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Re: A new foundation for correct reasoning

From olcott <polcott333@gmail.com>
Newsgroups sci.logic, comp.theory, sci.math, comp.ai.philosophy
Subject Re: A new foundation for correct reasoning
Date 2025-11-29 11:54 -0600
Organization A noiseless patient Spider
Message-ID <10gfc03$3j8a6$1@dont-email.me> (permalink)
References (5 earlier) <10g908c$16u06$1@dont-email.me> <10g9qtb$1hca0$1@dont-email.me> <10gbo88$28ikt$1@dont-email.me> <10gcgd9$2hrab$1@dont-email.me> <10geh87$38pe7$1@dont-email.me>

Cross-posted to 4 groups.

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On 11/29/2025 4:17 AM, Mikko wrote:
> olcott kirjoitti 28.11.2025 klo 17.51:
>> On 11/28/2025 2:58 AM, Mikko wrote:
>>> olcott kirjoitti 27.11.2025 klo 17.31:
>>>> On 11/27/2025 1:56 AM, Mikko wrote:
>>>>> olcott kirjoitti 26.11.2025 klo 17.39:
>>>>>> On 11/26/2025 5:37 AM, Mikko wrote:
>>>>>>> olcott kirjoitti 25.11.2025 klo 16.21:
>>>>>>>> On 11/25/2025 3:40 AM, Mikko wrote:
>>>>>>>>> olcott kirjoitti 25.11.2025 klo 2.53:
>>>>>>>>>> Eliminating undecidability and mathematical incompleteness
>>>>>>>>>> merely requires discarding model theory and fully integrating
>>>>>>>>>> semantics directly into the syntax of the formal language.
>>>>>>>>>>
>>>>>>>>>> The only inference step allowed is semantic logical
>>>>>>>>>> entailment and this is performed syntactically. A formal
>>>>>>>>>> language such as Montague Grammar or CycL of the Cyc
>>>>>>>>>> project can encode the semantics of anything that can
>>>>>>>>>> be expressed in language.
>>>>>>>>>
>>>>>>>>> The resulting theory is not formal unless both the definition of
>>>>>>>>> semantics and the definition of semantic logical entailment are
>>>>>>>>> fully formal.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> https://plato.stanford.edu/entries/montague-semantics/
>>>>>>>> https://en.wikipedia.org/wiki/CycL
>>>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science)
>>>>>>>>
>>>>>>>> *This was my original inspiration*
>>>>>>>> Kurt Gödel in his 1944 Russell's mathematical logic gave the 
>>>>>>>> following definition of the "theory of simple types" in a footnote:
>>>>>>>>
>>>>>>>> By the theory of simple types I mean the doctrine which says 
>>>>>>>> that the objects of thought (or, in another interpretation, the 
>>>>>>>> symbolic expressions) are divided into types, namely: 
>>>>>>>> individuals, properties of individuals, relations between 
>>>>>>>> individuals, properties of such relations, etc. (with a similar 
>>>>>>>> hierarchy for extensions), and that sentences of the form: " a 
>>>>>>>> has the property φ ", " b bears the relation R to c ", etc. are 
>>>>>>>> meaningless, if a, b, c, R, φ are not of types fitting together.
>>>>>>>
>>>>>>> That is a constraint on the language. Note that individuals of 
>>>>>>> all sorts
>>>>>>> are considered to be of the same type. For properies and relation 
>>>>>>> the
>>>>>>> alternative would be that a predicate is false if any of the 
>>>>>>> arguments
>>>>>>> are of wrong type. For functions it is harder to find a 
>>>>>>> reasonable value
>>>>>>> if an argument is of wrong type.
>>>>>>>
>>>>>>> This is of course irrelevant to the point that the resulting 
>>>>>>> theory is
>>>>>>> not formal unless both the definition of semantics and the 
>>>>>>> definition of
>>>>>>> semantic logical entailment are fully formal.
>>>>>>
>>>>>> The body of knowledge is defined in terms of Rudolf Carnap Meaning 
>>>>>> Postulates and stored in a knowledge ontology inheritance hierarchy.
>>>>>>
>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) where 
>>>>>> the predicate Married(x) is defined in terms of billions of other 
>>>>>> things such as all of the details of Human(x).
>>>>>
>>>>> That, too, is irrelevant to the point that the resulting theory is not
>>>>> formal unless both the definition of semantics and the definition of
>>>>> semantic logical entailment are fully formal.
>>>
>>>> In Olcott's Minimal Type Theory Rudolf Carnap Meaning
>>>> Postulates directly encode semantic meaning in the syntax.
>>>
>>> if the encoding is not fully formally specified the theory is not
>>> formal.
>>>
>>>> The meaningless finite string "Bachelor" is defined as
>>>> a semantic predicate through other already defined terms
>>>> ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))
>>>> Adapted by Olcott from Rudolf Carnap Meaning postulates.
>>>>
>>>> And encoded in the syntax of Olcott's Minimal Type Theory
>>>> https://philarchive.org/archive/PETMTT-4v2
>>>
>>> That page only tells how to define a sentence in terms of other
>>> sentences. As it does not permit any arguments on the left side of :=
>>> the expression ∀x (Bachelor(x) := (Male(x) ∧ Human(x) ∧ ~Married(x)))
>>> is syntactically invalid.
>>
>> ∀x ∈ Human (Bachelor(x) ↔ (Male(x) ∧ Adult(x) ∧ ~Married(x)))
> 
> That is a different sentence. The syntax rules of
>      https://philarchive.org/archive/PETMTT-4v2
> are different for := and =.
> 

