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Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable

From olcott <polcott333@gmail.com>
Newsgroups comp.theory, comp.lang.c++, comp.lang.c, comp.ai.philosophy
Subject Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable
Date 2025-10-03 18:57 -0500
Organization A noiseless patient Spider
Message-ID <10bpnsl$25vc4$1@dont-email.me> (permalink)
References (3 earlier) <20251002164524.463@kylheku.com> <10bn5ot$1bje3$1@dont-email.me> <20251003144904.146@kylheku.com> <10bphd5$24fi1$1@dont-email.me> <20251003155144.914@kylheku.com>

Cross-posted to 4 groups.

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On 10/3/2025 6:25 PM, Kaz Kylheku wrote:
> On 2025-10-03, olcott <polcott333@gmail.com> wrote:
>> On 10/3/2025 4:50 PM, Kaz Kylheku wrote:
>>> On 2025-10-03, olcott <polcott333@gmail.com> wrote:
>>>> This concept must be named or it cannot
>>>> be referenced. I must reference it.
>>>> It must be a simple and accurate name.
>>>>
>>>> WTF would you call it?
>>>>
>>>> The set of H/P pairs such that:
>>>> For decider H and input P
>>>> If H says halts then P loops
>>>> If H says loops then P halts
>>>> making H(P) always incorrect.
>>>
>>> This is not /your/ concept; it is something you should have
>>> understood properly 20 years ago.
>>>
>>
>> It isn't that I didn't understand this 22 years ago.
>> I understood this the whole time. It is that 22 years
> 
> As little as five years go or so you still believed that there
> is supposed to be a /single/ case that is undecidable.
> 

My words may have seemed to have indicated that.

>> ago I spotted its bogus liar paradox structure.
> 
> Because you didn't understand it at the time, but given what you should
> know now, you should see that it's not the same at all.
> 
> The diagonal case, though it contains a self-reference, is not a truth
> statement and it is not asserting its own falsehood.
> 
> The details of the self-reference matter.
> 

Yes that is why I coined the term pathological
self-reference(Olcott 2004). All my old posts
are still out there. I can still directly reply to them.

> For instance, these sentence are just as self-referential as the
> Liar Paradox, yet we can cheerfully assign them truth values:
> 
>    This sentence has five words.  (True)
>    This sentence has four words.  (False)
> 
> Like the Liar sentence, these sentences are making a logical assertion.
> Unlike the Liar sentence, they are not simply making a logical assertion
> about their truth value; they are making an assertion about a property
> different from their truth value.
> 
> By talking about something other than their own truth value, the
> logical assertion is anchored to something external.
> 
> The following sentence is self-referential, yet talks about nothing but
> its truth value:
> 
>    This sentence is true.
> 
> this is still just internal: the logical assertion talking about its
> own truth.  We can assign the value True or False to this sentence
> without contradiction---but that is a problem almost if not just as bad
> as not being able to assign a truth value!
> 

None-the-less it is still semantically faulty.

> So anyway, in the diagonal trick used for reasoning about halting,
> the self-reference is much more like:
> 
>    This sentence has four words.
> 
> than it is like:
> 
>    This sentence is false.
> 

Incorrect.

For the set of H/P pairs of
decider H and input P:
If H says halts then P loops
If H says loops then P halts
making H(P) always incorrect.

Is much more liar paradox like.
The pathological self-reference(Olcott 2004)
is indirect instead of direct.

> The H decider isn't asserting something about the truth value of its
> subject; it is anchored to a different property, halting,
> which is like word count, or any other property.
> 
> The "opposite behavior" is something as if we could make
> a sentence that changes its word count to something other than
> what it has been counted by some procedure.
> 
> Suppose H is a word count procedure. Let the sentence D be:
> 
>    In this sentence, 'Church-Turing' is two words, except if H says
>    that this sentence has an even number of words, in which case it
>    is one word.
> 
> Thus if we allow sentences to stipulate how many words comprise a
> hyphenated compound which occurs in them, and if we allow such
> stipulations to refer to word counting functions, then the word count
> function becomes incomputable. :)
> 


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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Thread

Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-02 15:59 -0500
  Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable dbush <dbush.mobile@gmail.com> - 2025-10-02 17:19 -0400
    Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-02 16:56 -0500
      Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Damon <Richard@Damon-Family.org> - 2025-10-05 16:46 -0400
  Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-02 23:31 +0000
    Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-02 18:40 -0500
      Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-02 23:54 +0000
        Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-02 19:35 -0500
          Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-03 21:50 +0000
            Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-03 17:01 -0500
              Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-03 15:06 -0700
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mikko <mikko.levanto@iki.fi> - 2025-10-04 12:05 +0300
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-04 20:10 -0700
            Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-03 17:06 -0500
              Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-03 23:25 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-03 18:57 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-04 05:02 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 07:56 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Heathfield <rjh@cpax.org.uk> - 2025-10-04 16:01 +0100
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 10:20 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-04 15:36 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 11:35 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-04 16:49 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-05 07:52 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Heathfield <rjh@cpax.org.uk> - 2025-10-04 17:44 +0100
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2025-10-04 15:32 +0100
          Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2025-10-04 00:11 +0100
            Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-03 18:28 -0500
              Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-03 23:52 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Heathfield <rjh@cpax.org.uk> - 2025-10-04 01:06 +0100
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-03 19:11 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-04 05:04 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 08:04 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable joes <noreply@example.org> - 2025-10-04 14:04 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 10:43 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-04 16:55 +0000
                Conventional HP diagonal case is succinctly proven unsatisfiable --- embedded_H olcott <polcott333@gmail.com> - 2025-10-05 07:58 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-05 08:17 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Damon <Richard@Damon-Family.org> - 2025-10-05 16:50 -0400
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Heathfield <rjh@cpax.org.uk> - 2025-10-04 16:06 +0100
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 10:22 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-04 20:21 -0700
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-04 16:24 +0000
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-04 20:17 -0700
          Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mikko <mikko.levanto@iki.fi> - 2025-10-04 12:00 +0300
            Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 22:56 -0500
              Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Heathfield <rjh@cpax.org.uk> - 2025-10-05 05:31 +0100
              Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mikko <mikko.levanto@iki.fi> - 2025-10-05 12:47 +0300
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-05 09:35 -0500
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Heathfield <rjh@cpax.org.uk> - 2025-10-05 16:28 +0100
                Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mikko <mikko.levanto@iki.fi> - 2025-10-06 12:07 +0300
  Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mikko <mikko.levanto@iki.fi> - 2025-10-03 13:12 +0300
    Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-03 08:20 -0500
      Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Mikko <mikko.levanto@iki.fi> - 2025-10-04 12:13 +0300
        Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 23:06 -0500
  Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Wuns Haerst <Wuns.Haerst@wurstfabrik.at> - 2025-10-04 17:23 +0200
    Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 10:25 -0500
    Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable olcott <polcott333@gmail.com> - 2025-10-04 10:27 -0500
  Re: Conventional notion of the HP diagonal case is succinctly proven unsatisfiable Richard Damon <Richard@Damon-Family.org> - 2025-10-05 16:46 -0400

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