Re: A proof of G in F

olcott

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Mar 24, 2023, 8:20:38 PM3/24/23

to

We are therefore confronted with a proposition which asserts
its own unprovability. (Gödel 1931:39-41)

In other words G asserts its own unprovability.

If we leave this as it is then it is simply false because G is provable
in meta-F.

When we limit the scope of G unprovability claim to F then:
G asserts its own unprovability in F.

There exists a proof of G in F that G cannot be proved in F is simply
false. A proof of G in F that proves that G cannot be proved in F is
simply self-contradictory.

--
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

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Mar 24, 2023, 8:47:04 PM3/24/23

to

On 3/24/23 8:20 PM, olcott wrote:
> We are therefore confronted with a proposition which asserts
> its own unprovability. (Gödel 1931:39-41)
>
> In other words G asserts its own unprovability.

Except that comment wasn't about G itself, but something DERIVED from G,
and in fact, the statement that asserts its own unprovabilty was about
an unprovabilty IN F (not meta-F) as the statement being analysed only
dealt with logic in F.

>
> If we leave this as it is then it is simply false because G is provable
> in meta-F.

But it never said anytbing about Meta-F

Obviously you don't understand that a proof is only allowed to use
statements in it "Theory"

>
> When we limit the scope of G unprovability claim to F then:
> G asserts its own unprovability in F.

Yes, From the statement G, we can show IN META-F, that from G we can
show that G being True proves that G can not be proven in F.

>
> There exists a proof of G in F that G cannot be proved in F is simply
> false. A proof of G in F that proves that G cannot be proved in F is
> simply self-contradictory.
>

Nope, because the proof that G can not be proven in F was done in Meta-F
not F.

In F, the only way to actually determine that G is true is to process
EVERY possible number g and see that it fails to satisfy that
Relationship, but since there is an infinite number of them, that can't
be done in a proof, as a proof must have a finite number of steps.

I think you don't understand that almost all the paper is writen in the
context of being in Meta-F, but using the property established that any
statment that doesn't use a concept out of Meta-F has exactly the same
Truth Value in F as in Meta-F since Meta-F has an exact copy of all the
"Truth-Makers" of F, and only adds additional concepts.

Thus, when he derives the specific Primative Recursvie Relationship that
maps to the statement that G is Provable in Meta-F, and that
relationship doesn't itself use any concepts from Meta-F, just the
properties of the numbers that exist in F, it can be transported into F
unchanged with no change in Truthfulness.

Thus, we have, **IN F** the statement G that no number g exists that
satisfies this particular Primative Recursive Relationship", which has
implications **SHOWN IN META-F** that if such a number existed, then
there would exist **IN F** a proof that G was true, and thus no such
number could exist.

Thus the contradictory meaning is only visable in META-F, not F, but the
truthfullness of the statement applies to both.

You don't seem to understand that one logic system, if properly endowed,
can talk about another logic system.

olcott

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Mar 24, 2023, 9:05:15 PM3/24/23

to

On 3/24/2023 7:20 PM, olcott wrote:
> We are therefore confronted with a proposition which asserts
> its own unprovability. (Gödel 1931:39-41)
>
> In other words G asserts its own unprovability.
>
> If we leave this as it is then it is simply false because G is provable
> in meta-F.
>
> When we limit the scope of G unprovability claim to F then:
> G asserts its own unprovability in F.
>
> There exists a proof of G in F that G cannot be proved in F is simply
> false. A proof of G in F that proves that G cannot be proved in F is
> simply self-contradictory.

There cannot be a proof in F that G is unprovable in F because this
proof would be self-contradictory, thus the existence of G in F that
proves that G is unprovable in F is simply false and nothing more.

∃G ∈ F (G ⇔ ¬(F ⊢ G)) is simply false any nothing more.

Richard Damon

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Mar 24, 2023, 9:13:34 PM3/24/23

to

On 3/24/23 9:05 PM, olcott wrote:
> On 3/24/2023 7:20 PM, olcott wrote:
>> We are therefore confronted with a proposition which asserts
>> its own unprovability. (Gödel 1931:39-41)
>>
>> In other words G asserts its own unprovability.
>>
>> If we leave this as it is then it is simply false because G is
>> provable in meta-F.
>>
>> When we limit the scope of G unprovability claim to F then:
>> G asserts its own unprovability in F.
>>
>> There exists a proof of G in F that G cannot be proved in F is simply
>> false. A proof of G in F that proves that G cannot be proved in F is
>> simply self-contradictory.
>
> There cannot be a proof in F that G is unprovable in F because this
> proof would be self-contradictory, thus the existence of G in F that
> proves that G is unprovable in F is simply false and nothing more.

And there isn't a proof in F that G is unprovable in F.

There is a proof in Meta-F that G is unprovable in F, and that G must be
True in F.

>
> ∃G ∈ F (G ⇔ ¬(F ⊢ G)) is simply false any nothing more.
>

But that isn't the statement.

Your logic doesn't seem to be able to represent statments that refer to
the truth/provability of a statement in another Theory.

And you are continuing to prove that you have the maturity of a
Three-Year old, which seems to match your intelect.

Richard Damon

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Mar 24, 2023, 9:20:42 PM3/24/23

to

On 3/24/23 9:05 PM, olcott wrote:

> On 3/24/2023 7:20 PM, olcott wrote:
>> We are therefore confronted with a proposition which asserts
>> its own unprovability. (Gödel 1931:39-41)
>>
>> In other words G asserts its own unprovability.
>>
>> If we leave this as it is then it is simply false because G is
>> provable in meta-F.
>>
>> When we limit the scope of G unprovability claim to F then:
>> G asserts its own unprovability in F.
>>
>> There exists a proof of G in F that G cannot be proved in F is simply
>> false. A proof of G in F that proves that G cannot be proved in F is
>> simply self-contradictory.
>
> There cannot be a proof in F that G is unprovable in F because this
> proof would be self-contradictory, thus the existence of G in F that
> proves that G is unprovable in F is simply false and nothing more.
>
> ∃G ∈ F (G ⇔ ¬(F ⊢ G)) is simply false any nothing more.
>
>
>

Perhaps you misunderstand the proof (seems obvious).

G itself, doesn't prove that G is unprovable, it is only because we know
of Meta-F and its relationship to G that allows us to prove IN META-F,
that G must be true in F (and Meta-F) and that it can not be proven in F.

The fact that we CAN construct G using the information in Meta-F which
knows all the "Truth-Makers" of F, shows that there exist statments in F
that are true and not provable.

Since the only requirements on F were that F was consistent, and that it
had sufficient power to represent the needed properties of natural
numbers, it is shows that given ANY such field, (consistent, supports
the properties of the Natural Numbers, and has a finite number of
truth-makers) MUST have statements in it that are True but not provable.

This shows an inherent power of the Natural Numbers.

olcott

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Mar 24, 2023, 9:32:23 PM3/24/23

to

On 3/24/2023 8:05 PM, olcott wrote:
> On 3/24/2023 7:20 PM, olcott wrote:
>> We are therefore confronted with a proposition which asserts
>> its own unprovability. (Gödel 1931:39-41)
>>
>> In other words G asserts its own unprovability.
>>
>> If we leave this as it is then it is simply false because G is
>> provable in meta-F.
>>
>> When we limit the scope of G unprovability claim to F then:
>> G asserts its own unprovability in F.
>>
>> There exists a proof of G in F that G cannot be proved in F is simply
>> false. A proof of G in F that proves that G cannot be proved in F is
>> simply self-contradictory.
>
> There cannot be a proof in F that G is unprovable in F because this
> proof would be self-contradictory, thus the existence of G in F that
> proves that G is unprovable in F is simply false and nothing more.
>
> ∃G ∈ F (G ⇔ ¬(F ⊢ G)) is simply false any nothing more.

G asserts its own unprovability in F. That G cannot be proven in F is
because G is self-contradictory in F not that F is incomplete.

Gödel admitted that he already knew why G was unprovable in F:

14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)

Any epistemological antinomy (self-contradictory expression) is never
provable because it is self-contradictory.

Richard Damon

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Mar 24, 2023, 9:50:31 PM3/24/23

to

On 3/24/23 9:32 PM, olcott wrote:
> On 3/24/2023 8:05 PM, olcott wrote:
>> On 3/24/2023 7:20 PM, olcott wrote:
>>> We are therefore confronted with a proposition which asserts
>>> its own unprovability. (Gödel 1931:39-41)
>>>
>>> In other words G asserts its own unprovability.
>>>
>>> If we leave this as it is then it is simply false because G is
>>> provable in meta-F.
>>>
>>> When we limit the scope of G unprovability claim to F then:
>>> G asserts its own unprovability in F.
>>>
>>> There exists a proof of G in F that G cannot be proved in F is simply
>>> false. A proof of G in F that proves that G cannot be proved in F is
>>> simply self-contradictory.
>>
>> There cannot be a proof in F that G is unprovable in F because this
>> proof would be self-contradictory, thus the existence of G in F that
>> proves that G is unprovable in F is simply false and nothing more.
>>
>> ∃G ∈ F (G ⇔ ¬(F ⊢ G)) is simply false any nothing more.
>
> G asserts its own unprovability in F. That G cannot be proven in F is
> because G is self-contradictory in F not that F is incomplete.

No, in Meta-F we can derive a statement from G that shows that G being
True says that G is not provable in F.

You aren't even following your own definitions.

>
> Gödel admitted that he already knew why G was unprovable in F:
>
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof. (Gödel 1931:39-41)
>
> Any epistemological antinomy (self-contradictory expression) is never
> provable because it is self-contradictory.
>

Note, he said "Can likewize be used for a similar" not that the proof
actually uses a antinomy as its direct self.

There is a step where the antinomy is transformed from a
self-contraditory statement that talks of its own truth, to a
non-self-contradictory statement that talks of its own provability.

You are just proving you are too stupid to understand this.

You are destroying any hope that someone will consider looking at your
ideas about "Correct Reasoning" as you are proving you don't understand
how to do anything like that.

And acting like a two-year old doesn't help (age goes down for repeating
it after being called out on it several times).

olcott

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Mar 25, 2023, 11:15:54 PM3/25/23

to

On 3/24/2023 7:20 PM, olcott wrote:

> We are therefore confronted with a proposition which asserts
> its own unprovability. (Gödel 1931:39-41)
>

a proposition which asserts its own unprovability. (Gödel 1931:39-41)

Is about a proposition that asserts ITS OWN unprovability.
Is about a proposition that asserts ITS OWN unprovability.
Is about a proposition that asserts ITS OWN unprovability.

Every rebuttal of this has been simply a dishonest dodge of the strawman
deception. We can't get to the second point because my reviewers lie
about the first point.

