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Nov 20, 2023, 4:39:46 PM11/20/23

to

...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.

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

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.

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

Nov 20, 2023, 5:40:43 PM11/20/23

to

On 11/20/23 4:39 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.

But that isn't what he did. He inserted a statement that actually was
> ...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.

true but not provable in L.

>

> So Gödel's quote is saying that a formal system <is> incomplete

> when it cannot prove or refute a self-contradictory expression.

lot of stuff in between them.

Thus, you made yourself into a LIAR.

>

> 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.

>

It seems you just skipped over all the parts that you don't understand.

This makes the error yours, not his.

Nov 20, 2023, 5:58:02 PM11/20/23

to

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.

>

When I do this then we can see that the definition of incompleteness
> ...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.

>

determines that a formal system is incomplete when it cannot prove

self-contradictory expressions.

Since self-contradictory expressions are defective then this proves

that the definition of incompleteness is terribly incorrect.

> So Gödel's quote is saying that a formal system <is> incomplete

> when it cannot prove or refute a self-contradictory expression.

>

then we see that Gödel is affirming that defective expressions do prove

that a formal system is incomplete, never noticing that the real issue

is that these expressions are defective.

Nov 20, 2023, 6:10:32 PM11/20/23

to

On 11/20/23 5:57 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.

>>

>

> When I do this then we can see that the definition of incompleteness

> determines that a formal system is incomplete when it cannot prove

> self-contradictory expressions.

Nope. SHhws your stupdity.
> 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.

>>

>

> When I do this then we can see that the definition of incompleteness

> determines that a formal system is incomplete when it cannot prove

> self-contradictory expressions.

A system is incomplete if there is a true statement in the system that

can't be proven in the system.

THAT what the definition says, so why do you try to change it.

I guess that just shows you don't understand the meaning of Truth, or

Defintions.

>

> Since self-contradictory expressions are defective then this proves

> that the definition of incompleteness is terribly incorrect.

x is an epistemological antinomy.

All you are showing is a lack of imagination about what is being talked

about.

>

>> So Gödel's quote is saying that a formal system <is> incomplete

>> when it cannot prove or refute a self-contradictory expression.

>>

>

> When I insert the term {epistemological antinomy} from his above quote

> then we see that Gödel is affirming that defective expressions do prove

> that a formal system is incomplete, never noticing that the real issue

> is that these expressions are defective.

>

That makes you a MORON.

He is saying that his proof could be modified to be based on the

structure of any other epistemological antinomy besides the liar.

The Liar says that L imples that L is not True. The statement morphology

used changes that into G implies that G is not Provable. (morphing

statements about Truth predicates to Proof Predicates).

You can use any other epistemological antinomy, morphed in the same way,

as the starting goal point in the proof. From that Goal statement, you

can build the needed Primative Recursive Relationship to build your

statement.

Nov 20, 2023, 6:16:16 PM11/20/23

to

On 11/20/2023 4:57 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 above is the actual mathematical definition of incomplete.
> 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)))

True and unprovable is merely an informal paraphrase.

Nov 20, 2023, 6:19:33 PM11/20/23

to

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 first incompleteness theorem states that in any consistent formal
> 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)))

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/

Nov 20, 2023, 6:52:07 PM11/20/23

to

On 11/20/23 6:16 PM, olcott wrote:

> On 11/20/2023 4:57 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 above is the actual mathematical definition of incomplete.

> True and unprovable is merely an informal paraphrase.

This seems to be more of your Red Herring, as it doesn't advance your
> On 11/20/2023 4:57 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 above is the actual mathematical definition of incomplete.

> True and unprovable is merely an informal paraphrase.

claims.

And ∃x ∈ Language(L) means that the statement x has a logical value (of

True or False), and the langugage is incomplete if you can't prove x or

its complement.

Since in "normal" logic system, either x or ¬x will be true, and you

can't prove a false statement, this can conventionally be transformed to

the simpler statement given.

x can NOT be an epistemological antinomy in a normal logic system, as

those are not members of the Language(L) (maybe you don't understand

what that means).

Nov 20, 2023, 6:52:09 PM11/20/23

to

On 11/20/23 6:19 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 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/

>

Right.
> 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 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/

>

Which he proves, and you haven't shown a problem with.

