On 11/20/2023 2:08 PM, olcott wrote:
> On 11/20/2023 1:25 PM, olcott wrote:
>> On 11/20/2023 12:56 PM, olcott wrote:
>>> On 11/19/2023 5:32 PM, olcott wrote:
>>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>>> theory differently.
>>>>>>>>>
>>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>>> unsound.
>>>>>>>>>
>>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>>
>>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>>> of their terms.
>>>>>>>>>
>>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>>> changing
>>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>>> incompleteness
>>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>>> system}
>>>>>>>>> as detailed above.
>>>>>>>>
>>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>>> {formal system} as detailed above.
>>>>>>>>
>>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>>> value that H returns.
>>>>>>>>
>>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>>> is simply screened out as erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> When we imagine that every detail of the body of human
>>>>>>> knowledge has been formalized as higher order logic then
>>>>>>> the only incompleteness are unknowns.
>>>>>>>
>>>>>>> This is the way that human knowledge actually works:
>>>>>>>
>>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>>
>>>>>>
>>>>>> This includes all human knowledge and excludes unknowns.
>>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>>> bother to notice that I was talking about the set of human knowledge.
>>>>>>
>>>>>>> then
>>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>>
>>>>>> Every expression that is neither provable nor refutable is
>>>>>> rejected as
>>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>>> antinomies are excluded and unknowns are excluded and there is
>>>>>> nothing
>>>>>> else left over.
>>>>>>
>>>>>
>>>>> When we stipulate that a truthmaker is what-so-ever makes an
>>>>> expression
>>>>> of language true then we can know by tautology that every truth has a
>>>>> truthmaker.
>>>>>
>>>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>>>> limit screws everything up.
>>>>>
>>>>> To define a proof as a finite set of inference steps creates the
>>>>> artificial notion of unprovable truths.
>>>>>
>>>>
>>>>
>>>> My most important point of all this is that epistemological antinomies
>>>> are finally understood to simply be semantic nonsense that do not
>>>> actually prove incompleteness, undecidability or undefinability.
>>>>
>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>> similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> ...14 Every epistemological antinomy
>>> AKA every self-contradictory expression
>>>
>>> can likewise be used for a similar undecidability proof...
>>>
>>> AKA can likewise be used to provide a sequence of
>>> inference steps proving that self-contradictory
>>> expressions cannot be proven.
>>
>> "By this logic, any proof that mentions epistemological
>> antinomies are invalid"
>>
>> Not at all. I didn't say anything like that.
>>
>> ...14 Every epistemological antinomy can likewise be used
>> for a similar undecidability proof...(Gödel 1931:43-44)
>>
>> *The above sentence proves that the above sentence is incorrect*
>
> "Note, As I have pointed out, Godel isn't saying that he is using an
> epistemological antinomy as a PREMISE to his proof, so your argument
> doesn't apply to it."
>
> *Since incompleteness already has a precise definition*
> ∀L ∈ Formal_System
> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>
> then the epistemological antinomy cannot possibly be correctly
> construed as anything besides x in the above expression.

*I have only been referring to this one quote*
*I have only been referring to this one quote*
*I have only been referring to this one quote*

....14 Every epistemological antinomy can likewise be
used for a similar undecidability proof...(Gödel 1931:43-44)

*I have not been referring to anything else*
*I have not been referring to anything else*
*I have not been referring to anything else*

"So, you are presuming (INCORRECTLY) that the x in this
formula is an epistemological antinomy in Godel's Proof"

*I am presuming nothing* There is no possible other place
to correctly insert the above quoted epistemological antinomy
in the definition of incompleteness besides x.