Jim Burns

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Mar 26, 2023, 12:03:36 AM3/26/23

to

On 3/25/2023 11:15 PM, olcott wrote:
> On 3/24/2023 7:20 PM, olcott wrote:

>> We are therefore confronted with
>> a proposition which asserts its own
>> unprovability. (Gödel 1931:39-41)

> Every rebuttal of this has been simply
> a dishonest dodge of the strawman deception.
> We can't get to the second point because
> my reviewers lie about the first point.

Define
G(x) :=
∃y:( Sbst(x,x,y) ∧ Unpr(y) )

Sbst(⌜G(x)⌝,⌜G(x)⌝,⌜G(⌜G(x)⌝)⌝)
asserts that
⌜G(⌜G(x)⌝)⌝ refers to G(⌜G(x)⌝)
which is G(x) with each free occurence
of x replaced with ⌜G(x)⌝
and ⌜G(x)⌝ refers to G(x)

Unpr(⌜G(⌜G(x)⌝)⌝)
asserts that
G(⌜G(x)⌝) is unprovable in F

G(⌜G(x)⌝) ⇔ Unpr(⌜G(⌜G(x)⌝)⌝)
is a theorem of F

That theorem asserts that
asserting G(⌜G(x)⌝)
is equivalent to
asserting that G(⌜G(x)⌝) is
unprovable in F

| We are therefore confronted with

| a proposition ...

G(⌜G(x)⌝)

| ... which asserts its own
| unprovability. (Gödel 1931:39-41)

olcott

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Mar 26, 2023, 12:24:55 AM3/26/23

to

That is not a proposition that asserts its own unprovability.
It is a kludge to simulate a provability predicate in a language that is
far far far too inexpressive to artificially contrive anything like an
actual provability predicate.

The barest possible essence of a proposition asserting its own
unprovability is G asserts its own unprovability.

G := ~Provable(G)

If we don't examine the barest possible essence we lose enormous
cognitive leverage and can never directly see what is really going on.

Not looking at the barest possible essence is succumbing to the
magicians misdirection away from the essence of the proof.

>
> | ... which asserts its own
> | unprovability. (Gödel 1931:39-41)
>
>

Jim Burns

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Mar 26, 2023, 1:22:52 AM3/26/23

to

It is a proposition provably equivalent
to the assertion that it is unprovable.

> It is a kludge to simulate
> a provability predicate in a language
> that is far far far too inexpressive to
> artificially contrive anything like
> an actual provability predicate.

In the 1931 paper,
what keeps Bew(x) from being
an actual provability predicate?

> The barest possible essence of
> a proposition asserting its own unprovability
> is G asserts its own unprovability.
>
> G := ~Provable(G)

But 'Provable' says nothing about
what it means.

That's what makes Provable()
an "actual provability predicate"
and the 1931 Bew(x) not
an "actual provability predicate"
Bew() has a series of definitions
telling us what it means.

I get it.
In order to be an actual provabilty
predicate, something must be
poorly-enough defined that you can
bullshit your way through a discussion.

> If we don't examine the barest possible
> essence we lose enormous cognitive leverage
> and can never directly see what is really
> going on.

Got it.
So, your key focus is to synergize the
core competencies of the elephant in the room.

> Not looking at the barest possible essence
> is succumbing to the magicians misdirection
> away from the essence of the proof.

Purely by coincidence,
not succumbing to the magician's misdirection
is the thing that takes the least effort,
by far, compared to something like trying
to understand Gödel's proofs.

olcott

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Mar 26, 2023, 1:52:04 AM3/26/23

to

There are far too many intermediate steps, we need to cut these
intermediate steps down to zero.

We are not merely grinding through the conventional proof.
We are evaluating the philosophical foundations of the notion of
mathematical incompleteness to verify that this notion is coherent.

>> It is a kludge to simulate
>> a provability predicate in a language
>> that is far far far too inexpressive to
>> artificially contrive anything like
>> an actual provability predicate.
>
> In the 1931 paper,
> what keeps Bew(x) from being
> an actual provability predicate?
>
>> The barest possible essence of
>> a proposition asserting its own unprovability
>> is G asserts its own unprovability.
>>
>> G := ~Provable(G)
>
> But 'Provable' says nothing about
> what it means.
>

G = ¬(F ⊢ G) // the ordinary meaning

> That's what makes Provable()
> an "actual provability predicate"
> and the 1931 Bew(x) not
> an "actual provability predicate"
> Bew() has a series of definitions
> telling us what it means.
>
> I get it.
> In order to be an actual provabilty
> predicate, something must be
> poorly-enough defined that you can
> bullshit your way through a discussion.

Standard Mendelson signified by this: ⊢

>
>> If we don't examine the barest possible
>> essence we lose enormous cognitive leverage
>> and can never directly see what is really
>> going on.
>
> Got it.
> So, your key focus is to synergize the
> core competencies of the elephant in the room.
>
>> Not looking at the barest possible essence
>> is succumbing to the magicians misdirection
>> away from the essence of the proof.
>
> Purely by coincidence,
> not succumbing to the magician's misdirection
> is the thing that takes the least effort,
> by far, compared to something like trying
> to understand Gödel's proofs.
>

We are not merely grinding through the conventional proof.
We are evaluating the philosophical foundations of the notion of
mathematical incompleteness to verify that this notion is coherent.

>>> | ... which asserts its own
>>> | unprovability. (Gödel 1931:39-41)
>>>
>>>
>>
>

Richard Damon

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Mar 26, 2023, 7:20:34 AM3/26/23

to

On 3/25/23 11:15 PM, olcott wrote:
> On 3/24/2023 7:20 PM, olcott wrote:
>> We are therefore confronted with a proposition which asserts
>> its own unprovability. (Gödel 1931:39-41)
>>
>
> a proposition which asserts its own unprovability. (Gödel 1931:39-41)
>
> Is about a proposition that asserts ITS OWN unprovability.
> Is about a proposition that asserts ITS OWN unprovability.
> Is about a proposition that asserts ITS OWN unprovability.
>
> Every rebuttal of this has been simply a dishonest dodge of the strawman
> deception. We can't get to the second point because my reviewers lie
> about the first point.
>

Right, but that proposition isn't "G" itself, but a statement that is a
derived from G in Meta-F and is a synonym to it, having an identical
truth value, because it can interpret the "meaning" of the relationship.

Also note, this is in a "Comment" in the proof, and doesn't use quite as
rigerous of langauge as the actual "Formal" part of the proof, so you
error in understanding the context of the statement.

You always seem to have trouble with context.

Note, almost all the work is being done in Meta-F, but being done with
an eye of showing something in F, based on the properties of how Meta-F
was defined, that make statements in F to be synonyms for the same
statement in Meta-F

In particular, the statement your quote referes to was developed in
Meta-F and proved in Meta-F to be a synonym for the actual G, but the
"unprovability" property is for it as a statement in F.

Your "self-referenctial equal untrue" arguement breaks down, because the
actual statement G, that this is a synonym, has no self-reference in it,
and is a pure mathematical statement, which MUST be a Truth-Bearer,
either a number will or will not exist that satisfies the specified
Primative Recursive Relationship. That is a basic established fact of
natural numbers.

That you intellect can't parse this fact, doesn't make it not true, just
beyond your understanding, as shown by your inability to make an actual
factual assertion about the proof, just quote statements from it out of
contex.

That technique is a well known technique for liars.

Richard Damon

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Mar 26, 2023, 7:21:23 AM3/26/23

to

Why?

>
> We are not merely grinding through the conventional proof.
> We are evaluating the philosophical foundations of the notion of
> mathematical incompleteness to verify that this notion is coherent.

But that isn't what Godel was doing, so you can't apply your criteria to
his proof.

>
>>> It is a kludge to simulate
>>> a provability predicate in a language
>>> that is far far far too inexpressive to
>>> artificially contrive anything like
>>> an actual provability predicate.
>>
>> In the 1931 paper,
>> what keeps Bew(x) from being
>> an actual provability predicate?
>>
>>> The barest possible essence of
>>> a proposition asserting its own unprovability
>>> is G asserts its own unprovability.
>>>
>>> G := ~Provable(G)
>>
>> But 'Provable' says nothing about
>> what it means.
>>
>
> G = ¬(F ⊢ G) // the ordinary meaning

But that "meaning" can only be seen in Meta-F

>
>> That's what makes Provable()
>> an "actual provability predicate"
>> and the 1931 Bew(x) not
>> an "actual provability predicate"
>> Bew() has a series of definitions
>> telling us what it means.
>>
>> I get it.
>> In order to be an actual provabilty
>> predicate, something must be
>> poorly-enough defined that you can
>> bullshit your way through a discussion.
>
> Standard Mendelson signified by this: ⊢

No, "⊢" signifies (if I am remembering correctly) that the logic model
on the left can prove the statement on the right, meaning that a finite
set of axioms, definitions, and sound logical rules exist in F that can
be strung together to from said proof.

(Something you seem incapable of doing)

>
>>
>>> If we don't examine the barest possible
>>> essence we lose enormous cognitive leverage
>>> and can never directly see what is really
>>> going on.
>>
>> Got it.
>> So, your key focus is to synergize the
>> core competencies of the elephant in the room.
>>
>>> Not looking at the barest possible essence
>>> is succumbing to the magicians misdirection
>>> away from the essence of the proof.
>>
>> Purely by coincidence,
>> not succumbing to the magician's misdirection
>> is the thing that takes the least effort,
>> by far, compared to something like trying
>> to understand Gödel's proofs.
>>
>
> We are not merely grinding through the conventional proof.
> We are evaluating the philosophical foundations of the notion of
> mathematical incompleteness to verify that this notion is coherent.

That may be YOUR goal, but you aren't doing it, because you don't seem
to understand the stuff you are reading, or know how to do actual proper
logic.

olcott

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Mar 26, 2023, 10:14:59 AM3/26/23

to

On 3/24/2023 7:20 PM, olcott wrote:

We are therefore confronted with a proposition which asserts
its own unprovability. (Gödel 1931:39-41)

Is about a proposition that asserts ITS OWN unprovability.
Is about a proposition that asserts ITS OWN unprovability.
Is about a proposition that asserts ITS OWN unprovability.

When a proposition asserts ITS OWN unprovability then this very same
proposition is self-contradictory making it unprovable because it
is self-contradictory thus not unprovable because its formal system is
incomplete.

Richard Damon

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Mar 26, 2023, 12:27:00 PM3/26/23

to

On 3/26/23 10:14 AM, olcott wrote:
> On 3/24/2023 7:20 PM, olcott wrote:
>
> We are therefore confronted with a proposition which asserts
> its own unprovability. (Gödel 1931:39-41)
>
> Is about a proposition that asserts ITS OWN unprovability.
> Is about a proposition that asserts ITS OWN unprovability.
> Is about a proposition that asserts ITS OWN unprovability.
>
> When a proposition asserts ITS OWN unprovability then this very same
> proposition is self-contradictory making it unprovable because it
> is self-contradictory thus not unprovable because its formal system is
> incomplete.
>

So, you keep repeating that, but you don't understand the statement that
does this, and what domain it does it in.

