLean wrote:
>>>>>> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote:
>>>>>>> On 10/07/2021 19:06, olcott wrote:
>>>>>>>> At most I have only proved that the conventional proofs of the
>>>>>>>> undecidability of the halting problem that rely on the Strachey
>>>>>>>> form,
>>>>>>>> are incorrect. This seems to include all textbook proofs.
>>>>>>> As you know, Linz gives a quite different proof; and there are
>>>>>>> several other proofs, inc one via "Busy Beaver" [see below].
>>>>>>>
>>>>>>> [...]
>>>>>>>> Goldbach's Conjecture is merely undecided and thus not undecidable.
>>>>>>> "Thus" is a step too far. But note the reference to Goldbach
>>>>>>> in the Wiki article on "Busy Beaver".
>>>>>>>
>>>>>>> [...]
>>>>>>>> Busy Beaver only seems intractable not undecidable.
>>>>>>> It's undecidable whether an arbitrary TM is a BB; and the
>>>>>>> BB function [ie, the "score" of a BB of given size] is uncomputable.
>>>>>>> That's a stronger result than intractability. The proof that the
>>>>>>> BB function is uncomputable is [reasonably] elementary, and does not
>>>>>>> rely on the HP [or recursion]. If you had a "halting decider", then
>>>>>>> you could find BBs by exhaustive [albeit intractable!] search and
>>>>>>> thus compute the BB function; so there's yet another HP proof.
>>>>>>>
>>>>>> If you have a busy beaver function and a simulating decider, the busy
>>>>>> beaver function tells you how many times you need to step the decider
>>>>>> before you can be certain it will never halt. So halting is
>>>>>> decideable if
>>>>>> busy beaver is decideable.
>>>>>>
>>>>>>
>>>>>
>>>>> Flibble understands this:
>>>>> What correct Boolean value can a TM return to an input that does the
>>>>> opposite of whatever it decides? : neither, is excluded from the
>>>>> solution set thus making the question itself incorrect.
>>>>>
>>>>
>>>> You still don't understand this "proof by contradiction" concept, do
>>>> you?
>>>
>>> We can say that the following expression is undecidable on the basis
>>> that both true and false derive contradictions:
>>> "This sentence is not true." That same sentence is used as the basis of
>>> the Tarski undefinability theorem.
>>>
>>> http://www.liarparadox.org/Tarski_247_248.pdf
>>> http://www.liarparadox.org/Tarski_275_276.pdf
>>>
>>>
>>>
>>> Although we have proven that it is undecidable on the basis of proof by
>>> contradiction we are ignoring the key detail that the proof by
>>> contradiction only succeeds because the expression of language is
>>> self-contradictory, thus not a truth bearer and therefore erroneous.
>>
>> Does P(I) Halt IS a Truth Bearing Sentence, as P(I) will either Halt or
>> it won't. We may not be able to prove that answer, but that is one
>> fundamental property of the Higher level Logic that includes mathematics.
>>
>
> That is not the actual question, you leave out the key context that
> makes the question incorrect. Ben played this same dishonest dodge since
> 2006. When you strip off the context of the question you change it into
> an entirely different question.
>
> Here is the actual question:
> When we ask what Boolean value can a halt decider return to an input
> that changes its behavior to contradict this value we cannot answer this
> question because it is an incorrect type mismatch error question.
But that ISN'T the question of the Halting Problem. The question of the
Halting Problem NEVER refers to the decider, only to the machine being
decided on. PERIOD.
>
> The answer is restricted to {true, false} thus excluding the correct
> answer of “neither” making the question itself incorrect.
>
> If we ask a man that has never been married:
> Have you stopped beating you wife?
> This is an incorrect question.
> Every polar question lacking a correct yes/no answer is incorrect.
STRAWMEN
>
> Every TM/input to a decision problem lacking a correct Boolean return
> value is an incorrect TM/input for this decision problem.
EVERY TM/Input has a correct value for the Halting Problem, either that
machine/input combination will halt, or it won't. Absolutely one answer
is correct.
>
> The TM / input pairs that “prove” the halting problem is undecidable
> have the same pathological self-reference(Olcott 2004) error as the
> self-contradictory liar paradox.
H^(H^) is either a Halting Computation or it isn't. There is no neither.
The key point to remember is that H^ is DEFINED to be based on GIVEN
machine H, as ^ is actually a machine transformation. Thus to even ask
about H^, we need to have first fixed what H is. Once we have fixed that
H, then H^(H^) has a defininte halting behavior, and it will always be
the opposite of what H(H^,H^) predicts (as long as H does predict this
question). Thus H is always shown to not be a proper Halting decider.
