On 11/20/2023 8:54 PM, olcott wrote:
> On 11/20/2023 6:36 PM, olcott wrote:
>> On 11/20/2023 3:39 PM, olcott wrote:
>>> ...14 Every epistemological antinomy can likewise be
>>> used for a similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> An epistemological antinomy is a self-contradictory expression.
>>>
>>> ∀L ∈ Formal_System
>>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>>
>>> The only possible place to insert Gödel's above reference
>>> to an epistemological antinomy in the above definition of
>>> Incompleteness is x.
>>>
>>> So Gödel's quote is saying that a formal system <is> incomplete
>>> when it cannot prove or refute a self-contradictory expression.
>>>
>>> He says this even though the actual reason that self-contradictory
>>> expressions cannot be proven or refuted is that there is something
>>> wrong with them.
>>
>> I am only referring to the above Gödel quote and stipulating that
>> [referring to] anything else that he ever said or did is an dishonest
>> dodge way from the point.
>>
>> I am also only referring to the above definition of incompleteness
>> thus not any naive paraphrase.
>>
>> The first incompleteness theorem states that in any consistent formal
>> system F within which a certain amount of arithmetic can be carried out,
>> there are statements of the language of F which can neither be proved
>> nor disproved in F.
>>
>> https://plato.stanford.edu/entries/goedel-incompleteness/
>
> ∀L ∈ Formal_System
> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>
> When we do plug "epistemological antinomy" into x we prove that
> the notion of mathematical incompleteness is incorrect because
> it determines that L is incomplete on the basis that x is self-
> contradictory.

"Problem, if x is an epistemological antinony, what is ¬x?"
*Was a particularly good point*

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 11/21/23 11:52 AM, olcott wrote:
> On 11/20/2023 8:54 PM, olcott wrote:
>> On 11/20/2023 6:36 PM, olcott wrote:
>>> On 11/20/2023 3:39 PM, olcott wrote:
>>>> ...14 Every epistemological antinomy can likewise be
>>>> used for a similar undecidability proof...(Gödel 1931:43-44)
>>>>
>>>> An epistemological antinomy is a self-contradictory expression.
>>>>
>>>> ∀L ∈ Formal_System
>>>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>>>
>>>> The only possible place to insert Gödel's above reference
>>>> to an epistemological antinomy in the above definition of
>>>> Incompleteness is x.
>>>>
>>>> So Gödel's quote is saying that a formal system <is> incomplete
>>>> when it cannot prove or refute a self-contradictory expression.
>>>>
>>>> He says this even though the actual reason that self-contradictory
>>>> expressions cannot be proven or refuted is that there is something
>>>> wrong with them.
>>>
>>> I am only referring to the above Gödel quote and stipulating that
>>> [referring to] anything else that he ever said or did is an dishonest
>>> dodge way from the point.
>>>
>>> I am also only referring to the above definition of incompleteness
>>> thus not any naive paraphrase.
>>>
>>> The first incompleteness theorem states that in any consistent formal
>>> system F within which a certain amount of arithmetic can be carried out,
>>> there are statements of the language of F which can neither be proved
>>> nor disproved in F.
>>>
>>> https://plato.stanford.edu/entries/goedel-incompleteness/
>>
>> ∀L ∈ Formal_System
>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> When we do plug "epistemological antinomy" into x we prove that
>> the notion of mathematical incompleteness is incorrect because
>> it determines that L is incomplete on the basis that x is self-
>> contradictory.
>
> "Problem, if x is an epistemological antinony, what is ¬x?"
> *Was a particularly good point*
>

One reason why useful logic system exclude logical self-contradiction
from them!

Incompleteness, as a concept, is mostly useful in "binary" systems,
where logic values are True and False (as verified by the operations of
Prove or Refute). Systems that move beyond that either need a revised
definition to include other predicates (like whatever you want to call
verified to not be a truth bearer), or just accept that they are
incomplete becuase they are trying to handle things beyond what
completeness can deal with.