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

On 11/20/23 4:20 PM, olcott wrote:
> On 11/20/2023 2:08 PM, olcott wrote:
>> On 11/20/2023 1:25 PM, olcott wrote:
>>> On 11/20/2023 12:56 PM, olcott wrote:
>>>> On 11/19/2023 5:32 PM, olcott wrote:
>>>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>>>> theory differently.
>>>>>>>>>>
>>>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>>>> unsound.
>>>>>>>>>>
>>>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>>>
>>>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>>>> of their terms.
>>>>>>>>>>
>>>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>>>> changing
>>>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>>>> incompleteness
>>>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>>>> system}
>>>>>>>>>> as detailed above.
>>>>>>>>>
>>>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>>>> {formal system} as detailed above.
>>>>>>>>>
>>>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>>>> value that H returns.
>>>>>>>>>
>>>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>>>> is simply screened out as erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When we imagine that every detail of the body of human
>>>>>>>> knowledge has been formalized as higher order logic then
>>>>>>>> the only incompleteness are unknowns.
>>>>>>>>
>>>>>>>> This is the way that human knowledge actually works:
>>>>>>>>
>>>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>>>
>>>>>>>
>>>>>>> This includes all human knowledge and excludes unknowns.
>>>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>>>> bother to notice that I was talking about the set of human
>>>>>>> knowledge.
>>>>>>>
>>>>>>>> then
>>>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>>>
>>>>>>> Every expression that is neither provable nor refutable is
>>>>>>> rejected as
>>>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>>>> antinomies are excluded and unknowns are excluded and there is
>>>>>>> nothing
>>>>>>> else left over.
>>>>>>>
>>>>>>
>>>>>> When we stipulate that a truthmaker is what-so-ever makes an
>>>>>> expression
>>>>>> of language true then we can know by tautology that every truth has a
>>>>>> truthmaker.
>>>>>>
>>>>>> When we arbitrarily limit the set of truthmakers then this
>>>>>> arbitrarily
>>>>>> limit screws everything up.
>>>>>>
>>>>>> To define a proof as a finite set of inference steps creates the
>>>>>> artificial notion of unprovable truths.
>>>>>>
>>>>>
>>>>>
>>>>> My most important point of all this is that epistemological antinomies
>>>>> are finally understood to simply be semantic nonsense that do not
>>>>> actually prove incompleteness, undecidability or undefinability.
>>>>>
>>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof...(Gödel 1931:43-44)
>>>>
>>>> ...14 Every epistemological antinomy
>>>> AKA every self-contradictory expression
>>>>
>>>> can likewise be used for a similar undecidability proof...
>>>>
>>>> AKA can likewise be used to provide a sequence of
>>>> inference steps proving that self-contradictory
>>>> expressions cannot be proven.
>>>
>>> "By this logic, any proof that mentions epistemological
>>> antinomies are invalid"
>>>
>>> Not at all. I didn't say anything like that.
>>>
>>> ...14 Every epistemological antinomy can likewise be used
>>> for a similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> *The above sentence proves that the above sentence is incorrect*
>>
>> "Note, As I have pointed out, Godel isn't saying that he is using an
>> epistemological antinomy as a PREMISE to his proof, so your argument
>> doesn't apply to it."
>>
>> *Since incompleteness already has a precise definition*
>> ∀L ∈ Formal_System
>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> then the epistemological antinomy cannot possibly be correctly
>> construed as anything besides x in the above expression.
>
>
> *I have only been referring to this one quote*
> *I have only been referring to this one quote*
> *I have only been referring to this one quote*
>
> ...14 Every epistemological antinomy can likewise be
> used for a similar undecidability proof...(Gödel 1931:43-44)
>
> *I have not been referring to anything else*
> *I have not been referring to anything else*
> *I have not been referring to anything else*
>
> "So, you are presuming (INCORRECTLY) that the x in this
> formula is an epistemological antinomy in Godel's Proof"
>
> *I am presuming nothing* There is no possible other place
> to correctly insert the above quoted epistemological antinomy
> in the definition of incompleteness besides x.
>
>
And why does he need to insert it in there? What is the rest of the
proof for then?

You just don't seem to understand what you are talking about.

This is likely because you are nothing more than a ignorant,
pathologically lying troll.

