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

From Kaz Kylheku <643-408-1753@kylheku.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 23:25 +0000
Organization A noiseless patient Spider
Message-ID <20251003155144.914@kylheku.com> (permalink)
References (2 earlier) <10bn2h1$1atqn$1@dont-email.me> <20251002164524.463@kylheku.com> <10bn5ot$1bje3$1@dont-email.me> <20251003144904.146@kylheku.com> <10bphd5$24fi1$1@dont-email.me>

Cross-posted to 4 groups.

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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.

> 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.

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!

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.

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. :)

-- 
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @Kazinator@mstdn.ca

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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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