On 11/21/2023 10:52 AM, olcott wrote:
> On 11/20/2023 8:54 PM, olcott wrote:
>> On 11/20/2023 6:36 PM, olcott wrote:
>>> On 11/20/2023 3:39 PM, olcott wrote:
>>>> ...14 Every epistemological antinomy can likewise be
>>>> used for a similar undecidability proof...(Gödel 1931:43-44)
>>>>
>>>> An epistemological antinomy is a self-contradictory expression.
>>>>
>>>> ∀L ∈ Formal_System
>>>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>>>
>>>> The only possible place to insert Gödel's above reference
>>>> to an epistemological antinomy in the above definition of
>>>> Incompleteness is x.
>>>>
>>>> So Gödel's quote is saying that a formal system <is> incomplete
>>>> when it cannot prove or refute a self-contradictory expression.
>>>>
>>>> He says this even though the actual reason that self-contradictory
>>>> expressions cannot be proven or refuted is that there is something
>>>> wrong with them.
>>>
>>> I am only referring to the above Gödel quote and stipulating that
>>> [referring to] anything else that he ever said or did is an dishonest
>>> dodge way from the point.
>>>
>>> I am also only referring to the above definition of incompleteness
>>> thus not any naive paraphrase.
>>>
>>> The first incompleteness theorem states that in any consistent formal
>>> system F within which a certain amount of arithmetic can be carried out,
>>> there are statements of the language of F which can neither be proved
>>> nor disproved in F.
>>>
>>> https://plato.stanford.edu/entries/goedel-incompleteness/
>>
>> ∀L ∈ Formal_System
>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> When we do plug "epistemological antinomy" into x we prove that
>> the notion of mathematical incompleteness is incorrect because
>> it determines that L is incomplete on the basis that x is self-
>> contradictory.
>
> "Problem, if x is an epistemological antinony, what is ¬x?"
> *Was a particularly good point*
>

"One reason why useful logic system exclude logical self-contradiction
from them!"

*That is my whole point, modern logic systems do not do that*

When we take the set of all human knowledge expressed as HOL
actually incompleteness is only unknown truths yet the

incompleteness criteria incorrectly determines that these systems
are also incomplete on the basis that they cannot prove self-
contradictory expressions.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 11/21/23 12:23 PM, olcott wrote:
> On 11/21/2023 10:52 AM, olcott wrote:
>> On 11/20/2023 8:54 PM, olcott wrote:
>>> On 11/20/2023 6:36 PM, olcott wrote:
>>>> On 11/20/2023 3:39 PM, olcott wrote:
>>>>> ...14 Every epistemological antinomy can likewise be
>>>>> used for a similar undecidability proof...(Gödel 1931:43-44)
>>>>>
>>>>> An epistemological antinomy is a self-contradictory expression.
>>>>>
>>>>> ∀L ∈ Formal_System
>>>>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>>>>
>>>>> The only possible place to insert Gödel's above reference
>>>>> to an epistemological antinomy in the above definition of
>>>>> Incompleteness is x.
>>>>>
>>>>> So Gödel's quote is saying that a formal system <is> incomplete
>>>>> when it cannot prove or refute a self-contradictory expression.
>>>>>
>>>>> He says this even though the actual reason that self-contradictory
>>>>> expressions cannot be proven or refuted is that there is something
>>>>> wrong with them.
>>>>
>>>> I am only referring to the above Gödel quote and stipulating that
>>>> [referring to] anything else that he ever said or did is an dishonest
>>>> dodge way from the point.
>>>>
>>>> I am also only referring to the above definition of incompleteness
>>>> thus not any naive paraphrase.
>>>>
>>>> The first incompleteness theorem states that in any consistent formal
>>>> system F within which a certain amount of arithmetic can be carried
>>>> out,
>>>> there are statements of the language of F which can neither be proved
>>>> nor disproved in F.
>>>>
>>>> https://plato.stanford.edu/entries/goedel-incompleteness/
>>>
>>> ∀L ∈ Formal_System
>>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>>
>>> When we do plug "epistemological antinomy" into x we prove that
>>> the notion of mathematical incompleteness is incorrect because
>>> it determines that L is incomplete on the basis that x is self-
>>> contradictory.
>>
>> "Problem, if x is an epistemological antinony, what is ¬x?"
>> *Was a particularly good point*
>>
>
> "One reason why useful logic system exclude logical self-contradiction
> from them!"
>
> *That is my whole point, modern logic systems do not do that*

Why do you say that?

Your epistemological antinomies are NOT elements of the language of any
useful binary logic system.

>
> When we take the set of all human knowledge expressed as HOL
> actually incompleteness is only unknown truths yet the
>
> incompleteness criteria incorrectly determines that these systems
> are also incomplete on the basis that they cannot prove self-
> contradictory expressions.
>

Except that they are not element of the Language, so they don't need to
be proven or refuted.

You don't seem to understand what Language(L) actually means, it isn't a
syntactic only constraint, but a semantic one.

Just like ghawfioyhaweofih might meet the syntactic rules for an English
word, it isn't an element of Language(English).

I think you have a fundamental misunderstanding of how logic works.

Also, it would be a very bad system that tried to establish ALL of
"human knowledge" as the Truth Makers of the system, as such a system is
horribly redundant.

Also, any of the knowledge that is Empirical (based on measurement and
senses) and thus about the model of the universe that we happen to be
in, should be left as Empirical Model Knowldege, not converted to
Axiometric over all models.

You then run into the fact that there are things that we know data
points for that we do not understand the fundamental laws that drive
themm, and thus "logic" isn't the right tool to solve things with.