It is equivalent. The term Bachelor(x) is still defined by
Male(x) ∧ Adult(x) ∧ ~Married(x) ∧ Human(x) thus never
circular at all as Willard Van Orman Quine insisted.


-- 
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 foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-24 18:53 -0600
  Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-25 11:40 +0200
    Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-25 08:21 -0600
      Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-26 13:37 +0200
        Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 09:39 -0600
          Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-26 12:44 -0500
          Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-27 09:56 +0200
            Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-27 09:31 -0600
              Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:58 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 09:51 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-28 11:04 -0500
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-29 12:17 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 11:54 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:22 +0200
        Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 09:54 -0600
          Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-26 12:49 -0500
          Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:43 +0000
            Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 14:04 -0600
              Re: A new foundation for correct reasoning Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 21:42 +0000
                Re: A new foundation for correct reasoning Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 21:49 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 15:54 -0600
                Re: A new foundation for correct reasoning "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:33 -0800
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-26 15:50 -0600
              Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 11:26 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-02 07:22 -0600
          Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-27 10:00 +0200
            Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-27 09:43 -0600
              Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-28 11:01 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 09:54 -0600
                Re: A new foundation for correct reasoning Alan Mackenzie <acm@muc.de> - 2025-11-28 17:32 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 12:40 -0600
                Re: A new foundation for correct reasoning Alan Mackenzie <acm@muc.de> - 2025-11-28 18:51 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-28 13:21 -0600
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 08:43 -0600
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 19:59 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-11-28 16:49 -0500
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 20:07 -0600
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 20:30 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-29 12:20 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 11:57 -0600
                Re: A new foundation for correct reasoning Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-29 11:27 -0800
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-11-29 13:33 -0600
                Re: A new foundation for correct reasoning Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-30 10:33 -0800
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:58 +0200
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-04 02:32 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-03 20:39 -0600
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-04 08:06 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:38 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 11:43 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:30 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-06 06:50 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-07 13:02 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-08 13:49 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-08 11:13 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-08 13:09 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-10 12:04 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 08:10 -0600
                Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-10 15:01 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 10:14 -0600
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-10 18:10 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 14:01 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-11 10:42 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-11 08:17 -0600
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-11 23:28 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-11 17:49 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-11 19:52 -0500
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-12 10:50 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-12 08:19 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-12 09:24 -0500
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-14 19:03 +0000
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-13 12:19 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-13 08:43 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-13 13:36 -0500
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-14 12:05 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 17:14 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 19:13 -0500
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 18:46 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 19:53 -0500
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 19:08 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 20:46 -0500
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 20:05 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 21:23 -0500
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 20:09 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-14 21:27 -0500
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-14 21:22 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-15 07:33 -0500
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-15 11:04 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-15 08:03 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-16 11:44 +0200
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-16 11:48 +0200
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-05 10:49 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 11:05 -0600
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-06 08:24 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-06 06:08 -0600
                Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-06 13:03 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-06 07:14 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-08 11:18 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-08 13:12 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-10 12:10 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-10 10:29 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-11 10:40 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-11 08:15 -0600
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-12 10:46 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-12 08:16 -0600
                Re: A new foundation for correct reasoning Richard Damon <Richard@Damon-Family.org> - 2025-12-12 09:22 -0500
                Re: A new foundation for correct reasoning Mikko <mikko.levanto@iki.fi> - 2025-12-13 12:42 +0200
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-13 09:37 -0600
                Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-13 15:42 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 11:00 -0600
                Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-05 22:17 +0000
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 16:24 -0600
                Re: A new foundation for correct reasoning Python <python@cccp.invalid> - 2025-12-05 22:45 +0000
                Re: A new foundation for correct reasoning Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-12-05 15:16 -0800
                Re: A new foundation for correct reasoning olcott <polcott333@gmail.com> - 2025-12-05 17:45 -0600
  Re: A new foundation for correct reasoning Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-12 13:16 +0000

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