Just proves your ignorance, and your inability to learn.

Note, the proposition that is making this assertion, only directly makes
this assertion in Meta-F, but the assertion is about itself in F.

Also, the actual statement that makes this assertion, when viewed in its
basic form in F, isn't "self-referential" thus can't be
"self-contradictiory", and any "logic" that claims it is must be
incorrect, and has created a "F" that doesn't meet the requirements,
either it isn't consistant or can't handle the needed properties of the
whole numbers.

You don't seem to understand, unless you can point to an actual step in
the proof that is invalid, by claiming a different results, all you are
doing is PROVING that your logic system is inconsistent, and thus worthless.

olcott

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Mar 26, 2023, 1:38:27 PM3/26/23

to

On 3/26/2023 9:14 AM, olcott wrote:
> On 3/24/2023 7:20 PM, olcott wrote:
>
> We are therefore confronted with a proposition which asserts
> its own unprovability. (Gödel 1931:39-41)
>
> Is about a proposition that asserts ITS OWN unprovability.
> Is about a proposition that asserts ITS OWN unprovability.
> Is about a proposition that asserts ITS OWN unprovability.
>
> When a proposition asserts ITS OWN unprovability then this very same
> proposition is self-contradictory making it unprovable because it
> is self-contradictory thus not unprovable because its formal system is
> incomplete.
>

When anyone changes the subject of a proposition asserting its own
unprovability as a rebuttal to a proposition asserting its own
unprovability they know that they themselves are deceivers.

Richard Damon

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Mar 26, 2023, 1:54:44 PM3/26/23

to

On 3/26/23 1:38 PM, olcott wrote:
> On 3/26/2023 9:14 AM, olcott wrote:
>> On 3/24/2023 7:20 PM, olcott wrote:
>>
>> We are therefore confronted with a proposition which asserts
>> its own unprovability. (Gödel 1931:39-41)
>>
>> Is about a proposition that asserts ITS OWN unprovability.
>> Is about a proposition that asserts ITS OWN unprovability.
>> Is about a proposition that asserts ITS OWN unprovability.
>>
>> When a proposition asserts ITS OWN unprovability then this very same
>> proposition is self-contradictory making it unprovable because it
>> is self-contradictory thus not unprovable because its formal system is
>> incomplete.
>>
>
> When anyone changes the subject of a proposition asserting its own
> unprovability as a rebuttal to a proposition asserting its own
> unprovability they know that they themselves are deceivers.
>

So, you admit that you are a deceiver, as you have changed the subject
of the proposition you are talking about, perhaps just because you are
too dumb do understand what you are reading.

Thank you.

Richard Damon

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Mar 26, 2023, 2:06:19 PM3/26/23

to

On 3/26/23 1:38 PM, olcott wrote:

> On 3/26/2023 9:14 AM, olcott wrote:
>> On 3/24/2023 7:20 PM, olcott wrote:
>>
>> We are therefore confronted with a proposition which asserts
>> its own unprovability. (Gödel 1931:39-41)
>>
>> Is about a proposition that asserts ITS OWN unprovability.
>> Is about a proposition that asserts ITS OWN unprovability.
>> Is about a proposition that asserts ITS OWN unprovability.
>>
>> When a proposition asserts ITS OWN unprovability then this very same
>> proposition is self-contradictory making it unprovable because it
>> is self-contradictory thus not unprovable because its formal system is
>> incomplete.
>>
>
> When anyone changes the subject of a proposition asserting its own
> unprovability as a rebuttal to a proposition asserting its own
> unprovability they know that they themselves are deceivers.
>

Do you even understand the actual proposition that this comment applies to?

You seem to be making your own comments based on taking words out of
context.

Yes, we have a proposition that shows that it isn't provable, but it
doesn't do that by just claiming it, like you seem to want to make it say.

Thus showing that YOU are the one changing the subject of a proposition.

olcott

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Mar 26, 2023, 2:39:03 PM3/26/23

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"We are therefore confronted with a proposition which asserts its own
unprovability." (Gödel 1931:39-41)

When Gödel refers to a proposition asserting its own unprovability then
within the precise focus on these exact words we can see that such a
proposition would be unprovable because it would be self-contradictory.

F ⊢ GF ↔ ¬ProvF (┌GF┐).
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

When we simply strip away the reference to Gödel numbers thus requiring
F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).

When we convert to more standard notational conventions an add an
existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))

A proof of G in F that proves that G cannot be proved in F is simply

self-contradictory, thus no such G exists in F.

Richard Damon

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Mar 26, 2023, 3:05:54 PM3/26/23

to

On 3/26/23 2:39 PM, olcott wrote:
> "We are therefore confronted with a proposition which asserts its own
> unprovability." (Gödel 1931:39-41)
>
> When Gödel refers to a proposition asserting its own unprovability then
> within the precise focus on these exact words we can see that such a
> proposition would be unprovable because it would be self-contradictory.
>
> F ⊢ GF ↔ ¬ProvF (┌GF┐).

And where does Godel actually SAY THAT?

> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

So, you go by someones summary of what he is saying, not what he
actually say. That seems to imply you don't actually understand what he
is saying.

>
> When we simply strip away the reference to Gödel numbers thus requiring
> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).

IE, you are admitting that you are changing the subject of the
proposition. i.e. admitting to using the Strawman fallacy.

Note, the Reference to the Godel Numbers is the key part of the proof.
Stripping them out means you aren't

>
> When we convert to more standard notational conventions an add an
> existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))

Except that is just proven to be a dishonest dodge. He used perfectly
fine notational conventions and meant what he wrote.

He is showing that you can express that sort of idea, WITHOUT the
explicit statement, because of the expressiveness of numbers. The only
way you can remove the truth of his "notation" is to just ban
semi-advanced forms of math. But, it seems that is beyound your
understanding.

>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.
>
>

A "Proof" Can't be "Contradictory". A set of statements can be, at which
point you can point out the exact contradiction in them, which you
haven't done, you just CLAIM that it is impossible for something to be
True but not provable, but you can't show that such a claim is actually
true.

The only way for a proof to be contradictory is for the whole logic
system to be inconsistent, so your claim that when you add your ideas
into the logic, that the proof is contradictory, just proves that your
addidtion break the system and make it inconsistent.

YOU LOSE.

olcott

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Mar 26, 2023, 3:29:38 PM3/26/23

to

On 3/26/2023 1:39 PM, olcott wrote:
> "We are therefore confronted with a proposition which asserts its own
> unprovability." (Gödel 1931:39-41)
>
> When Gödel refers to a proposition asserting its own unprovability then
> within the precise focus on these exact words we can see that such a
> proposition would be unprovable because it would be self-contradictory.
>
> F ⊢ GF ↔ ¬ProvF (┌GF┐).
> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>
> When we simply strip away the reference to Gödel numbers thus requiring
> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>
> When we convert to more standard notational conventions an add an
> existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))
>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.
>
>

Thus proving that when the above G is neither provable nor refutable in
F it is because G is self-contradictory in F thus not because F is
incomplete.

Richard Damon

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Mar 26, 2023, 3:49:42 PM3/26/23

to

On 3/26/23 3:29 PM, olcott wrote:
> On 3/26/2023 1:39 PM, olcott wrote:
>> "We are therefore confronted with a proposition which asserts its own
>> unprovability." (Gödel 1931:39-41)
>>
>> When Gödel refers to a proposition asserting its own unprovability then
>> within the precise focus on these exact words we can see that such a
>> proposition would be unprovable because it would be self-contradictory.
>>
>> F ⊢ GF ↔ ¬ProvF (┌GF┐).
>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
>>
>> When we simply strip away the reference to Gödel numbers thus requiring
>> F to have its own provability predicate: F ⊢ GF ↔ ¬ProvF (GF).
>>
>> When we convert to more standard notational conventions an add an
>> existential quantifier: ∃G ∈ F (G ↔ ¬(F ⊢ G))
>>
>> A proof of G in F that proves that G cannot be proved in F is simply
>> self-contradictory, thus no such G exists in F.
>>
>>
>
> Thus proving that when the above G is neither provable nor refutable in
> F it is because G is self-contradictory in F thus not because F is
> incomplete.
>

Using FALSE statements doesn't prove anything except that you are an idiot.

The above ISN'T the G of Godel, so your statement is meaningless except
to prove that you are stupid.

Note, any statement made that doesn't show what you are trying to rebut,
automatically loses most of its ability to rebut the statement.

You are just showing you have nothing to actually base you claims, and
all the errors pointed out in messages you don't reply to are actually
correctlly pointing out errors.

That is how "debate" works.

You are just proving you are anti-social, as you refuse to work within
the social convetions.

You are also proving you are anti-logic, as you refuse to work within
the accepted logical system.

You are just proving that your life was wasted and NO ONE will ever
consider your work worthly to examine, as it has been so thoughly
rebuted and you haven't actually tried to answer the rebutalls,
effectively agreeein gto them.

olcott

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Mar 26, 2023, 5:02:52 PM3/26/23

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On 3/26/2023 12:22 AM, Jim Burns wrote:

*The scope of this post is* ∃G ∈ F (G ↔ ¬(F ⊢ G))

There exists a G in F such that G is logically equivalent to its own
unprovability in F.

It makes no difference at all even if Gödel explicitly stated that he
isn't talking about anything like this.

The idea here is to examine the philosophical foundation of the
mathematical notion of incompleteness making sure that it is coherent.

A proof of G in F that proves that G cannot be proved in F is simply

self-contradictory, thus no such G exists in F.

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

Thus proving that when the above G is neither provable nor refutable in
F it is because G is self-contradictory in F thus not because F is
incomplete.

Richard Damon

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Mar 26, 2023, 5:22:24 PM3/26/23

to

On 3/26/23 5:02 PM, olcott wrote:
> On 3/26/2023 12:22 AM, Jim Burns wrote:
>
> *The scope of this post is* ∃G ∈ F (G ↔ ¬(F ⊢ G))

So, nothing to do with Godels Incompletnes proof.

An thus you trying to connect it to Godel is just a Strawman Error.

>
> There exists a G in F such that G is logically equivalent to its own
> unprovability in F.
>
> It makes no difference at all even if Gödel explicitly stated that he
> isn't talking about anything like this.

But it does, you can't put words in another persons mouth and be correct.

You are just admitting that you system is based on LIES.

>
> The idea here is to examine the philosophical foundation of the
> mathematical notion of incompleteness making sure that it is coherent.

Which actually just proves that YOUR concepts are incoherent.

>
> A proof of G in F that proves that G cannot be proved in F is simply
> self-contradictory, thus no such G exists in F.

Which since Godel never claimed a proof of G in F, in fact he claims
that such a proof can not exist, so your logic is proved to b UNSOUND,
and that you are an idiot.

>
> The conventional definition of incompleteness:
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Thus proving that when the above G is neither provable nor refutable in
> F it is because G is self-contradictory in F thus not because F is
> incomplete.
>

Based on what?

