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Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism)

Subject Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism)
Newsgroups comp.theory, comp.ai.philosophy, comp.ai.nat-lang, sci.lang.semantics
References (18 earlier) <slrnrfru06.g1a.alan@video.sabir.com> <r72dnTOKtfM7nmPDnZ2dnUU7-L3NnZ2d@giganews.com> <slrnrfsp9e.g1a.alan@video.sabir.com> <B4ydnW0Y7KTf8mPDnZ2dnUU7-IvNnZ2d@giganews.com> <rdmeqm$jgu$1@dont-email.me>
From olcott <NoOne@NoWhere.com>
Date 2020-07-03 00:36 -0500
Message-ID <NLadnUYQmcdzXmPDnZ2dnUU7-TOdnZ2d@giganews.com> (permalink)

Cross-posted to 4 groups.

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On 7/3/2020 12:13 AM, André G. Isaak wrote:
> On 2020-07-02 17:35, olcott wrote:
>> On 7/2/2020 5:52 PM, Chris Buckley wrote:
>>> On 2020-07-02, olcott <NoOne@NoWhere.com> wrote:
>>>> On 7/2/2020 10:06 AM, Chris Buckley wrote:
>>>>> On 2020-07-02, olcott <NoOne@NoWhere.com> wrote:
>>>>>>
>>>>>> Is this true or false:
>>>>>> ∃F ∈ Formal_Systems ∃G ∈ WFF(F) (G ↔ (F ⊬ G))
>>>>>
>>>>> It is completely undetermined.  You have never presented a 
>>>>> definition of
>>>>> 1. Formal System
>>>>> 2. WFF
>>>>> 3. The model in which the entire sentence is expressed.
>>>>>
>>>>> Chris
>>>>>
>>>>
>>>>       Satisfiability
>>>>       A formula is satisfiable if it is possible to find an 
>>>> interpretation
>>>>       (model) that makes the formula true.
>>>>       https://en.wikipedia.org/wiki/Satisfiability
>>>>
>>>>       Interpretation (logic)
>>>>       An interpretation is an assignment of meaning to the symbols of a
>>>>       formal language. https://en.wikipedia.org
>>>>       /wiki/Interpretation_(logic)
>>>>
>>>>       Model theory
>>>>       A model of a theory is a structure (e.g. an interpretation)
>>>>       that satisfies the sentences of that theory.
>>>>       https://en.wikipedia.org/wiki/Model_theory
>>>>
>>>> The conventional meaning of the symbols and their conventional relation
>>>> to each other.
>>>>
>>>> In English this means:
>>>> There exists a WFF G of formal system F such that G is logically
>>>> equivalent to its own unprovability.
>>>
>>> All those are much better definitions than your normal. Very Good!
>>>
>>> But all are meaningless outside of a formal theory and YOU HAVE NO 
>>> FORMAL
>>> THEORY to be talking about.  Your logic symbols are just syntactic sugar
>>> without an underlying theory.  They have no more power than your 
>>> hand-waving
>>> English statements.
>>>
>>> You must define your theory that allows you to talk about "Formal 
>>> System"
>>> within that theory.  And you must define what Formal System means within
>>> that theory.
>>>
>>> In addition, all sorts of other things must be defined, because you 
>>> are using
>>> terms differently than everybody else.  You need to start from scratch.
>>>
>>> Chris
>>>
>>
>> This redefines the formal systems of symbolic logic to conform to the 
>> sound deductive inference model
>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C)  ↔ True(F, C))
>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔ NonSequitur(F, 
>> C))
>>
>> The conventional definition of incompleteness:
>> A theory T is incomplete if and only if there is some sentence φ such 
>> that (T ⊬ φ) and (T ⊬ ¬φ).
>>
>> Becomes: A Sentence φ of theory T is Invalid if and only if
>> (T ⊬ φ) and (T ⊬ ¬φ).
> 
> So according to you (A ∧ ¬A) is valid?
> 
> André
> 

If a formal system cannot prove φ and the same formal system cannot 
prove ¬φ then something is screwy with φ.

(A ∧ ¬A) is simply false.

-- 
Copyright 2020 Pete Olcott

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Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-26 20:03 -0500
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 11:04 -0500
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 11:14 -0500
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 11:58 -0500
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 17:09 -0500
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 20:15 -0500
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-28 16:32 -0500
          Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-28 21:45 -0500
            Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-28 21:27 -0600
              Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-28 21:59 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 00:48 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-28 23:57 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 13:28 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 12:33 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 14:33 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 13:52 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 15:02 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 14:14 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 15:39 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 15:13 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 17:09 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 21:21 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 01:09 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 00:24 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 16:46 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 16:46 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 18:24 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 18:15 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 19:33 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 19:18 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 20:34 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 20:06 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 21:31 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 20:54 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-01 11:03 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-01 10:35 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-01 17:35 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-01 22:47 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 07:01 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 10:51 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 10:46 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 13:59 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 13:37 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 09:52 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-02 15:06 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 10:56 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-02 22:52 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 18:35 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-02 23:48 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 18:57 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 22:03 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 23:13 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 00:36 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 23:43 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 12:50 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 12:19 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 13:21 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 12:33 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 13:48 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 13:55 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 13:06 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 13:07 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 12:56 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 14:14 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 13:38 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 15:59 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 22:54 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-04 08:56 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-04 08:12 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-04 10:06 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-04 09:31 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V20 (Text Analysis) olcott <NoOne@NoWhere.com> - 2020-07-04 14:31 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V20 (Text Analysis) André G. Isaak <agisaak@gm.invalid> - 2020-07-04 15:17 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V20 (Text Analysis) olcott <NoOne@NoWhere.com> - 2020-07-04 17:29 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-05 13:01 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-05 16:40 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-05 23:52 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-06 00:53 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-06 10:15 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 10:48 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 13:55 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-07 22:13 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-07 22:44 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-06 11:49 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 11:27 -0600
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