You only have attacked Strawmen you claim to be his proof.

You seem to want to claim that his statement that he claims to be true

is an epistemological antinomy, which it clearly isn't if you see what

his statememt actually is.

Thus, you are just wrong.

Nov 20, 2023, 6:58:35 PM11/20/23

to

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)

>

> used for a similar undecidability proof...(Gödel 1931:43-44)

>

"x can NOT be an epistemological antinomy in a normal logic

system, as those are not members of the Language(L)"

In other words you are saying that Gödel was referring
system, as those are not members of the Language(L)"

to a situation that he knew can't possibly ever occur.

*I think that it may be time for you to give up rebuttal mode*

Nov 20, 2023, 7:04:53 PM11/20/23

to

On 11/20/23 6:58 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)

>>

>

> "x can NOT be an epistemological antinomy in a normal logic

> system, as those are not members of the Language(L)"

>

> In other words you are saying that Gödel was referring

> to a situation that he knew can't possibly ever occur.

Why do you say that?
> 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)

>>

>

> "x can NOT be an epistemological antinomy in a normal logic

> system, as those are not members of the Language(L)"

>

> In other words you are saying that Gödel was referring

> to a situation that he knew can't possibly ever occur.

You seem to be stuck in your falsehood.

His G is most certainly an element of the Language(F), as it turns out

that his G is a true statement, there is no Natural Number that

satisifies that particular Primative Recursive Relationship.

I suspect Godel didn't imagine anyone could be so stupid as to think

what you are thinking.

>

> *I think that it may be time for you to give up rebuttal mode*

Nov 20, 2023, 7:16:04 PM11/20/23

to

On 11/20/2023 5:58 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)

>>

>

> "x can NOT be an epistemological antinomy in a normal logic

> system, as those are not members of the Language(L)"

>

> In other words you are saying that Gödel was referring

> to a situation that he knew can't possibly ever occur.

>

> *I think that it may be time for you to give up rebuttal mode*

> 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)

>>

>

> "x can NOT be an epistemological antinomy in a normal logic

> system, as those are not members of the Language(L)"

>

> In other words you are saying that Gödel was referring

> to a situation that he knew can't possibly ever occur.

>

> *I think that it may be time for you to give up rebuttal mode*

"His G is most certainly an element of the Language(F)"

I have only been referring to the single quote above
for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

I have only been referring to the single quote above

for the last fifty posts and you know this.

Nov 20, 2023, 7:20:03 PM11/20/23

to

On 11/20/23 7:16 PM, olcott wrote:

> On 11/20/2023 5:58 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)

>>>

>>

>> "x can NOT be an epistemological antinomy in a normal logic

>> system, as those are not members of the Language(L)"

>>

>> In other words you are saying that Gödel was referring

>> to a situation that he knew can't possibly ever occur.

>>

>> *I think that it may be time for you to give up rebuttal mode*

>

> "His G is most certainly an element of the Language(F)"

>

> I have only been referring to the single quote above

> for the last fifty posts and you know this.

And what make you think that this applies to the point you claim it does?
> On 11/20/2023 5:58 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)

>>>

>>

>> "x can NOT be an epistemological antinomy in a normal logic

>> system, as those are not members of the Language(L)"

>>

>> In other words you are saying that Gödel was referring

>> to a situation that he knew can't possibly ever occur.

>>

>> *I think that it may be time for you to give up rebuttal mode*

>

> "His G is most certainly an element of the Language(F)"

>

> I have only been referring to the single quote above

> for the last fifty posts and you know this.

As I have repled each time.

YOU know this, and have ignored it because you are too stupid to understand.

When you refer to the incompleteness proof, and the statement that is

unprovable, that IS "G", which I have described.

It is not the "epistemological antinomy" that the above quote refers to.

They are two different things, so trying to make them the same is just

an ERROR, showing you are stupid.

Your throwing a tantrum, just shows your immaturity.

Nov 20, 2023, 7:32:48 PM11/20/23

to

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
> 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.

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/

Nov 20, 2023, 7:36:37 PM11/20/23

to

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.

> 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/

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/

Nov 20, 2023, 9:34:31 PM11/20/23

to

On 11/20/23 7:32 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

> anything else that he ever said or did is an dishonest dodge

> way from the point.