You LIES?

Of course if you start from the wrong G, your break proof. Since you "G"
isn't Gode's G, you just commited the Stram man error, and to claim
otherwords just proves you are a LIAR.

Please show the exact location in Godels ACTUAL PROOF where he makes the
claim you say hbe does.

FAILURE TO REPLY IS ADMISSION YOU ARE A LIAR.

Jim Burns

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Mar 30, 2023, 5:14:56 PM3/30/23

to

Which is What?

x|y
means
Ez: z =< x & x = y*z

Prime(x)
means
~Ez: z =<x z /= 1 z/=x x> 1

Jim Burns

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Yes, G can not be proved IN F, but that doesn't mean that we can't prove
that G is True in F with a proof in a Meta-Theory that knows about the
rules of F.

There CAN be a proof in the Meta-Theory that shows that, in F, there is
an infinite sequence of steps in F that demonstrate G, making G true in
F, but not provable. The additional properties of the Meta-Theory can
demonstrate this in a finite number of steps in the Meta-Theory, thus
PROVING that G is True in F, and unprovable.

olcott

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Apr 15, 2023, 6:18:35 PM4/15/23

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G is unsatisfiable in F because G is self-contradictory in F

Richard Damon

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Apr 15, 2023, 7:23:04 PM4/15/23

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Maybe your FAKE G, but the ACTUAL G is fully statisfiable in F, and this
is actually proven in his proof.

You are just too stupid to understand that actual proof, and need to
make incorrect simplifications to try to understand it.

You are just showing that you are not qualified to deal with complicated
logic.

olcott

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Apr 15, 2023, 7:44:54 PM4/15/23

Richard Damon

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Apr 15, 2023, 8:39:37 PM4/15/23

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Nope, Truth just requires a CONNECTION, which can be infinite.

For US to do it would be impossible, but that doesn't mean the
connection doesn't exist.

You are showing your ignorance of what Truth actually is, confusing it
with Knowldege, which is something different.

I suppose this would be an easy mistake for someone who thinks they are
God, since for the REAL God, all Truth is actually known, since God is
actually infinite, and thus can know things that need infinite to know.

But you are finite, and thus can only know what is finite, so not all
Truth is knowable.

olcott

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Apr 15, 2023, 8:44:21 PM4/15/23

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Truth might allow this Satisfiability does not.

Richard Damon

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Apr 15, 2023, 8:45:21 PM4/15/23

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But that doesn't matter, because it isn't the statement that proves that
all sufficiently powerful systems are inconsistent.

Note, the fact that it would be impossible to actually prove your
pseudo-G in F doesn't mean that it can't be true.

Note, it can't be False, but its status of being a Truth Bearer can't be
proven in F.

Maybe you need to learn to read, because my answer DOES answer your
question and show that you are wrong.

Just shows the level of your intelect.

Another point, you are showing that you don't understand what
"self-contradictory" means.

"This statement is not Provable" is NOT Self-Contradictory, as it has a
possible set of truth values that makes it satisified, that is being
True but Unprovable.

That is a VALID combination of truth values

Being Proven but untrue would be contradictory, as Proven requires True.

So, you are just furthering your proof that you don't understand what
you are talking about.

You have locked into your mind some false statements, and they make you
whole logic system invalid.

Richard Damon

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Apr 15, 2023, 8:50:08 PM4/15/23

to

In mathematical logic, a formula is satisfiable if it is true under some
assignment of values to its variables.

So, to be satisfiable, we just need a set of values that makes it true.

There are NO "variables" in G, just an assertion, and that assertion is
true.

Thus, G is statisfiable.

Note, the term isn't really applicable to a statement that no value
exists that meets a requirement.

olcott

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Apr 15, 2023, 8:56:52 PM4/15/23

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When G asserts its own unprovability in F is proven in F this requires a

sequence of inference steps in F that proves there is no such sequence
of inference steps in F.

Try and show how you would provide a sequence of inference steps in F
that correctly proves that no such set of inference steps exists in F.

Richard Damon

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Apr 15, 2023, 9:15:36 PM4/15/23

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But G isn't PROVEN in F, it just is TRUE in F.

The fact that I can't show the existance of such a sequence doesn't mean
that they don't exist.

We can postualte that an infinite sequence of steps might somehow exist
to show that G is true, but not provable, and the fact that such a
postulate doesn't lead to a contradiction, shows that the statme that G
asserts its own non-provablity isn't "Self-Contradictory".

YOU have the burden of proof if you want to make the claim it is.

You have a FUNDAMENTAL problem (or maybe it is a funny mental problem)
about Truth and Proofs. Things are allowed to be True that are unproven,
and even unprovable. Things that are proven, must be True.

For something to be "Known" it needs to be provable, but not necessarily
in the same "Theory" as the statement is made. This is shown for the
ACTUAL G of Godel, which is True in F, and the Truth is Proven in
Meta-F, so we can KNOW that G is True in F, even though we can't prove
it there. (Knowledge can carry across pocket of logic, under proper
conditions)

You inability to stay on the ACTUAL point, and get stuck on your
unimportant side points just reinforces the fact that you don't really

olcott

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Apr 15, 2023, 9:26:46 PM4/15/23

to

When G asserts that it is unprovable in F this cannot be proven F ONLY
because this proof requires a sequence of inference steps in F that
proves there is no such sequence of inference steps in F, not because F
is in any way incomplete.

Richard Damon

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Apr 15, 2023, 9:35:27 PM4/15/23

to

But G DOESN'T "assert" it is unprovable in F, so that doesn't matter.

It can be DERIVED (in Meta-F) that G is unprovable in F.

Note, the DEFINITION of "Incompleteness" is that a system is Incomplete
if there exists a true statement in the system that can not be proven.

G is such a statement, it is True if F, and it can not be proven in F.

That makes F incomplete.

Your arguing about it just shows you don't understand the meaning of the
words you are using.

What don't you get about the fact that G can not be proven in F, but it
is also established (not proven in F) that G is True in F so, BY
DEFINITION F is Incomplete.

You are just proving your ignorance.

olcott

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Apr 15, 2023, 9:59:10 PM4/15/23

to

*I am stipulating that it does. Try and follow my reasoning on this*

When G asserts that it is unprovable in F this cannot be proven F ONLY
because this proof requires a sequence of inference steps in F that
proves there is no such sequence of inference steps in F, not because F
is in any way incomplete.

Richard Damon

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Apr 15, 2023, 10:24:26 PM4/15/23

to

So you are stipulating that you aren't working on Godel's Proof?

>
> When G asserts that it is unprovable in F this cannot be proven F ONLY
> because this proof requires a sequence of inference steps in F that
> proves there is no such sequence of inference steps in F, not because F
> is in any way incomplete.
>

So, you admit you don't understand the meaning of Incomplete as applied
to Logic.

Yes, F is incomplete because there is no "Proof" of G in F, even though
G is TRUE in F. That BY DEFINITION makes F Incomplete.

PERIOD.

Yes, if you just stipulate a statement like that but don't make it True,
then that, by itself, doesn't make the Theory incomplete. The Theory
might not be powerful enough to express Godel's proof in it, and thus
might not be powerful enough to be forced to be incomplete.

There ARE simple enough logic systems that can be complete, not all
logic systems are incomplete. The proof just requires that the system be
able to handle certain properties of whole numbers to be incomplete.

You repeating your argument just points out that you don't actually
understand the meaning of the words you have been claiming to be an
expert in all these years.

You have just proven yourself ignorant.

Your repeated reusing of terms from proofs that you try to redefine to
mean something not quite what they meant, is a good sign that you are
trying to be deceptive, as has been pointed out many times in the past.

olcott

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Apr 15, 2023, 10:30:39 PM4/15/23

to

The reason that G is unprovable in F is clearly that there is something
wrong with G and not that there is anything wrong with F.

Richard Damon

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Apr 15, 2023, 10:46:07 PM4/15/23

to

Nope.

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

Why is a statement that is unprovable have something "wrong" about it.

That just shows your mind has a problem with handling things it doesn't
understand.

You are just proving your ignorance.

Can you actually PROVE what you saying, if not, you are just proving
yourself to b a Hippocrite.

And that means an ACTUAL PROOF, stating the accepted truth-makers you
are starting with, and use actual LOGIC to derive the results.

This is just above your mental ability.

olcott

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Apr 15, 2023, 10:54:56 PM4/15/23

to

G is unprovable because it is self-contradictory, making it erroneous.

Richard Damon

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Apr 16, 2023, 7:16:30 AM4/16/23

to

On 4/15/23 10:54 PM, olcott wrote:

> G is unprovable because it is self-contradictory, making it erroneous.
>

Since you don't understand the meaning of self-contradictory, that claim
is erroneous.

You are also working with a Strawman, because you can't understand the
actual statement G, so even if you were right about the statement you
are talking about, you would still be wrong about the actual statement.

The ACTUAL G has no "Self-Reference" in it, so can't be
"Self-Contradictory".

You are just proving how ignorant you are of logic.

olcott

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Apr 22, 2023, 5:08:40 PM4/22/23

to

On 4/16/2023 6:16 AM, Richard Damon wrote:
> On 4/15/23 10:54 PM, olcott wrote:
>
>> G is unprovable because it is self-contradictory, making it erroneous.
>>
>
> Since you don't understand the meaning of self-contradictory, that claim
> is erroneous.
>

When G asserts its own unprovability in F:

Any proof of G in F requires a sequence of inference steps in F that
prove that they themselves do not exist in F.

This is precisely analogous to you proving that you yourself never
existed.

> You are also working with a Strawman, because you can't understand the
> actual statement G, so even if you were right about the statement you
> are talking about, you would still be wrong about the actual statement.
>
> The ACTUAL G has no "Self-Reference" in it, so can't be
> "Self-Contradictory".
>
> You are just proving how ignorant you are of logic.
>

Richard Damon

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Apr 22, 2023, 5:27:14 PM4/22/23

to

On 4/22/23 5:08 PM, olcott wrote:
> On 4/16/2023 6:16 AM, Richard Damon wrote:
>> On 4/15/23 10:54 PM, olcott wrote:
>>
>>> G is unprovable because it is self-contradictory, making it erroneous.
>>>
>>
>> Since you don't understand the meaning of self-contradictory, that
>> claim is erroneous.
>>
>
> When G asserts its own unprovability in F:

But Godel's G doesn't do that.

>
> Any proof of G in F requires a sequence of inference steps in F that
> prove that they themselves do not exist in F.

It is of course impossible to prove in F that a statement is true but
not provable in F.

You don't need to do the proof in F, Godel shows how to construct a
Meta-F system from F that allows construction a proof IN META-F that
shows that his G is True in F, and not provable in F.

>
> This is precisely analogous to you proving that you yourself never
> existed.

Nope, you are just proving you can't do your strawman, because you have
straw for brains.

You start from an incorrect assertion, that G actually asserts its own
unprovability, and then continue to make errors in asserting that this
is proven in F itself.

