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Re: A new category of thought

From olcott <polcott333@gmail.com>
Newsgroups comp.theory, sci.logic, sci.math, sci.lang
Subject Re: A new category of thought
Date 2025-12-03 09:59 -0600
Organization A noiseless patient Spider
Message-ID <10gpmpn$3emj7$1@dont-email.me> (permalink)
References (7 earlier) <10gjsku$18h21$1@dont-email.me> <10gkiev$1h8eo$1@dont-email.me> <10gm9do$24og8$1@dont-email.me> <10gmre5$2blfd$1@dont-email.me> <10gp441$37f5l$1@dont-email.me>

Cross-posted to 4 groups.

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On 12/3/2025 4:41 AM, Mikko wrote:
> olcott kirjoitti 2.12.2025 klo 16.00:
>> On 12/2/2025 2:53 AM, Mikko wrote:
>>> olcott kirjoitti 1.12.2025 klo 19.15:
>>>> On 12/1/2025 5:02 AM, Mikko wrote:
>>>>> olcott kirjoitti 29.11.2025 klo 23.59:
>>>>>
>>>>> G := (F ⊬ G) // G says of itself that it is unprovable in F
>>>>>
>>>>> With a reasonable type system that is a type error:
>>>>> - the symbol ⊬ requires a sentence on the right side
>>>>> - the value of the ⊬ operation is a truth value
>>>>> - the symbol := requires the same type on both sides
>>>>> - thus G must be both a sentence and a truth value
>>>>>
>>>>> But G cannot be both. A sentence has a truth value but it isn't one.
>>>>>
>>>>
>>>> % This sentence cannot be proven in F
>>>> ?- G = not(provable(F, G)).
>>>> G = not(provable(F, G)).
>>>> ?- unify_with_occurs_check(G, not(provable(F, G))).
>>>> false.
>>>>
>>>> It is an expression of language having no truth value
>>>> because it is not a logic sentence.
>>>>
>>>> https://en.wikipedia.org/wiki/Sentence_(mathematical_logic)
>>>
>>> Yes, that is the exxential difference between the two G's.
>>> The expession F ⊬ G has a truth value because it is either
>>> true or false 
>>
>> I propose that is a false assumption.
> 
> If you want to propose anygthng like that you should
> (a) specify what is the assumption you want to propose as false
> (b) why should that assumption be considered false
> (c) what assumption would be true or at least less obviously false
> 

?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.

G is neither True nor False its resolution remains stuck
in an infinite loop.

BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:

equal(X, X).
?- equal(foo(Y), Y).

that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y,
which appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)


-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

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Thread

A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 10:32 -0600
  Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 17:53 +0000
    Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 12:07 -0600
      Re: A new category of thought dbush <dbush.mobile@gmail.com> - 2025-11-29 13:19 -0500
        Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-01 16:55 +0000
          Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 11:04 -0600
        Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:49 +0200
          Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-02 09:26 -0600
            Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-04 08:46 -0600
              Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:52 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 11:21 -0600
                Re: A new category of thought André G. Isaak <agisaak@gm.invalid> - 2025-12-05 19:57 -0700
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 21:18 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:01 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:40 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:47 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 09:16 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 02:04 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:21 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 09:55 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 12:43 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-06 22:16 -0500
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-06 21:50 -0600
                Re: A new category of thought Python <python@cccp.invalid> - 2025-12-07 05:32 +0000
                Re: A new category of thought Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2025-12-07 15:49 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 11:38 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 07:32 -0500
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 07:37 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 17:55 -0500
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-07 17:15 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 21:50 -0500
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:26 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 07:40 -0500
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 12:47 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 19:18 -0500
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-08 19:00 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 21:24 -0500
                Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 20:34 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 21:57 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 21:16 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 22:22 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 21:50 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 23:20 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 22:30 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-09 10:05 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 02:14 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:21 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 07:07 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 10:41 -0600
                Re: A new category of thought Python <python@cccp.invalid> - 2025-12-08 19:39 +0000
            Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:57 +0200
              Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 11:30 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 10:53 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:33 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:42 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 09:03 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 06:12 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 07:59 -0600
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 10:18 -0600
      Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 20:23 +0000
        Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 14:51 -0600
          Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 16:27 -0500
            Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 15:53 -0800
              Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 19:17 -0500
                Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 16:35 -0800
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 20:10 -0500
                Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 19:49 -0800
                Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 19:50 -0800
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:59 +0000
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-01 23:11 -0500
          Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 21:39 +0000
            Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 15:59 -0600
              Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 22:44 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 17:19 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 19:21 -0500
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:13 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 19:50 -0600
              Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-01 13:02 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 11:15 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-02 10:53 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-02 08:00 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-03 12:41 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-03 09:59 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:48 +0200
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-05 09:30 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 10:41 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 10:37 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:24 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:39 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 08:59 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-09 15:15 +0200
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-09 12:04 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-14 13:02 +0200
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:39 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 20:01 -0600
          Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-01 17:37 +0000
            Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 13:44 -0600
  Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 15:08 -0500

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