There is no 'pathological' self-reference, as there is absolutely no
requrement that H can get the answer right, so the only 'pathology' in
the situation is to the existance of H.
>
> It has been at least 2000 years since the liar paradox was discovered
> and academicians still do not understand the because self-contradictory
> sentences do not map to a Boolean value they are not truth bearers.
But the Halting Problem ISN'T your 'pathological' question.
>
>> If you want to keep to the concept that something is only true if you
>> can prove it, then you must restrict yourself to only First Order Logic,
>> or you WILL eventually run into an inconsistency in your logic system.
>>
>
> Not at all. Not in the least.
> When Gödel's 1931 incompleteness theorem is translated into HOL that has
> its own provability predicate thus no need for the purely extraneous
> complexity of Gödel numbers then it is very obvious that it is modeled
> after the liar paradox>
> Gödel himself said that the liar paradox could be used as his
> incompleteness basis.
>
> there is also a close relationship with the “liar”
> antinomy,14
>
> We are therefore confronted with a proposition which
> asserts its own unprovability
>
> 14 Every epistemological antinomy can likewise be
> used for a similar undecidability proof.
>
> This is HOL with its in provability predicate:
> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>
>
> I have examples that show the propositions that assert their own
> unprovability are only undecidable because there is an infinite cycle in
> their directed graph.
>
> The problem is that like the liar paradox that have a vacuous truth
> object. This sentence is not true. This sentence is not provable. Have
> no truth object that they are true or provable about.
>
> "It is true that this sentence is a dump truck."
> has a truth object thus enabling the sentence to be evaluated as false.
>
> "This sentence is true"
> "This sentence is false"
> "This sentence is provable"
>
> Have no truth object, thus specify an infinite cycle in the directed
> graph of their resolution.
>
>> Yes, if you make that restriction to your logic, you can use that
>> property, but you can not express the fullness of mathematics in your
>> logic.
>>
>> This is well established.
>>
>
> I reestablished it correctly this time.
>
No, you haven't. PERIOD. You seem incapable of handling any complex logic.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2021-07-14 09:56 -0500 |
| Subject | Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) |
| Message-ID | <mt2dnW0d9rCOZnP9nZ2dnUU7-cnNnZ2d@giganews.com> |
| In reply to | #36298 |
On 7/13/2021 11:45 PM, Richard Damon wrote:
> On 7/13/21 8:36 AM, olcott wrote:
>> On 7/12/2021 10:27 PM, Richard Damon wrote:
>>> On 7/12/21 3:51 PM, olcott wrote:
>>>> On 7/12/2021 10:33 AM, David Brown wrote:
>>>>> On 12/07/2021 16:25, olcott wrote:
>>>>>> On 7/12/2021 8:19 AM, Malcolm McLean wrote:
>>>>>>> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote:
>>>>>>>> On 10/07/2021 19:06, olcott wrote:
>>>>>>>>> At most I have only proved that the conventional proofs of the
>>>>>>>>> undecidability of the halting problem that rely on the Strachey
>>>>>>>>> form,
>>>>>>>>> are incorrect. This seems to include all textbook proofs.
>>>>>>>> As you know, Linz gives a quite different proof; and there are
>>>>>>>> several other proofs, inc one via "Busy Beaver" [see below].
>>>>>>>>
>>>>>>>> [...]
>>>>>>>>> Goldbach's Conjecture is merely undecided and thus not undecidable.
>>>>>>>> "Thus" is a step too far. But note the reference to Goldbach
>>>>>>>> in the Wiki article on "Busy Beaver".
>>>>>>>>
>>>>>>>> [...]
>>>>>>>>> Busy Beaver only seems intractable not undecidable.
>>>>>>>> It's undecidable whether an arbitrary TM is a BB; and the
>>>>>>>> BB function [ie, the "score" of a BB of given size] is uncomputable.
>>>>>>>> That's a stronger result than intractability. The proof that the
>>>>>>>> BB function is uncomputable is [reasonably] elementary, and does not
>>>>>>>> rely on the HP [or recursion]. If you had a "halting decider", then
>>>>>>>> you could find BBs by exhaustive [albeit intractable!] search and
>>>>>>>> thus compute the BB function; so there's yet another HP proof.