This just shows you fundamentally don't understand how the logic works,
and that you are too stupid to be able to be taught it.

olcott

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Apr 22, 2023, 5:36:49 PM4/22/23

to

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Apr 22, 2023, 6:49:09 PM4/22/23

to

When one level of indirect reference is applied to the Liar Paradox it
becomes actually true. There was no "if".

This sentence is not true: "This sentence is not true" <IS> TRUE.

> Your
>
>>
>> We can do the same thing when G asserts its own unprovability in F.
>> G cannot be proved in F because this requires a sequence of inference
>> steps in F that prove that they themselves do not exist in F.
>
> Right, you can't prove, in F, that G is true, but you can prove, in
> Meta-F, that G is true in F, and that G is unprovable in F, which is
> what is required.
>

When G asserts its own unprovability in F it cannot be proved in F

because this requires a sequence of inference steps in F that prove that

they themselves do not exist.

Meta-F merely removes the self-contradiction the same way Tarski's Meta-
theory removed the self-contradiction.

> You are just showing that your mind can't handle the basics of logic, or
> truth.
>

It may seem that way to someone that learns things by rote and mistakes
this for actual understanding of exactly how all of the elements of a
proof fit together coherently or fail to do so.

> It sounds like you are too stupid to learn, and that you have
> intentionaally hamstrung yourself to avoid being "polluted" by
> "rote-learning" so you are just self-inflicted ignorant.
>
> If you won't even try to learn the basics, you have just condemned
> yourself into being a pathological liar because you just don't any better.
>

I do at this point need to understand model theory very thoroughly.

Learning the details of these things could have boxed me into a corner
prior to my philosophical investigation of seeing how the key elements
fail to fit together coherently.

It is true that the set of analytical truth is simply a set of semantic
tautologies. It is true that formal systems grounded in this foundation
cannot be incomplete nor have any expressions of language that are
undecidable. Now that I have this foundation I have a way to see exactly
how the concepts of math diverge from correct reasoning.

>>
>> You and I can see both THAT G cannot be proved in F and WHY G cannot be
>> proved in F. G cannot be proved in F for the same pathological
>> self-reference(Olcott 2004) reason that the Liar Paradox cannot be
>> proved in Tarski's theory.
>>
>
> Which he didn't do, but you are too stupid to understand claissic
> arguement forms.
>

It is not that I do not understand, it is that I can directly see where
and how formal mathematical systems diverge from correct reasoning.

Because you are a learned-by-rote person you make sure to never examine
whether or not any aspect of math diverges from correct reasoning, you
simply assume that math is the gospel even when it contradicts itself.

>>> Just shows you are ignorant.
>>>
>>> Too bad you are going to die in such disgrace.
>>>
>>> All you need to do is show that there exist a (possibly infinte) set
>>> of steps from the truth makers in F, using the rules of F, to G. Youy
>>> don't need to actually DO this in F, if you have a system that knowns
>>> about F.
>>>
>>> Your mind is just too small.
>>
>

Richard Damon

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Apr 22, 2023, 7:19:31 PM4/22/23

to

But since you are discussing Formal Logic, you need to use the rules of
Formal logic.

The other way to say it is that your "Correct Reasoning" diverges from
the accepted and proven system of Formal Logic.

>
> Because you are a learned-by-rote person you make sure to never examine
> whether or not any aspect of math diverges from correct reasoning, you
> simply assume that math is the gospel even when it contradicts itself.

Nope, I know that with logic, if you follow the rules, you will get the
correct answer by the rules.

If you break the rules, you have no idea where you will go.

As I have told you before, if you want to see what your "Correct
Reasoning" can do as a replaceent logic system, you need to start at the
BEGINNING, and see wht it gets.

To just try to change things at the end is just PROOF that your "Correct
Reasoning" has to not be based on any real principles of logic.

Since it is clear that you want to change some of the basics of how
logic works, you are not allowed to just use ANY of classical logic
until you actually show what part of it is still usable under your
system and what changes happen.

Considering your current status, I would start working hard on that
right away, as with your current reputation, once you go, NO ONE is
going to want to look at your ideas, because you have done such a good
job showing that you don't understand how things work.

I haven't been able to get out of you exactly what you want to do with
your "Correct Reasoning", and until you show a heart to actually try to
do something constructive with it, and not just use it as an excuse for
bad logic, I don't care what it might be able to do, because, frankly, I
don't think you have the intellect to come up with something like that.

But go ahead and prove me wrong, write an actual paper on the basics of
your "Correct Reasoning" and show how it actually works, and compare it
to "Classical Logic" and show what is different. Then maybe you can
start to work on showing it can actually do something useful.

olcott

unread,

Apr 22, 2023, 7:57:52 PM4/22/23

to

I have never been talking about formal logic. I have always been talking
about the philosophical foundations of correct reasoning.

> The other way to say it is that your "Correct Reasoning" diverges from
> the accepted and proven system of Formal Logic.
>

It is correct reasoning in the absolute sense that I refer to.
If anyone has the opinion that arithmetic does not exist they are
incorrect in the absolute sense of the word: "incorrect".

>>
>> Because you are a learned-by-rote person you make sure to never examine
>> whether or not any aspect of math diverges from correct reasoning, you
>> simply assume that math is the gospel even when it contradicts itself.
>
> Nope, I know that with logic, if you follow the rules, you will get the
> correct answer by the rules.
>
> If you break the rules, you have no idea where you will go.
>

In other words you never ever spend any time on making sure that these
rules fit together coherently.

> As I have told you before, if you want to see what your "Correct > Reasoning" can do as a replaceent logic system, you need to start at the
> BEGINNING, and see wht it gets.
>

The foundation of correct reasoning is that the entire body of
analytical truth is a set of semantic tautologies.

This means that all correct inference always requires determining the
semantic consequence of expressions of language. This semantic
consequence can be specified syntactically, and indeed must be
represented syntactically to be computable.

> To just try to change things at the end is just PROOF that your "Correct
> Reasoning" has to not be based on any real principles of logic.
>
> Since it is clear that you want to change some of the basics of how
> logic works, you are not allowed to just use ANY of classical logic
> until you actually show what part of it is still usable under your
> system and what changes happen.
>

Whenever an expression of language is derived as the semantic
consequence of other expressions of language we have valid inference.

The semantic consequence must be specified syntactically so that it can
be computed or examined in formal systems.

Just like in sound deductive inference when the premises are known to be
true, and the reasoning valid (a semantic consequence) then the
conclusion is necessarily true.

> Considering your current status, I would start working hard on that
> right away, as with your current reputation, once you go, NO ONE is
> going to want to look at your ideas, because you have done such a good
> job showing that you don't understand how things work.
>

My reputation on one very important group has risen to quite credible

> I haven't been able to get out of you exactly what you want to do with
> your "Correct Reasoning", and until you show a heart to actually try to
> do something constructive with it, and not just use it as an excuse for
> bad logic, I don't care what it might be able to do, because, frankly, I
> don't think you have the intellect to come up with something like that.
>

Until we establish the foundation of correct reasoning in terms of a
consistent and complete True(L,X) all AI systems will be anchored in the
shifting sands of opinions.

> But go ahead and prove me wrong, write an actual paper on the basics of
> your "Correct Reasoning" and show how it actually works, and compare it
> to "Classical Logic" and show what is different. Then maybe you can
> start to work on showing it can actually do something useful.
>

The most important aspect of the tiny little foundation of a formal
system that I already specified immediately above is self-evident:
True(L,X) can be defined and incompleteness is impossible.

People that spend 99.99% of their attention on trying to show errors in
what I say rather than paying any attention understanding what I say
might not notice these dead obvious things

>>>>> Just shows you are ignorant.
>>>>>
>>>>> Too bad you are going to die in such disgrace.
>>>>>
>>>>> All you need to do is show that there exist a (possibly infinte)
>>>>> set of steps from the truth makers in F, using the rules of F, to
>>>>> G. Youy don't need to actually DO this in F, if you have a system
>>>>> that knowns about F.
>>>>>
>>>>> Your mind is just too small.
>>>>
>>>
>>
>

Richard Damon

unread,

Apr 22, 2023, 8:27:16 PM4/22/23

to

No, you have been talking about theorys DEEP in formal logic. You can't
talk about the "errors" in those theories, with being in formal logic.

IF you think you can somehow talk about the foundations, while working
in the penthouse, you have just confirmed that you do not understand how
ANY form of logic works.

PERIOD.

>
>> The other way to say it is that your "Correct Reasoning" diverges from
>> the accepted and proven system of Formal Logic.
>>
>
> It is correct reasoning in the absolute sense that I refer to.
> If anyone has the opinion that arithmetic does not exist they are
> incorrect in the absolute sense of the word: "incorrect".
>

IF you reject the logic that a theory is based on, you need to reject
the logic system, NOT the theory.

You are just showing that you have wasted your LIFE because you
don'tunderstnad how to work ligic.

>>>
>>> Because you are a learned-by-rote person you make sure to never examine
>>> whether or not any aspect of math diverges from correct reasoning, you
>>> simply assume that math is the gospel even when it contradicts itself.
>>
>> Nope, I know that with logic, if you follow the rules, you will get
>> the correct answer by the rules.
>>
>> If you break the rules, you have no idea where you will go.
>>
>
> In other words you never ever spend any time on making sure that these
> rules fit together coherently.

The rules work together just fine.

YOU don't like some of the results, but they work just fine for most of
the field.

You are just PROVING that you have no idea how to actually discuss a new
foundation for logic, likely because you are incapable of actually
comeing up with a consistent basis for working logic.

>
>> As I have told you before, if you want to see what your "Correct >
>> Reasoning" can do as a replaceent logic system, you need to start at the
>> BEGINNING, and see wht it gets.
>>
>
> The foundation of correct reasoning is that the entire body of
> analytical truth is a set of semantic tautologies.
>
> This means that all correct inference always requires determining the
> semantic consequence of expressions of language. This semantic
> consequence can be specified syntactically, and indeed must be
> represented syntactically to be computable

Meaningless gobbledy-good until you actually define what you mean and
spell out the actual rules that need to be followed.

Note, "Computability" is actually a fairly late in the process concept.
You first need to show that you logic can actually do something useful

>
>> To just try to change things at the end is just PROOF that your
>> "Correct Reasoning" has to not be based on any real principles of logic.
>>
>> Since it is clear that you want to change some of the basics of how
>> logic works, you are not allowed to just use ANY of classical logic
>> until you actually show what part of it is still usable under your
>> system and what changes happen.
>>
>
> Whenever an expression of language is derived as the semantic
> consequence of other expressions of language we have valid inference.

And, are you using the "classical" definition of "semantic" (which makes
this sentence somewhat cirular) or do you mean something based on the
concept you sometimes use of "the meaning of the words".

