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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 2025-12-01 19:50 -0600
Organization A noiseless patient Spider
Message-ID <10glgm1$1st18$1@dont-email.me> (permalink)
References (5 earlier) <20251129132843.374@kylheku.com> <10gfqb6$3p2df$1@dont-email.me> <20251129141108.632@kylheku.com> <10gfv2d$3r0mk$1@dont-email.me> <10glegf$1roie$1@dont-email.me>

Cross-posted to 4 groups.

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On 12/1/2025 7:13 PM, Tristan Wibberley wrote:
> On 29/11/2025 23:19, olcott wrote:
> 
>> Gödel, Kurt 1931.
>> On Formally Undecidable Propositions of Principia Mathematica And
>> Related Systems
> 
> Do you have a reference to the original and also English translation of
> his 1938 paper "On Formally Undecidable Propositions of Principia
> Mathematica And Related Systems II"?
>                                  ^^
> 

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And 
Related Systems

https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf 


I never look at things in terms of their complex verbosity.
As a software engineer with decades of experience I boil
them down to their breast essence.

> His 1931 paper says he'll followup with a completed proof and
> generalisation to more systems - so I think that's what we have to look
> at to understand what people refer to as his first incompleteness proof
> and theorem. I've been told (albeit by a chatbot) that the title and
> year above is what I should look for.
> 
> 
>> If you think that I am wrong then don't fucking guess
>> show exactly what his sentence actually says without
>> the ruse of Gödel numbers in a language has its own
>> self-reference operator and provability operator.
> 
> You've gone off the deep end there.
> 

Maybe with the swearing, these people have proven to
be incorrigible, that is why I blocked half of them.

> 
>> I say it says this:
>> G := (F ⊬ G) // G says of itself that it is unprovable in F
> 
> 
> It says that G is not a theorem of F, and perhaps it does so

That is short-hand.

> epitheoretically because of the use of ":=" which often nominates a
> substitution to apply to get an object of F, and that would /almost/
> trivially make it true, albeit not for all possible F.
> 

*YACC Syntax of Olcott Minimal Type Theory*
https://philarchive.org/archive/PETMTT-4v2
I used the "defined as" operator to allow
direct self-reference.

> "[fact] in [a system]" conventionally can mean [fact] for all definition
> extensions of [a system] when mathematicians are talking because they
> add definitions when using the system and examine the consequences "/in/
> the system". The prepositions are ambiguous across specialisms, clearly.
> 

I mean every fact that can be axiomatized in the
the verbal model of the actual world.

"cats" <are> "animals" stipulates relations between
finite strings Implementing Gödel's "theory of simple types"
in a type hierarchy of Rudolf Carnap Meaning Postulates.

https://lawrencecpaulson.github.io/papers/Russells-mathematical-logic.pdf 
bottom of page 9

https://liarparadox.org/Meaning_Postulates_Rudolf_Carnap_1952.pdf

> There are some more ambiguities so reflecting and responding usefully on
> Olcott's expression is difficult and nondeterministic.
> 

*YACC Syntax of Olcott Minimal Type Theory*
https://philarchive.org/archive/PETMTT-4v2

Here I show Olcott's Minimal Type Theory and
Prolog side-by-side with the Clocksin & Mellish
showing the same infinite expansion.

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

In Olcott's Minimal Type Theory
LP := ~True(LP)
that expands to: ~True(~True(~True(~True(~True(LP)))))

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)

% 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.


-- 
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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