On 11/20/23 4:15 PM, olcott wrote:
> On 11/20/2023 2:08 PM, olcott wrote:
>> On 11/20/2023 1:25 PM, olcott wrote:
>>> On 11/20/2023 12:56 PM, olcott wrote:
>>>> On 11/19/2023 5:32 PM, olcott wrote:
>>>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>>>> theory differently.
>>>>>>>>>>
>>>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>>>> unsound.
>>>>>>>>>>
>>>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>>>
>>>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>>>> of their terms.
>>>>>>>>>>
>>>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>>>> changing
>>>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>>>> incompleteness
>>>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>>>> system}
>>>>>>>>>> as detailed above.
>>>>>>>>>
>>>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>>>> {formal system} as detailed above.
>>>>>>>>>
>>>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>>>> value that H returns.
>>>>>>>>>
>>>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>>>> is simply screened out as erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When we imagine that every detail of the body of human
>>>>>>>> knowledge has been formalized as higher order logic then
>>>>>>>> the only incompleteness are unknowns.
>>>>>>>>
>>>>>>>> This is the way that human knowledge actually works:
>>>>>>>>
>>>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>>>
>>>>>>>
>>>>>>> This includes all human knowledge and excludes unknowns.
>>>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>>>> bother to notice that I was talking about the set of human
>>>>>>> knowledge.
>>>>>>>
>>>>>>>> then
>>>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>>>
>>>>>>> Every expression that is neither provable nor refutable is
>>>>>>> rejected as
>>>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>>>> antinomies are excluded and unknowns are excluded and there is
>>>>>>> nothing
>>>>>>> else left over.
>>>>>>>
>>>>>>
>>>>>> When we stipulate that a truthmaker is what-so-ever makes an
>>>>>> expression
>>>>>> of language true then we can know by tautology that every truth has a
>>>>>> truthmaker.
>>>>>>
>>>>>> When we arbitrarily limit the set of truthmakers then this
>>>>>> arbitrarily
>>>>>> limit screws everything up.
>>>>>>
>>>>>> To define a proof as a finite set of inference steps creates the
>>>>>> artificial notion of unprovable truths.
>>>>>>
>>>>>
>>>>>
>>>>> My most important point of all this is that epistemological antinomies
>>>>> are finally understood to simply be semantic nonsense that do not
>>>>> actually prove incompleteness, undecidability or undefinability.
>>>>>
>>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof...(Gödel 1931:43-44)
>>>>
>>>> ...14 Every epistemological antinomy
>>>> AKA every self-contradictory expression
>>>>
>>>> can likewise be used for a similar undecidability proof...
>>>>
>>>> AKA can likewise be used to provide a sequence of
>>>> inference steps proving that self-contradictory
>>>> expressions cannot be proven.
>>>
>>> "By this logic, any proof that mentions epistemological
>>> antinomies are invalid"
>>>
>>> Not at all. I didn't say anything like that.
>>>
>>> ...14 Every epistemological antinomy can likewise be used
>>> for a similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> *The above sentence proves that the above sentence is incorrect*
>>
>> "Note, As I have pointed out, Godel isn't saying that he is using an
>> epistemological antinomy as a PREMISE to his proof, so your argument
>> doesn't apply to it."
>>
>> *Since incompleteness already has a precise definition*
>> ∀L ∈ Formal_System
>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> then the epistemological antinomy cannot possibly be correctly
>> construed as anything besides x in the above expression.
>
> "So, you are presuming (INCORRECTLY) that the x in this
> formula is an epistemological antinomy in Godel's Proof"
>
> *I am presuming nothing* There is no possible other place
> to correctly insert the epistemological antinomy in the
> definition of incompleteness besides x.
>
> Also again and again and again I have only been talking
> about this one freaking quote in everyone of my last
> very many messages:
>
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof...(Gödel 1931:43-44)
>
>
>

Which doesn't mean what you think it does.

And your instance that it does, even after it has been explained
otherwise, just shows that you are just an ignorant lying troll.

You seem to think that the only way you can use something is as a
predicate of a logical operation.

Your imagination is defective.