>
> The semantic consequence must be specified syntactically so that it can
> be computed or examined in formal systems.
>
> Just like in sound deductive inference when the premises are known to be
> true, and the reasoning valid (a semantic consequence) then the
> conclusion is necessarily true.

So, what is the difference in your system from classical Formal Logic?

You keep on talking like you are making some major change, but you can't
seem to specify what that is. And when asked to define, you just waffle.

You are just showing thw shallowness of even what you are trying to
think up.

>
>> Considering your current status, I would start working hard on that
>> right away, as with your current reputation, once you go, NO ONE is
>> going to want to look at your ideas, because you have done such a good
>> job showing that you don't understand how things work.
>>
>
> My reputation on one very important group has risen to quite credible

What group?

>
>> I haven't been able to get out of you exactly what you want to do with
>> your "Correct Reasoning", and until you show a heart to actually try
>> to do something constructive with it, and not just use it as an excuse
>> for bad logic, I don't care what it might be able to do, because,
>> frankly, I don't think you have the intellect to come up with
>> something like that.
>>
>
> Until we establish the foundation of correct reasoning in terms of a
> consistent and complete True(L,X) all AI systems will be anchored in the
> shifting sands of opinions.
>
>> But go ahead and prove me wrong, write an actual paper on the basics
>> of your "Correct Reasoning" and show how it actually works, and
>> compare it to "Classical Logic" and show what is different. Then maybe
>> you can start to work on showing it can actually do something useful.
>>
>
> The most important aspect of the tiny little foundation of a formal
> system that I already specified immediately above is self-evident:
> True(L,X) can be defined and incompleteness is impossible.

I don't think your system is anywhere near establish far enough for you
to say that.

>
> People that spend 99.99% of their attention on trying to show errors in
> what I say rather than paying any attention understanding what I say
> might not notice these dead obvious things

What, that we can tell when you are lying because your mouth is moving?

You "logic" has been shown to be totally broken. I don't think you
really know what you are talking about. You are just showing your own
stupidity,

olcott

unread,

Apr 24, 2023, 10:40:11 AM4/24/23

to

Proving that G is true in F requires a sequence of inference steps that
prove that they themselves don't exist.

You might be bright enough to understand that is self-contradictory.

olcott

unread,

Apr 24, 2023, 11:25:05 AM4/24/23

to

In classical logic, intuitionistic logic and similar logical systems,
the principle of explosion

ex falso [sequitur] quodlibet,
'from falsehood, anything [follows]'

ex contradictione [sequitur] quodlibet,
'from contradiction, anything [follows]')

https://en.wikipedia.org/wiki/Principle_of_explosion

∴ FALSE ⊢ Donald Trump is the Christ
∴ FALSE ⊢ Donald Trump is Satan

*Correction abolishing the POE nonsense*
Semantic Necessity operator: ⊨□
FALSE ⊨□ FALSE
(P ∧ ¬P) ⊨□ FALSE

>>
>> Because you are a learned-by-rote person you make sure to never examine
>> whether or not any aspect of math diverges from correct reasoning, you
>> simply assume that math is the gospel even when it contradicts itself.
>
> Nope, I know that with logic, if you follow the rules, you will get the
> correct answer by the rules.
>

Then you must agree that Trump is the Christ and Trump is Satan both of
those were derived from correct logic.

> If you break the rules, you have no idea where you will go.
>
> As I have told you before, if you want to see what your "Correct
> Reasoning" can do as a replaceent logic system, you need to start at the
> BEGINNING, and see wht it gets.
>

I would be happy to talk this through with you.

The beginning is that

valid inference an expression X of language L must be a semantic
consequence of its premises in L

sound inference expression X of language L must be a semantic
consequence of the axioms of L.

For formal systems such as FOL the semantics is mostly the meaning of
the logic symbols.

These two logic symbols are abolished ⇒ → and replaced with this:
Semantic Necessity operator: ⊨□

> To just try to change things at the end is just PROOF that your "Correct
> Reasoning" has to not be based on any real principles of logic.
>

No logic must be based on correct reasoning any logic that prove Donal
Trump is the Christ is incorrect reasoning, thus the POE is abolished

These two logic symbols are abolished ⇒ → and replaced with this:
Semantic Necessity operator: ⊨□

Explosions have been abolished
FALSE ⊨□ FALSE
(P ∧ ¬P) ⊨□ FALSE

> Since it is clear that you want to change some of the basics of how
> logic works, you are not allowed to just use ANY of classical logic
> until you actually show what part of it is still usable under your
> system and what changes happen.
>

Yes lets apply my ideas to FOL. I have already sketched out many
details.

> Considering your current status, I would start working hard on that
> right away, as with your current reputation, once you go, NO ONE is
> going to want to look at your ideas, because you have done such a good
> job showing that you don't understand how things work.
>
> I haven't been able to get out of you exactly what you want to do with
> your "Correct Reasoning", and until you show a heart to actually try to
> do something constructive with it, and not just use it as an excuse for
> bad logic, I don't care what it might be able to do, because, frankly, I
> don't think you have the intellect to come up with something like that.
>

I showed how the POE is easily abolished.
I showed how Provable(L,x) and True(L,x) are defined.

> But go ahead and prove me wrong, write an actual paper on the basics of
> your "Correct Reasoning" and show how it actually works, and compare it
> to "Classical Logic" and show what is different. Then maybe you can
> start to work on showing it can actually do something useful.
>

I need a dialogue to vet aspects of my ideas.
The key thing that I have not yet filled in is how to specify the
semantics of every FOL expression.

This semantics seems fully specified:
∀n ∈ ℕ ∀m ∈ ℕ ((n > m) ⊨□ (n+1 > m))

>>>>> Just shows you are ignorant.
>>>>>
>>>>> Too bad you are going to die in such disgrace.
>>>>>
>>>>> All you need to do is show that there exist a (possibly infinte)
>>>>> set of steps from the truth makers in F, using the rules of F, to
>>>>> G. Youy don't need to actually DO this in F, if you have a system
>>>>> that knowns about F.
>>>>>
>>>>> Your mind is just too small.
>>>>
>>>
>>
>

olcott

unread,

Apr 24, 2023, 11:58:27 AM4/24/23

to

*Principle of explosion*
An alternate argument for the principle stems from model theory. A
sentence P is a semantic consequence of a set of sentences Γ only if
every model of Γ is a model of P. However, there is no model of the
contradictory set (P ∧ ¬P) A fortiori, there is no model of (P ∧ ¬P)
that is not a model of Q. Thus, vacuously, every model of (P ∧ ¬P) is a
model of Q. Thus, Q is a semantic consequence of (P ∧ ¬P).
https://en.wikipedia.org/wiki/Principle_of_explosion

Vacuous truth does not count as truth.
All variables must be quantified

"all cell phones in the room are turned off" will be true when no cell
phones are in the room.

∃cp ∈ cell_phones (in_this_room(cp)) ∧ turned_off(cp))

>>
>> The semantic consequence must be specified syntactically so that it can
>> be computed or examined in formal systems.
>>
>> Just like in sound deductive inference when the premises are known to be
>> true, and the reasoning valid (a semantic consequence) then the
>> conclusion is necessarily true.
>
> So, what is the difference in your system from classical Formal Logic?
>

Semantic Necessity operator: ⊨□

FALSE ⊨□ FALSE // POE abolished
(P ∧ ¬P) ⊨□ FALSE // POE abolished

⇒ and → symbols are replaced by ⊨□

The sets that the variables range over must be defined
all variables must be quantified

// x is a semantic consequence of its premises in L
Provable(P,x) ≡ ∃x ∈ L, ∃P ⊆ L (P ⊨□ x)

// x is a semantic consequence of the axioms of L
True(L,x) ≡ ∃x ∈ L (Axioms(L) ⊨□ x)

*The above is all that I know right now*

>> The most important aspect of the tiny little foundation of a formal
>> system that I already specified immediately above is self-evident:
>> True(L,X) can be defined and incompleteness is impossible.
>
> I don't think your system is anywhere near establish far enough for you
> to say that.

Try and show exceptions to this rule and I will fill in any gaps that
you find.

G asserts its own unprovability in F

The reason that G cannot be proved in F is that this requires a
sequence of inference steps in F that proves no such sequence
of inference steps exists in F.

olcott

unread,

Apr 24, 2023, 12:13:10 PM4/24/23

to

∃sequence_of_inference_steps ⊆ F (sequence_of_inference_steps ⊢
∄sequence_of_inference_steps ⊆ F)

Richard Damon

unread,

Apr 24, 2023, 7:35:33 PM4/24/23

to

So, you don't understand the differnce between the INFINITE set of
sequence steps that show that G is True, and the FINITE number of steps
that need to be shown to make G provable.

You are just showing you don't understand what you talking about and
just spouting word (or symbol) salad.

You are oriving you are an IDIOT.

Richard Damon

unread,

Apr 24, 2023, 7:35:36 PM4/24/23

to

Right, if a logic system can prove a contradiction, that out of that
contradiction you can prove anything

>
> https://en.wikipedia.org/wiki/Principle_of_explosion
>
> ∴ FALSE ⊢ Donald Trump is the Christ
> ∴ FALSE ⊢ Donald Trump is Satan

Which isn't what was being talked about.

You clearly don't understand how the principle of explosion works, which
isn't surprising considering how many misconseptions you have about how
logic works.

Right now, I would say you are to ignorant on that basics of logic to be
able to explain, even in basic terms, how it works, you have shown
yourself to be that stupid.

>
> *Correction abolishing the POE nonsense*
> Semantic Necessity operator: ⊨□
> FALSE ⊨□ FALSE
> (P ∧ ¬P) ⊨□ FALSE
>

So, FULLY define what you mean by that.

>
>>>
>>> Because you are a learned-by-rote person you make sure to never examine
>>> whether or not any aspect of math diverges from correct reasoning, you
>>> simply assume that math is the gospel even when it contradicts itself.
>>
>> Nope, I know that with logic, if you follow the rules, you will get
>> the correct answer by the rules.
>>
>
> Then you must agree that Trump is the Christ and Trump is Satan both of
> those were derived from correct logic.
>
>> If you break the rules, you have no idea where you will go.
>>
>> As I have told you before, if you want to see what your "Correct
>> Reasoning" can do as a replaceent logic system, you need to start at
>> the BEGINNING, and see wht it gets.
>>
>
> I would be happy to talk this through with you.
>
> The beginning is that
>
> valid inference an expression X of language L must be a semantic
> consequence of its premises in L

And what do you mean by "semantic"

because, conventional logic defines semantic consequence as the
conclusion must be true if the premise is true.

You seem to mean something diffent, but haven't explained what you mean
by that.

>
> sound inference expression X of language L must be a semantic
> consequence of the axioms of L.
>
> For formal systems such as FOL the semantics is mostly the meaning of
> the logic symbols.
>
> These two logic symbols are abolished ⇒ → and replaced with this:
> Semantic Necessity operator: ⊨□

Why do you need to abolish shows symbols? You do understand that the
statment that A -> B is equivalent to the asserting of (~A | B) is
ALWAYS TRUE (which might be part of your problem, as you don't seem to
understand that categorical meaning of ALL and NO), so either you need
to outlaw the negation operator, or the or operator to do this.