So, since that statement doesn't mention incompleteness, your arguement
> 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

> anything else that he ever said or did is an dishonest dodge

> way from the point.

is just incoherent.

And, if you widen the context that it is in his incompleteness proof, he

doesn't say that the epistemological antinomy has anything to do

directly with the sentence that shows the Formal System to be incomplete.

Only by you applying your strawman INCORRECT presumptions can you

attempt to link them.

Thus, you are shown to just be a ignorant pathological lying troll

>

> I am also only referring to the above definition of incompleteness

> thus not any naive paraphrase.

doesn't apply.

>

> 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/

>

Note, by bringing in the theorem, and are talking about the proof, you

have brought into the discussion the WHOLE proof.

And yes, he claims that there is a statement in F which can neither be

proven nor disproven in F, and comes up with that statement, which is

commonly called G, and can be expressed appoximately in the words:

G: There does not exist a Natural Number g that satisfies a particular

Primitive Recursive Relationship (which is developed in detail in the proof)

Note, this G, is NOT an epistemologal antinomy, as it is simple to show

that such a statment MUST be either True or False.

Thus, it is shown that you claim that he is some how referencing the

"sentence" that shows the system to be incomplete when he talks about

the epistemological antinomy used in the proof is incorrect, and you

attempts to try to limit it to that is just a deception.

Thus, your whole arguement is shown to be incorrect due to a total lack

of understanding by yourself of what is being done.

Nov 20, 2023, 9:34:32 PM11/20/23

to

On 11/20/23 7:36 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.

> 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.

So, since that statement doesn't mention incompleteness, your arguement

is just incoherent.

And, if you widen the context that it is in his incompleteness proof, he

doesn't say that the epistemological antinomy has anything to do

directly with the sentence that shows the Formal System to be incomplete.

Only by you applying your strawman INCORRECT presumptions can you

attempt to link them.

Thus, you are shown to just be a ignorant pathological lying troll

>

is just incoherent.

And, if you widen the context that it is in his incompleteness proof, he

doesn't say that the epistemological antinomy has anything to do

directly with the sentence that shows the Formal System to be incomplete.

Only by you applying your strawman INCORRECT presumptions can you

attempt to link them.

Thus, you are shown to just be a ignorant pathological lying troll

>

> I am also only referring to the above definition of incompleteness

> thus not any naive paraphrase.

And since that statement didn't mention incompleteness, the definition
> thus not any naive paraphrase.

doesn't apply.

>

> 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/

>

>

> 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/

>

>

Nov 20, 2023, 9:54:55 PM11/20/23

to

the notion of mathematical incompleteness is incorrect because

it determines that L is incomplete on the basis that x is self-

contradictory.

Nov 20, 2023, 10:05:21 PM11/20/23

to

I guess you don't understand that an episttemological antinomy is never

a member of Language(L), so that isn't a valid insertion, and Godel

never says to do it either.

Thus, your argument just proves itself to be a LIE.

So, by using an input outside the domain of the function you get

non-sense out you are claiming that you show the function is illogical.

WRONG.

That is like saying that the function arc-cosine is incorrect in the

domain of real numbers because arc-cosine(2) doesn't have an answer.

You are just proving your utter stupidity.

Nov 20, 2023, 10:13:22 PM11/20/23

to

And by what justification do you plug a

epistemological antinomy into "x?"

epistemological antinomy into "x?"

...14 Every epistemological antinomy can likewise be

used for a similar undecidability proof...(Gödel 1931:43-44)

*Paraphrasing that*
used for a similar undecidability proof...(Gödel 1931:43-44)

No epistemological antinomy can be prohibited from being

used for a similar undecidability proof

Nov 20, 2023, 10:28:00 PM11/20/23

to

build the Primitive Recursive Relationship in his proof.

Since you aren't understanding what he is saying, of course you get

nonsense.

If we could just plug any old epistemological antinomy into the

definition to show it, what is the rest of the proof there for?

You are just proving your utter ignorance of what you speak about.

You are just piling more coals on the trash heap that your reputation

(and later yourself) is getting burned up on.

Sorry, you are just proving yourself to be just too stupid for your

ideas to be given any real consideration.

Your arguements just become a "Target Rich" environment, the biggest

problem is deciding which parts to shoot down first.