On 11/20/23 4:10 PM, olcott wrote:
> On 11/20/2023 2:08 PM, olcott wrote:
>> On 11/20/2023 1:25 PM, olcott wrote:
>>> On 11/20/2023 12:56 PM, olcott wrote:
>>>> On 11/19/2023 5:32 PM, olcott wrote:
>>>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>>>> theory differently.
>>>>>>>>>>
>>>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>>>> unsound.
>>>>>>>>>>
>>>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>>>
>>>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>>>> of their terms.
>>>>>>>>>>
>>>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>>>> changing
>>>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>>>> incompleteness
>>>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>>>> system}
>>>>>>>>>> as detailed above.
>>>>>>>>>
>>>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>>>> {formal system} as detailed above.
>>>>>>>>>
>>>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>>>> value that H returns.
>>>>>>>>>
>>>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>>>> is simply screened out as erroneous.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When we imagine that every detail of the body of human
>>>>>>>> knowledge has been formalized as higher order logic then
>>>>>>>> the only incompleteness are unknowns.
>>>>>>>>
>>>>>>>> This is the way that human knowledge actually works:
>>>>>>>>
>>>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>>>
>>>>>>>
>>>>>>> This includes all human knowledge and excludes unknowns.
>>>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>>>> bother to notice that I was talking about the set of human
>>>>>>> knowledge.
>>>>>>>
>>>>>>>> then
>>>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>>>
>>>>>>> Every expression that is neither provable nor refutable is
>>>>>>> rejected as
>>>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>>>> antinomies are excluded and unknowns are excluded and there is
>>>>>>> nothing
>>>>>>> else left over.
>>>>>>>
>>>>>>
>>>>>> When we stipulate that a truthmaker is what-so-ever makes an
>>>>>> expression
>>>>>> of language true then we can know by tautology that every truth has a
>>>>>> truthmaker.
>>>>>>
>>>>>> When we arbitrarily limit the set of truthmakers then this
>>>>>> arbitrarily
>>>>>> limit screws everything up.
>>>>>>
>>>>>> To define a proof as a finite set of inference steps creates the
>>>>>> artificial notion of unprovable truths.
>>>>>>
>>>>>
>>>>>
>>>>> My most important point of all this is that epistemological antinomies
>>>>> are finally understood to simply be semantic nonsense that do not
>>>>> actually prove incompleteness, undecidability or undefinability.
>>>>>
>>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof...(Gödel 1931:43-44)
>>>>
>>>> ...14 Every epistemological antinomy
>>>> AKA every self-contradictory expression
>>>>
>>>> can likewise be used for a similar undecidability proof...
>>>>
>>>> AKA can likewise be used to provide a sequence of
>>>> inference steps proving that self-contradictory
>>>> expressions cannot be proven.
>>>
>>> "By this logic, any proof that mentions epistemological
>>> antinomies are invalid"
>>>
>>> Not at all. I didn't say anything like that.
>>>
>>> ...14 Every epistemological antinomy can likewise be used
>>> for a similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> *The above sentence proves that the above sentence is incorrect*
>>
>> "Note, As I have pointed out, Godel isn't saying that he is using an
>> epistemological antinomy as a PREMISE to his proof, so your argument
>> doesn't apply to it."
>>
>> *Since incompleteness already has a precise definition*
>> ∀L ∈ Formal_System
>> (Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
>>
>> then the epistemological antinomy cannot possibly be correctly
>> construed as anything besides x in the above expression.
>
> "So, you are presuming (INCORRECTLY) that the x in this
> formula is an epistemological antinomy in Godel's Proof"
>
> *I am presuming nothing* There is no possible other place
> to correctly insert the epistemological antinomy in the
> definition of incompleteness besides x.
>
>

Who said he inserted the epistemological antinomy in the definition of
incompleteness.

Incompleteness is just defined as there exists a statement in the system
tha is True but not Provable.

An epistemological antinomy can't be such a statement, as it isn't true.

The incompleteness PROOF, (which is diffent than an definition) just
creates a statement, which can be shown to be true in the system, but
not provable. That statement is NOT an epistemological antinomy, as that
couldn't be shown to be true.

Your problem seems to be that your limited imagination can't handle the
logic of the proof.

Yes, the proof has, in effect, the structure of a given epistemological
antinomy included within it, but only a structural basis, the
epistemological antinomy having been changed by making it assert about
provability instead of truthfulness, which yields a statement which has
a valid solution.