Again, what does "Semantic Necessity" operator mean?

Note, one issue with your use of symbols, so many of the symbols can
have slightly diffferent meanings based on the context and system you
are working in.

>
>
>> To just try to change things at the end is just PROOF that your
>> "Correct Reasoning" has to not be based on any real principles of logic.
>>
>
> No logic must be based on correct reasoning any logic that prove Donal
> Trump is the Christ is incorrect reasoning, thus the POE is abolished

You CAN'T abolish the Principle of Explosion unless you greatly restrict
the power of your logic.

>
> These two logic symbols are abolished ⇒ → and replaced with this:
> Semantic Necessity operator: ⊨□
>
> Explosions have been abolished

Nope.

> FALSE ⊨□ FALSE
> (P ∧ ¬P) ⊨□ FALSE

Again DEFINE this operator, and the words you use to define it.

>
>> Since it is clear that you want to change some of the basics of how
>> logic works, you are not allowed to just use ANY of classical logic
>> until you actually show what part of it is still usable under your
>> system and what changes happen.
>>
>
> Yes lets apply my ideas to FOL. I have already sketched out many
> details.

Go ahead, try to fully define your ideas.

Remember, until you get to supporting the Higher Order Logics, you can't
get to the incompleteness, as that has been only established for systems
with second order logic, which is also needed for the needed properties
of the whole numbers. First Order Peano Arithmatic might be complete,
but can't be proved (within itself) to be consistent. Second Order
Peaano Arithmatic (which adds the principle of Induction) IS incomplete
as it supports enough of the natural number to support Godel's proof.

>
>> Considering your current status, I would start working hard on that
>> right away, as with your current reputation, once you go, NO ONE is
>> going to want to look at your ideas, because you have done such a good
>> job showing that you don't understand how things work.
>>
>> I haven't been able to get out of you exactly what you want to do with
>> your "Correct Reasoning", and until you show a heart to actually try
>> to do something constructive with it, and not just use it as an excuse
>> for bad logic, I don't care what it might be able to do, because,
>> frankly, I don't think you have the intellect to come up with
>> something like that.
>>
>
> I showed how the POE is easily abolished.

Nope.

> I showed how Provable(L,x) and True(L,x) are defined.

Note clearly. For instance, A statment x is provable or True in a
SYSTEM/THEORY (depending on your terminology) and NOT dependent on some
other statement in the system, as you definition seemed to imply. You
don't "Prove" something based on a statement, but in a System/Theory.

>
>> But go ahead and prove me wrong, write an actual paper on the basics
>> of your "Correct Reasoning" and show how it actually works, and
>> compare it to "Classical Logic" and show what is different. Then maybe
>> you can start to work on showing it can actually do something useful.
>>
>
> I need a dialogue to vet aspects of my ideas.
> The key thing that I have not yet filled in is how to specify the
> semantics of every FOL expression.
>
> This semantics seems fully specified:
> ∀n ∈ ℕ ∀m ∈ ℕ ((n > m) ⊨□ (n+1 > m))

Nope, you need to actually FULLY DEFINE what you mean by your symbols,
you can't just rely on refering to classical meaning since you clearly
disagree with some of the classical meanings.

You seem to have some disjoint ideas, but seem to be unable to come up
with a cohesive whole. You use words that you don't seem to be able to
actually fully define.

Since you are trying to reject some of the basics of classical logic,
you need to FULLY define how your logic works. Name ALL the basic
operation that you allow. Do you allow "Not", "Or", "And", "Equals",
etc. What are your rules for logical inference. How do you ACTUALLY
prove a statement given a set of "Truthmakers".

Remember, if you want to reject classical logic, you can't use it to
define your system.

Richard Damon

unread,

Apr 24, 2023, 7:35:38 PM4/24/23

to

Except that G is proved in Meta-F to be "True in F".

With a finite number of steps in Meta-F, we can prove that the infinite
number of steps in F exist and are true.

In particular, in F, we need to check every number individual to see if
it satisfies the relationship, and we have no short cut to make this
operation finite, so we can't prove it. But in Meta-F, we know something
about the relationship, and are able to prove that no number can satisfy
the relationship, and do so in a finite number of steps.

Thus, we can prove in Meta-F that G must be true in F.

The sequence of steps in F is infinite, so not a proof in F.

In fact, in Meta-F we are also able to prove that there CAN'T be a
finite sequence set of steps that prove G true in F.

Thus, with logic in Meta-F, we can prove that, G is True in F and can

not be proven in F.

You just don't seem to understand how Meta-Logic works. And, it turns
out, that meta-logic is a very important tool for proving things, so
this is one of your Kryponites.

olcott

unread,

Apr 24, 2023, 11:28:13 PM4/24/23

to

The experts seem to believe that unless a proof can be transformed into
a finite sequence of steps it is no actual proof at all. Try and cite a
source that says otherwise.

We can imagine an Oracle machine that can complete these proofs in the
same sort of way that we can imagine a magic fairy that waves a magic
wand.

> You are just showing you don't understand what you talking about and
> just spouting word (or symbol) salad.
>
> You are oriving you are an IDIOT.

I am seeing these things at a deeper philosophical level than you are. I
know that is hard to believe.

You are so sure that I must be wrong that you don't bother to understand
what I am saying.

It seem that the time has come for me to spend the little time that it
takes to understand the technical details of Gödel's proof.

I am estimating that have very good understanding of the preface to the
proof and the SEP article should provide this.

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

olcott

unread,

Apr 25, 2023, 12:03:16 AM4/25/23

to

The two logic symbols already say semantic necessity, model theory may
have screwed up the idea of semantics by allowing vacuous truth.
I must become a master expert of at least basic model theory.

>>
>>>>
>>>> Because you are a learned-by-rote person you make sure to never examine
>>>> whether or not any aspect of math diverges from correct reasoning, you
>>>> simply assume that math is the gospel even when it contradicts itself.
>>>
>>> Nope, I know that with logic, if you follow the rules, you will get
>>> the correct answer by the rules.
>>>
>>
>> Then you must agree that Trump is the Christ and Trump is Satan both of
>> those were derived from correct logic.
>>
>>> If you break the rules, you have no idea where you will go.
>>>
>>> As I have told you before, if you want to see what your "Correct
>>> Reasoning" can do as a replaceent logic system, you need to start at
>>> the BEGINNING, and see wht it gets.
>>>
>>
>> I would be happy to talk this through with you.
>>
>> The beginning is that
>>
>> valid inference an expression X of language L must be a semantic
>> consequence of its premises in L
>
>
> And what do you mean by "semantic"
>

What does meaning mean?
The premise that
the Moon if made from green cheese ⊨□ The Moon is made from cheese.

All of the conventional logic symbols retain their original meaning.
Variable are quantified and of a specific type.
Meaning postulates can axiomatise meaning.

The connection between elements of the proof must be at least as good as
relevance logic.

> because, conventional logic defines semantic consequence as the
> conclusion must be true if the premise is true.
>
> You seem to mean something diffent, but haven't explained what you mean
> by that.
>

You never heard of ordinary sound deductive inference?

>>
>> sound inference expression X of language L must be a semantic
>> consequence of the axioms of L.
>>
>> For formal systems such as FOL the semantics is mostly the meaning of
>> the logic symbols.
>>
>> These two logic symbols are abolished ⇒ → and replaced with this:
>> Semantic Necessity operator: ⊨□
>
> Why do you need to abolish shows symbols?

They seem to lead to the principle of explosion.

> You do understand that the
> statment that A -> B is equivalent to the asserting of (~A | B) is
> ALWAYS TRUE (which might be part of your problem, as you don't seem to
> understand that categorical meaning of ALL and NO), so either you need
> to outlaw the negation operator, or the or operator to do this.
>
> Again, what does "Semantic Necessity" operator mean?

A ⊨□ B the meaning of B is an aspect of the meaning of A.

>
> Note, one issue with your use of symbols, so many of the symbols can
> have slightly diffferent meanings based on the context and system you
> are working in.
>

I don't see this can you provide examples?
I am stipulating standard meanings.

>>
>>
>>> To just try to change things at the end is just PROOF that your
>>> "Correct Reasoning" has to not be based on any real principles of logic.
>>>
>>
>> No logic must be based on correct reasoning any logic that prove Donal
>> Trump is the Christ is incorrect reasoning, thus the POE is abolished
>
> You CAN'T abolish the Principle of Explosion unless you greatly restrict
> the power of your logic.
>

My two axioms abolish it neatly. All that I am getting rid of is
incompleteness and undecidability and I am gaining a universal True(L,x)
predicate.

>>
>> These two logic symbols are abolished ⇒ → and replaced with this:
>> Semantic Necessity operator: ⊨□
>>
>> Explosions have been abolished
>
> Nope.
>
>> FALSE ⊨□ FALSE
>> (P ∧ ¬P) ⊨□ FALSE
>
> Again DEFINE this operator, and the words you use to define it.
>

The semantic meaning of B is necessitated by the semantic meaning of A.
If I have a dog then I have an animal because a dog is an animal.

>>
>>> Since it is clear that you want to change some of the basics of how
>>> logic works, you are not allowed to just use ANY of classical logic
>>> until you actually show what part of it is still usable under your
>>> system and what changes happen.
>>>
>>
>> Yes lets apply my ideas to FOL. I have already sketched out many
>> details.
>
> Go ahead, try to fully define your ideas.
>
> Remember, until you get to supporting the Higher Order Logics, you can't
> get to the incompleteness, as that has been only established for systems

I have always been talking about HOL in terms of MTT

> with second order logic, which is also needed for the needed properties
> of the whole numbers. First Order Peano Arithmatic might be complete,
> but can't be proved (within itself) to be consistent. Second Order
> Peaano Arithmatic (which adds the principle of Induction) IS incomplete
> as it supports enough of the natural number to support Godel's proof.
>
>>
>>> Considering your current status, I would start working hard on that
>>> right away, as with your current reputation, once you go, NO ONE is
>>> going to want to look at your ideas, because you have done such a
>>> good job showing that you don't understand how things work.
>>>
>>> I haven't been able to get out of you exactly what you want to do
>>> with your "Correct Reasoning", and until you show a heart to actually
>>> try to do something constructive with it, and not just use it as an
>>> excuse for bad logic, I don't care what it might be able to do,
>>> because, frankly, I don't think you have the intellect to come up
>>> with something like that.
>>>
>>
>> I showed how the POE is easily abolished.
>
> Nope.
>

If axioms stipulate that explosion cannot occur then it cannot occur.

