Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss

Gödel's huge mistake

39 views
Skip to first unread message

olcott

unread,
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

Richard Damon

unread,
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
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.

Nope, you are connecting two things with a straight line when there is a
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.
>

No, You are just too stupid to understand what he is saying.

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

This makes the error yours, not his.

olcott

unread,
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
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.
>

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.

Richard Damon

unread,
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.

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.

Nope, Again, in the definition of incompleteness, where does it say that
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.
>
And what on earth makes you think that is what he is saying to do?

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.

olcott

unread,
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.
True and unprovable is merely an informal paraphrase.

olcott

unread,
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
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/

Richard Damon

unread,
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
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).

Richard Damon

unread,
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.

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.

olcott

unread,
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)
>

"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*

Richard Damon

unread,
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?

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*

No, it is time for you to leave "Stupid" mode, if that is possible.

olcott

unread,
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*

"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.

Richard Damon

unread,
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?

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.

olcott

unread,
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
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/

olcott

unread,
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.

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/


Richard Damon

unread,
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
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 the statement didn't mention incompeteness, the definition
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/
>

So, you are LYING that you are only using that first quote?

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.

Richard Damon

unread,
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.


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

>
> 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
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/
>
>


olcott

unread,
Nov 20, 2023, 9:54:55 PM11/20/23
to
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.

Richard Damon

unread,
Nov 20, 2023, 10:05:21 PM11/20/23
to
And by what justification do you plug a epistemological antinomy into x?

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.

olcott

unread,
Nov 20, 2023, 10:13:22 PM11/20/23
to
And by what justification do you plug a
epistemological antinomy into "x?"

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

*Paraphrasing that*
No epistemological antinomy can be prohibited from being
used for a similar undecidability proof

Richard Damon

unread,
Nov 20, 2023, 10:28:00 PM11/20/23
to
Right, not as the sentence x in the definition, but as a structure 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.

Richard Damon

unread,
Nov 20, 2023, 10:35:10 PM11/20/23
to
Perhaps to be clearer, you "Paraphrase" is incorrect in the assumption
that it means put into the x in the definition in the definition of
Incompleteness.

olcott

unread,
Nov 20, 2023, 10:43:09 PM11/20/23
to
It <is> the case that an epistemological antinomy inserted in
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.

Richard Damon

unread,
Nov 20, 2023, 11:26:17 PM11/20/23
to
Problem, if x is an epistemological antinony, what is ¬x?

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.

Right,

>
> Another way of saying this is whether or not it is logically
> impossible to precisely correctly formalize the Liar Paradox.

Depends on what you mean by "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.
>

All of which does NOTHING about your argument that Godel doesn't show
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.

olcott

unread,
Nov 21, 2023, 12:26:45 AM11/21/23
to
Finally a decent review that does not use dishonest dodge as the
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."

It is incorrect to determine that a formal system is incomplete on the
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.

Richard Damon

unread,
Nov 21, 2023, 9:49:30 AM11/21/23
to
WhY?

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.

Then they shouldn't admit those statement as statements they claim to be
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.
>

So, you are admitting that you are falling for your own Red Herring?

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.

olcott

unread,
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*

Richard Damon

unread,
Nov 21, 2023, 12:07:06 PM11/21/23
to
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.

olcott

unread,
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*

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.

Richard Damon

unread,
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.
>

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.
0 new messages