>>>>>>>>
>>>>>>> If you have a busy beaver function and a simulating decider, the busy
>>>>>>> beaver function tells you how many times you need to step the decider
>>>>>>> before you can be certain it will never halt. So halting is
>>>>>>> decideable if
>>>>>>> busy beaver is decideable.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Flibble understands this:
>>>>>> What correct Boolean value can a TM return to an input that does the
>>>>>> opposite of whatever it decides? : neither, is excluded from the
>>>>>> solution set thus making the question itself incorrect.
>>>>>>
>>>>>
>>>>> You still don't understand this "proof by contradiction" concept, do
>>>>> you?
>>>>
>>>> We can say that the following expression is undecidable on the basis
>>>> that both true and false derive contradictions:
>>>> "This sentence is not true." That same sentence is used as the basis of
>>>> the Tarski undefinability theorem.
>>>>
>>>> http://www.liarparadox.org/Tarski_247_248.pdf
>>>> http://www.liarparadox.org/Tarski_275_276.pdf
>>>>
>>>>
>>>>
>>>> Although we have proven that it is undecidable on the basis of proof by
>>>> contradiction we are ignoring the key detail that the proof by
>>>> contradiction only succeeds because the expression of language is
>>>> self-contradictory, thus not a truth bearer and therefore erroneous.
>>>
>>> Does P(I) Halt IS a Truth Bearing Sentence, as P(I) will either Halt or
>>> it won't. We may not be able to prove that answer, but that is one
>>> fundamental property of the Higher level Logic that includes mathematics.
>>>
>>
>> That is not the actual question, you leave out the key context that
>> makes the question incorrect. Ben played this same dishonest dodge since
>> 2006. When you strip off the context of the question you change it into
>> an entirely different question.
>>
>> Here is the actual question:
>> When we ask what Boolean value can a halt decider return to an input
>> that changes its behavior to contradict this value we cannot answer this
>> question because it is an incorrect type mismatch error question.
>
> But that ISN'T the question of the Halting Problem.
That is the question of this specific TM/input pair applied to the
halting problem.
When we ask someone that has never been married :
Have you stopped beating your wife?
Within the full context that it is someone that has never been married
then this question becomes incorrect. If we simply ignore the context
then the analysis is incomplete.
For the decision problem of the halting problem some TM/input pairs are
incorrect and others are correct, the context of TM/input pair must be
considered or the analysis is incomplete.
Since the above two questions are isomorphic we can know with complete
certainty that the context of the TM/input pair must be considered.
I am the creator of the whole idea of incorrect questions. I created
this concept in this forum for the sole purpose of showing that
pathological self-reference(Olcott 2004) is an error.
> The question of the
> Halting Problem NEVER refers to the decider, only to the machine being
> decided on. PERIOD.
>>
>> The answer is restricted to {true, false} thus excluding the correct
>> answer of “neither” making the question itself incorrect.
>>
>> If we ask a man that has never been married:
>> Have you stopped beating you wife?
>> This is an incorrect question.
>> Every polar question lacking a correct yes/no answer is incorrect.
>
> STRAWMEN
>
>>
>> Every TM/input to a decision problem lacking a correct Boolean return
>> value is an incorrect TM/input for this decision problem.
>
> EVERY TM/Input has a correct value for the Halting Problem, either that
> machine/input combination will halt, or it won't. Absolutely one answer
> is correct.
>
>>
>> The TM / input pairs that “prove” the halting problem is undecidable
>> have the same pathological self-reference(Olcott 2004) error as the
>> self-contradictory liar paradox.
>
> H^(H^) is either a Halting Computation or it isn't. There is no neither.
>
> The key point to remember is that H^ is DEFINED to be based on GIVEN
> machine H, as ^ is actually a machine transformation. Thus to even ask
> about H^, we need to have first fixed what H is. Once we have fixed that
> H, then H^(H^) has a defininte halting behavior, and it will always be
> the opposite of what H(H^,H^) predicts (as long as H does predict this
> question). Thus H is always shown to not be a proper Halting decider.
>
> There is no 'pathological' self-reference, as there is absolutely no
> requrement that H can get the answer right, so the only 'pathology' in
> the situation is to the existance of H.
>
>
>>
>> It has been at least 2000 years since the liar paradox was discovered
>> and academicians still do not understand the because self-contradictory
>> sentences do not map to a Boolean value they are not truth bearers.
>
> But the Halting Problem ISN'T your 'pathological' question.
>>
>>> If you want to keep to the concept that something is only true if you
>>> can prove it, then you must restrict yourself to only First Order Logic,
>>> or you WILL eventually run into an inconsistency in your logic system.
