Re: on deciding this sentence is false

From	Alan Mackenzie <acm@muc.de>
Newsgroups	comp.theory
Subject	Re: on deciding this sentence is false
Date	2025-11-28 21:08 +0000
Organization	muc.de e.V.
Message-ID	<10gd312$2aou$1@news.muc.de> (permalink)
References	<10g93ic$13hj8$8@dont-email.me> <10gcmj1$1avi$2@news.muc.de> <10gd1ft$2krs3$2@dont-email.me>

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dart200 <user7160@newsgrouper.org.invalid> wrote:
> On 11/28/25 9:36 AM, Alan Mackenzie wrote:
>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>> does the logical construction:

>>> "this sentence is false"

>>> place a hard limit on our ability to understand truth:

>>> yes/no???

>> No, not at all.  Anybody beyond early childhood will recognise it as a
>> mere frivolous distraction from any seeking after the truth.

> so why does anyone think such a construct places a meaningful limit in a 
> formal system then?

People, in general, don't, apart from one or two exceptions.

> "this sentence has no proof"

That is a world apart from "This sentence is false.".  It's the kernel
of Gödel's proof (as you know, of course).  "This sentence has no proof"
turns out to be true and unprovable (for a precisely defined meaning of
"unprovable").

> "this program loops forever iff it's decided that it halts"

As you also know, this is the contradiction reached in one of the proofs
of the Halting Theorem.  This is also not the same as "This sentence is
false.", though it is inspired by that nonsense.

None of these sentences/nonsenses limit our ability to understand truth.
They are part of the truth that we understand.  They delineate
fundamental boundaries of what can be known and proven, in particular
that truth is more subtle than provability.

This opens the possibility that some mathematical conjectures may be
true but unprovable.  That's just part of existence.

> -- 
> a burnt out swe investigating into why our tooling doesn't involve
> basic semantic proofs like halting analysis

> please excuse my pseudo-pyscript,

> ~ nick

-- 
Alan Mackenzie (Nuremberg, Germany).

Thread

on deciding this sentence is false dart200 <user7160@newsgrouper.org.invalid> - 2025-11-27 00:53 -0800
  Re: on deciding this sentence is false Alan Mackenzie <acm@muc.de> - 2025-11-28 17:36 +0000
    Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-28 12:20 -0600
      Re: on deciding this sentence is false Richard Damon <Richard@Damon-Family.org> - 2025-11-28 13:31 -0500
      Re: on deciding this sentence is false Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:51 +0200
        Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-29 10:59 -0600
          Re: on deciding this sentence is false Mikko <mikko.levanto@iki.fi> - 2025-12-01 11:42 +0200
            Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-12-01 06:43 -0600
    Re: on deciding this sentence is false dart200 <user7160@newsgrouper.org.invalid> - 2025-11-28 12:42 -0800
      Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-28 14:45 -0600
        Re: on deciding this sentence is false Richard Damon <Richard@Damon-Family.org> - 2025-11-28 16:51 -0500
        Re: on deciding this sentence is false Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-28 23:40 +0000
      Re: on deciding this sentence is false Alan Mackenzie <acm@muc.de> - 2025-11-28 21:08 +0000
        A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-28 16:03 -0600
          Re: A new foundation for correct reasoning +++ Richard Damon <Richard@Damon-Family.org> - 2025-11-28 17:33 -0500
          Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-28 22:54 +0000
            Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-28 17:14 -0600
              Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-29 11:55 +0000
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-29 09:18 -0600
                Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-29 20:48 +0000
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-29 15:31 -0600
                Re: A new foundation for correct reasoning +++ Richard Damon <Richard@Damon-Family.org> - 2025-11-29 17:04 -0500
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-01 12:31 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-01 06:19 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:56 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-02 08:07 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-03 13:17 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-03 10:13 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-04 11:29 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-04 08:18 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:03 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-05 11:31 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:39 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-06 06:53 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-07 13:08 +0200
                Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-08 13:56 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-14 13:05 +0200
                Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-12-01 13:28 +0000
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:30 +0200
        Re: on deciding this sentence is false dart200 <user7160@newsgrouper.org.invalid> - 2025-11-29 10:48 -0800
          Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-29 12:54 -0600
          Re: on deciding this sentence is false Alan Mackenzie <acm@muc.de> - 2025-11-29 20:00 +0000
            Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-29 14:08 -0600
            Re: on deciding this sentence is false dart200 <user7160@newsgrouper.org.invalid> - 2025-11-29 12:43 -0800
              Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-29 14:58 -0600
              Re: on deciding this sentence is false Alan Mackenzie <acm@muc.de> - 2025-11-29 21:24 +0000
                Re: on deciding this sentence is false olcott <polcott333@gmail.com> - 2025-11-29 15:46 -0600
                Re: on deciding this sentence is false Alan Mackenzie <acm@muc.de> - 2025-11-30 14:17 +0000
                The entire body of general knowledge that can be expressed in language olcott <polcott333@gmail.com> - 2025-11-30 09:58 -0600
                Re: The entire body of general knowledge that can be expressed in language Alan Mackenzie <acm@muc.de> - 2025-11-30 16:41 +0000
                Re: The entire body of general knowledge that can be expressed in language olcott <polcott333@gmail.com> - 2025-11-30 11:35 -0600
                Re: The entire body of general knowledge that can be expressed in language dbush <dbush.mobile@gmail.com> - 2025-11-30 12:37 -0500
                Re: The entire body of general knowledge that can be expressed in language Alan Mackenzie <acm@muc.de> - 2025-11-30 18:17 +0000
                Re: The entire body of general knowledge that can be expressed in language olcott <polcott333@gmail.com> - 2025-11-30 15:19 -0600
                Re: The entire body of general knowledge that can be expressed in language Richard Damon <Richard@Damon-Family.org> - 2025-11-30 16:58 -0500
                Re: The entire body of general knowledge that can be expressed in language Alan Mackenzie <acm@muc.de> - 2025-11-30 22:10 +0000
                Re: The entire body of general knowledge that can be expressed in language olcott <polcott333@gmail.com> - 2025-11-30 17:30 -0600
                Re: The entire body of general knowledge that can be expressed in language Richard Damon <Richard@Damon-Family.org> - 2025-11-30 21:39 -0500
                Re: The entire body of general knowledge that can be expressed in language Richard Damon <Richard@Damon-Family.org> - 2025-11-30 14:41 -0500
                Re: on deciding this sentence is false Richard Damon <Richard@Damon-Family.org> - 2025-11-30 14:37 -0500
                Re: on deciding this sentence is false dart200 <user7160@newsgrouper.org.invalid> - 2025-11-29 22:55 -0800
                Re: on deciding this sentence is false Dude <user2891@newsgrouper.org.invalid> - 2025-11-30 17:36 +0000
              Re: on deciding this sentence is false "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 15:00 -0800

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