Nov 20, 2023, 10:35:10 PM11/20/23

to

that it means put into the x in the definition in the definition of

Incompleteness.

Nov 20, 2023, 10:43:09 PM11/20/23

to

x does cause the incompleteness criteria to determine that

formal system L <is> incomplete even though the actual issue

is that x is self-contradictory.

The only last step of this is whether or not it is possible

or logically impossible to define a formal system that can

express actual epistemological antinomies in its language.

Another way of saying this is whether or not it is logically

impossible to precisely correctly formalize the Liar Paradox.

If we can precisely formalize the Liar Paradox then we know

that it is not logically impossible to formalize epistemological

antinomies.

Nov 20, 2023, 11:26:17 PM11/20/23

to

And yes, a logical system that admits self-contradictory statements as

elements of its language is incomplete, but that doesn't invaldate the

concept of Incompleteness, just shows that it may not mean a lot in edge

cases that have other problems.

>

> The only last step of this is whether or not it is possible

> or logically impossible to define a formal system that can

> express actual epistemological antinomies in its language.

>

> Another way of saying this is whether or not it is logically

> impossible to precisely correctly formalize the Liar Paradox.

What is wrong with L: L <-> ~L

That has the formal syntax, it just has problems assign "Truth Value" to

it in a binary system. Many non-binary systems can handle it just fine

>

> If we can precisely formalize the Liar Paradox then we know

> that it is not logically impossible to formalize epistemological

> antinomies.

>

tha that incompleteness for "normal" logic systems is a real thing.

He shows that for sufficiently powerful system (can handle Natural

Numbers for instance) there exist statements which are actually "True"

in the system, that can not be "Proven" in it.

And you are just back to your old habits of serving Herring with Red sauce.

You are STILL WRONG about "Incompleteness" not being a thing, or that

Godel didn't prove that most useful systems are incomplete.

Nov 21, 2023, 12:26:45 AM11/21/23

to

rebuttal tactic.

"And yes, a logical system that admits self-contradictory statements

as elements of its language is incomplete, but that doesn't invaldate

the concept of Incompleteness, just shows that it may not mean a lot

in edge cases that have other problems."

basis of its inability to prove or refute self-contradictory statements.

Formal systems cannot be required to prove or refute self-contradictory

expressions.

We will have to get back to your other points after we finish this one.

Nov 21, 2023, 9:49:30 AM11/21/23

to

What "Rule" does it break?

You may find it morally objectional (but since you appear to think Child

Porn to be acceptable, seems strange to draw a line there), but morals

are part of logic, but ethics.

Remember, we are talking about a system that accepted these

self-contradictory statements, so expecting it to actually be able to

fully handle them doesn't seem out of bounds.

Also, what is actually wrong with a system being "Incomplete". All that

does is admit that the system is limited in a certain ways. It is good

to know our limitations. Maybe that is part of your problem, you can't

let yourself look at your own limitation, so you think you know stuff

you don't, which makes you totally stupid, as the greatest wisdom is

knowing what you don't know.

>

> Formal systems cannot be required to prove or refute self-contradictory

> expressions.

able to handle.

Remember, the meaning of "x ∈ Language(L)" is that Language L admits the

statement x as something that it can handle.

If you claim to be able to be able to handle all languages, but actually

can only work with those in the Latin alphabet, you are incomplete in

your claim.

>

> We will have to get back to your other points after we finish this one.

>

Just shows your stupidity. The fact that you think you can show your

point for a marginal case that isn't actually the focus of the Theory,

doesn't mean a thing for the Theory.

Remember, one of the conditions for Godel's Incompleteness Theory is the

system must be CONSITANT. I suspect that a system that allows

self-inconsistent statements as part of its language will likely fail to

be consistent itself.

Nov 21, 2023, 11:52:22 AM11/21/23

to

"Problem, if x is an epistemological antinony, what is ¬x?"

*Was a particularly good point*
Nov 21, 2023, 12:07:06 PM11/21/23

to

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.

Nov 21, 2023, 12:24:01 PM11/21/23

to

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

from them!"

*That is my whole point, modern logic systems do not do that*
from them!"

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.

Nov 21, 2023, 12:57:34 PM11/21/23

to

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.

>

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.

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