>>>
>>
>> Not at all. Not in the least.
>> When Gödel's 1931 incompleteness theorem is translated into HOL that has
>> its own provability predicate thus no need for the purely extraneous
>> complexity of Gödel numbers then it is very obvious that it is modeled
>> after the liar paradox>
>> Gödel himself said that the liar paradox could be used as his
>> incompleteness basis.
>>
>> there is also a close relationship with the “liar”
>> antinomy,14
>>
>> We are therefore confronted with a proposition which
>> asserts its own unprovability
>>
>> 14 Every epistemological antinomy can likewise be
>> used for a similar undecidability proof.
>>
>> This is HOL with its in provability predicate:
>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>
>>
>> I have examples that show the propositions that assert their own
>> unprovability are only undecidable because there is an infinite cycle in
>> their directed graph.
>>
>> The problem is that like the liar paradox that have a vacuous truth
>> object. This sentence is not true. This sentence is not provable. Have
>> no truth object that they are true or provable about.
>>
>> "It is true that this sentence is a dump truck."
>> has a truth object thus enabling the sentence to be evaluated as false.
>>
>> "This sentence is true"
>> "This sentence is false"
>> "This sentence is provable"
>>
>> Have no truth object, thus specify an infinite cycle in the directed
>> graph of their resolution.
>>
>>> Yes, if you make that restriction to your logic, you can use that
>>> property, but you can not express the fullness of mathematics in your
>>> logic.
>>>
>>> This is well established.
>>>
>>
>> I reestablished it correctly this time.
>>
>
> No, you haven't. PERIOD. You seem incapable of handling any complex logic.
>
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2021-07-14 21:48 -0600 |
| Subject | Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) |
| Message-ID | <6eOHI.25853$VU3.1696@fx46.iad> |
| In reply to | #36304 |
On 7/14/21 8:56 AM, olcott wrote: > On 7/13/2021 11:45 PM, Richard Damon wrote: >> On 7/13/21 8:36 AM, olcott wrote: >>> On 7/12/2021 10:27 PM, Richard Damon wrote: >>>> On 7/12/21 3:51 PM, olcott wrote: >>>>> On 7/12/2021 10:33 AM, David Brown wrote: >>>>>> On 12/07/2021 16:25, olcott wrote: >>>>>>> On 7/12/2021 8:19 AM, Malcolm McLean wrote: >>>>>>>> On Monday, 12 July 2021 at 14:13:15 UTC+1, Andy Walker wrote: >>>>>>>>> On 10/07/2021 19:06, olcott wrote: >>>>>>>>>> At most I have only proved that the conventional proofs of the >>>>>>>>>> undecidability of the halting problem that rely on the Strachey >>>>>>>>>> form, >>>>>>>>>> are incorrect. This seems to include all textbook proofs. >>>>>>>>> As you know, Linz gives a quite different proof; and there are >>>>>>>>> several other proofs, inc one via "Busy Beaver" [see below]. >>>>>>>>> >>>>>>>>> [...] >>>>>>>>>> Goldbach's Conjecture is merely undecided and thus not >>>>>>>>>> undecidable. >>>>>>>>> "Thus" is a step too far. But note the reference to Goldbach >>>>>>>>> in the Wiki article on "Busy Beaver". >>>>>>>>> >>>>>>>>> [...] >>>>>>>>>> Busy Beaver only seems intractable not undecidable. >>>>>>>>> It's undecidable whether an arbitrary TM is a BB; and the >>>>>>>>> BB function [ie, the "score" of a BB of given size] is >>>>>>>>> uncomputable. >>>>>>>>> That's a stronger result than intractability. The proof that the >>>>>>>>> BB function is uncomputable is [reasonably] elementary, and >>>>>>>>> does not >>>>>>>>> rely on the HP [or recursion]. If you had a "halting decider", >>>>>>>>> then >>>>>>>>> you could find BBs by exhaustive [albeit intractable!] search and >>>>>>>>> thus compute the BB function; so there's yet another HP proof. >>>>>>>>> >>>>>>>> If you have a busy beaver function and a simulating decider, the >>>>>>>> busy >>>>>>>> beaver function tells you how many times you need to step the >>>>>>>> decider >>>>>>>> before you can be certain it will never halt. So halting is >>>>>>>> decideable if >>>>>>>> busy beaver is decideable. >>>>>>>> >>>>>>>> >>>>>>> >>>>>>> Flibble understands this: >>>>>>> What correct Boolean value can a TM return to an input that does the >>>>>>> opposite of whatever it decides? : neither, is excluded from the >>>>>>> solution set thus making the question itself incorrect. >>>>>>> >>>>>> >>>>>> You still don't understand this "proof by contradiction" concept, do >>>>>> you? >>>>> >>>>> We can say that the following expression is undecidable on the basis >>>>> that both true and false derive contradictions: >>>>> "This sentence is not true." That same sentence is used as the >>>>> basis of >>>>> the Tarski undefinability theorem. >>>>> >>>>> http://www.liarparadox.org/Tarski_247_248.pdf >>>>> http://www.liarparadox.org/Tarski_275_276.pdf >>>>> >>>>> >>>>> >>>>> Although we have proven that it is undecidable on the basis of >>>>> proof by >>>>> contradiction we are ignoring the key detail that the proof by >>>>> contradiction only succeeds because the expression of language is >>>>> self-contradictory, thus not a truth bearer and therefore erroneous. >>>> >>>> Does P(I) Halt IS a Truth Bearing Sentence, as P(I) will either Halt or >>>> it won't. We may not be able to prove that answer, but that is one >>>> fundamental property of the Higher level Logic that includes >>>> mathematics. >>>> >>> >>> That is not the actual question, you leave out the key context that >>> makes the question incorrect. Ben played this same dishonest dodge since >>> 2006. When you strip off the context of the question you change it into >>> an entirely different question. >>> >>> Here is the actual question: >>> When we ask what Boolean value can a halt decider return to an input >>> that changes its behavior to contradict this value we cannot answer this >>> question because it is an incorrect type mismatch error question. >> >> But that ISN'T the question of the Halting Problem. > > That is the question of this specific TM/input pair applied to the > halting problem. NO. The question is "Does P(I) Halt?" When P = H^ built from your definiton of H, the answer is an unequivocal YES. It HAS a definite answer. H just didn't give it, so it was wrong. > > When we ask someone that has never been married : > Have you stopped beating your wife? Will you stop making dumb comments? > > Within the full context that it is someone that has never been married > then this question becomes incorrect. If we simply ignore the context > then the analysis is incomplete. > > For the decision problem of the halting problem some TM/input pairs are > incorrect and others are correct, the context of TM/input pair must be > considered or the analysis is incomplete. No. Show ONE Turing Machine which neither 'Halts in finite time' or 'Never Halts'. There is no such machine (there are some we don't know which answer it is, but all machines will do one or the other). You only get you contradiction with the WRONG QUESTION. > > Since the above two questions are isomorphic we can know with complete > certainty that the context of the TM/input pair must be considered. If you mean "Does H^(H^) Halt" and "what answer can H give to be right?" These are NOT isomorphic, because the second one is improperly formed. The only answer that H CAN give is the one that its algorithm says it will, and if that is wrong, then H is wrong. In fact, the whole bases of Linz's proof is showing that your second question has no valid answer, and thus, an H that gives the right answer doesn't exist. > > I am the creator of the whole idea of incorrect questions. I created > this concept in this forum for the sole purpose of showing that > pathological self-reference(Olcott 2004) is an error. Great wording, Yes you are GREAT at creating the wrong question, I not sure you should really be that proud of doing that. Maybe you should actually try to learn what the actual questions are so you stop fighting Strawan and thinking you have actually done something.
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| From | Malcolm McLean <malcolm.arthur.mclean@gmail.com> |
|---|---|
| Date | 2021-07-15 03:43 -0700 |
| Subject | Re: Olcott's theory [ Flibble understands this ] ( isomorphic thus correct ) |
| Message-ID | <c5ef9870-82b2-42f1-a710-cdfcbe298ce2n@googlegroups.com> |
| In reply to | #36325 |
On Thursday, 15 July 2021 at 04:48:23 UTC+1, Richard Damon wrote: > On 7/14/21 8:56 AM, olcott wrote: > > > > > > When we ask someone that has never been married : > > Have you stopped beating your wife? > Will you stop making dumb comments? > It spoils them when you have to explain them. But the point of the joke is not that the the person of whom the question is being asked is a bachelor. It's assumed that he is married. It's that the question presumes that he habitually beat his wife in the past. So if he answers "no" that means he is still beating his wife, and if he answers "yes" then that confirms that he beat his wife in the past. There's no answer he can give which implies "I never beat my wife". Technically the correct answer is "no". But that's even more damning than "yes".
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