>> I showed how Provable(L,x) and True(L,x) are defined.
>
> Note clearly. For instance, A statment x is provable or True in a
> SYSTEM/THEORY (depending on your terminology) and NOT dependent on some
> other statement in the system, as you definition seemed to imply. You
> don't "Prove" something based on a statement, but in a System/Theory.
>

F ⊢ A is used to express (in the meta-level) that A
is derivable in F, that is, that there is a proof of
A in F, or, in other words, that A is a theorem of F.
https://plato.stanford.edu/entries/goedel-incompleteness/

>>
>>> But go ahead and prove me wrong, write an actual paper on the basics
>>> of your "Correct Reasoning" and show how it actually works, and
>>> compare it to "Classical Logic" and show what is different. Then
>>> maybe you can start to work on showing it can actually do something
>>> useful.
>>>
>>
>> I need a dialogue to vet aspects of my ideas.
>> The key thing that I have not yet filled in is how to specify the
>> semantics of every FOL expression.
>>
>> This semantics seems fully specified:
>> ∀n ∈ ℕ ∀m ∈ ℕ ((n > m) ⊨□ (n+1 > m))
>
> Nope, you need to actually FULLY DEFINE what you mean by your symbols,
> you can't just rely on refering to classical meaning since you clearly
> disagree with some of the classical meanings.

in the above case I can switch to conventional symbols without losing
anything ∀n ∈ ℕ ∀m ∈ ℕ ((n > m) ⊢ (n+1 > m))

Implication does a poor job of if-then
p---q---(p ⇒ q)---(if p then q)
T---T------T------------T
T---F------F------------F
F---T------T------------undefined
F---F------T------------undefined

> You seem to have some disjoint ideas, but seem to be unable to come up
> with a cohesive whole. You use words that you don't seem to be able to
> actually fully define.
>
> Since you are trying to reject some of the basics of classical logic,
> you need to FULLY define how your logic works. Name ALL the basic
> operation that you allow. Do you allow "Not", "Or", "And", "Equals",
> etc. What are your rules for logical inference. How do you ACTUALLY
> prove a statement given a set of "Truthmakers".
>

All of the details that I provided are all of the detail that I know
right now.

> Remember, if you want to reject classical logic, you can't use it to
> define your system.

I can take it as a basis and add and subtract things from it

olcott

unread,

Apr 25, 2023, 12:17:17 AM4/25/23

to

When you assume that infinite proofs are not a thing then
When you understood rather than ignore that a proof of G in F requires a
sequence of inference steps in F that prove that they themselves don't
exist then and only then is it possible to understand that a proof of G
in F cannot be done only because it is self-contradictory.

Ignoring this doesn't make it go away. Assuming this it is not needed
requires another way of proving in F that G cannot be proved in F.
An infinite proof is always impossible so that way is out.

>
> With a finite number of steps in Meta-F, we can prove that the infinite
> number of steps in F exist and are true.
>

That is cheating. The purpose here is to see WHY rather than merely THAT
G is unprovable in F.

> In particular, in F, we need to check every number individual to see if
> it satisfies the relationship, and we have no short cut to make this
> operation finite,

Then it doesn't count for jack shit. You might as well resort to a magic
fairy waving a magic wand.

> so we can't prove it. But in Meta-F, we know something
> about the relationship, and are able to prove that no number can satisfy
> the relationship, and do so in a finite number of steps.
>

When we write G in Meta-F to begin with then Meta-F can recognize the
contradiction and report the non-sequitur error.

> Thus, we can prove in Meta-F that G must be true in F.
>
> The sequence of steps in F is infinite, so not a proof in F.
>
> In fact, in Meta-F we are also able to prove that there CAN'T be a
> finite sequence set of steps that prove G true in F.
>
> Thus, with logic in Meta-F, we can prove that, G is True in F and can
> not be proven in F.
>
> You just don't seem to understand how Meta-Logic works. And, it turns
> out, that meta-logic is a very important tool for proving things, so
> this is one of your Kryponites.
>

Actually I understand how Meta-F works better than most. We need no F
and Meta-F we write G in Meta-F to begin with and it rejects G as
semantically erroneous.

Richard Damon

unread,

Apr 25, 2023, 7:56:26 AM4/25/23

to

WHy? Because I agree with that. A Proof needs to be done in a finite
number of steps.

The question is why the infinite number of steps in F that makes G true
don't count for making it true.

Yes, you can't write that out to KNOW it to be true, but that is the
differece between knowledge and fact.

>
> We can imagine an Oracle machine that can complete these proofs in the
> same sort of way that we can imagine a magic fairy that waves a magic
> wand.
>
>> You are just showing you don't understand what you talking about and
>> just spouting word (or symbol) salad.
>>
>> You are oriving you are an IDIOT.
>
> I am seeing these things at a deeper philosophical level than you are. I
> know that is hard to believe.

But not according to the rules of the system you are talking about.

You don't get to change the rules on a system.

>
> You are so sure that I must be wrong that you don't bother to understand
> what I am saying.

No, I understand what you are saying and see where you are WRONG.

Richard Damon

unread,

Apr 25, 2023, 7:56:27 AM4/25/23

to

But you are using the wrong symbol

False -> Donald Trump is the Christ

Is the statement that this is implying.

You seem to have a confusion between the implication operator and the
proves operator.

>
>> Right now, I would say you are to ignorant on that basics of logic to
>> be able to explain, even in basic terms, how it works, you have shown
>> yourself to be that stupid.
>>
>>
>>>
>>> *Correction abolishing the POE nonsense*
>>> Semantic Necessity operator: ⊨□
>>> FALSE ⊨□ FALSE
>>> (P ∧ ¬P) ⊨□ FALSE
>>>
>>
>> So, FULLY define what you mean by that.
>>
>
> The two logic symbols already say semantic necessity, model theory may
> have screwed up the idea of semantics by allowing vacuous truth.
> I must become a master expert of at least basic model theory.

So, you don't understand what it means to DEFINE something.

I guess your theory is dead them.

By your examples, your logical necessisty operator can only establish a
falsehood. Seems about right for the arguments you have been making.

>
>>>
>>>>>
>>>>> Because you are a learned-by-rote person you make sure to never
>>>>> examine
>>>>> whether or not any aspect of math diverges from correct reasoning, you
>>>>> simply assume that math is the gospel even when it contradicts itself.
>>>>
>>>> Nope, I know that with logic, if you follow the rules, you will get
>>>> the correct answer by the rules.
>>>>
>>>
>>> Then you must agree that Trump is the Christ and Trump is Satan both of
>>> those were derived from correct logic.
>>>
>>>> If you break the rules, you have no idea where you will go.
>>>>
>>>> As I have told you before, if you want to see what your "Correct
>>>> Reasoning" can do as a replaceent logic system, you need to start at
>>>> the BEGINNING, and see wht it gets.
>>>>
>>>
>>> I would be happy to talk this through with you.
>>>
>>> The beginning is that
>>>
>>> valid inference an expression X of language L must be a semantic
>>> consequence of its premises in L
>>
>>
>> And what do you mean by "semantic"
>>
>
> What does meaning mean?
> The premise that
> the Moon if made from green cheese ⊨□ The Moon is made from cheese.
>
> All of the conventional logic symbols retain their original meaning.
> Variable are quantified and of a specific type.
> Meaning postulates can axiomatise meaning.

So, you have no "Formal Logic" since you are allowing the addition of
new "axioms" based on "meaning" (which you admit you can't define).

>
> The connection between elements of the proof must be at least as good as
> relevance logic.

So, your logic system is WEAKER than stadard logic. Have you gone back
to the formal proofs that establish fields like Computability Theory and
see what still remains after the requirement of relevance logic?

>
>> because, conventional logic defines semantic consequence as the
>> conclusion must be true if the premise is true.
>>
>> You seem to mean something diffent, but haven't explained what you
>> mean by that.
>>
>
> You never heard of ordinary sound deductive inference?

Yes, I have, but you aren't using it. for instance, you allow a logical
conclusion to be made from an false premise. You seem to want to remove
parts of the logic, but can't actually define what you mean.

>
>>>
>>> sound inference expression X of language L must be a semantic
>>> consequence of the axioms of L.
>>>
>>> For formal systems such as FOL the semantics is mostly the meaning of
>>> the logic symbols.
>>>
>>> These two logic symbols are abolished ⇒ → and replaced with this:
>>> Semantic Necessity operator: ⊨□
>>
>> Why do you need to abolish shows symbols?
>
> They seem to lead to the principle of explosion.

No, they are often used in the proof, but the mere ability to assert
simple logic.

Allowing the following sort of logic is enough:

IT is True that A
Therefore it is True that A | B

and

It is True that A | B
It is False that A
Therefore B must be True.

You can build the principle of explosion from simple logic like that, so
unless you eliminate the "and" and the "or" predicate, you get the

principle of explosion.

>
>> You do understand that the statment that A -> B is equivalent to the
>> asserting of (~A | B) is ALWAYS TRUE (which might be part of your
>> problem, as you don't seem to understand that categorical meaning of
>> ALL and NO), so either you need to outlaw the negation operator, or
>> the or operator to do this.
>>
>> Again, what does "Semantic Necessity" operator mean?
>
> A ⊨□ B the meaning of B is an aspect of the meaning of A.
>

So, you seem to be saying that you will not be able to prove the
pythogrean theorem, since the conclusion doesn't have a "meaning" that
is an aspect of the "meaning" of the conditions.

>
>>
>> Note, one issue with your use of symbols, so many of the symbols can
>> have slightly diffferent meanings based on the context and system you
>> are working in.
>>
>
> I don't see this can you provide examples?
> I am stipulating standard meanings.

WHICH standard meaning.

That is your problem, you don't seem to know enough to understand that
there are shades of meaning in things.

>
>>>
>>>
>>>> To just try to change things at the end is just PROOF that your
>>>> "Correct Reasoning" has to not be based on any real principles of
>>>> logic.
>>>>
>>>
>>> No logic must be based on correct reasoning any logic that prove
>>> Donal Trump is the Christ is incorrect reasoning, thus the POE is
>>> abolished
>>
>> You CAN'T abolish the Principle of Explosion unless you greatly
>> restrict the power of your logic.
>>
>
> My two axioms abolish it neatly. All that I am getting rid of is
> incompleteness and undecidability and I am gaining a universal True(L,x)
> predicate.

Nope, you don't understand how the Principle of Explosion works.

No AXIOMS can affect it, as it comes out of a couple of simple logical
rules.

>
>>>
>>> These two logic symbols are abolished ⇒ → and replaced with this:
>>> Semantic Necessity operator: ⊨□
>>>
>>> Explosions have been abolished
>>
>> Nope.
>>
>>> FALSE ⊨□ FALSE
>>> (P ∧ ¬P) ⊨□ FALSE
>>
>> Again DEFINE this operator, and the words you use to define it.
>>
>
> The semantic meaning of B is necessitated by the semantic meaning of A.
> If I have a dog then I have an animal because a dog is an animal.

So you seem to be limited to categorical logic only. As I have pointed
out, this means you can't prove the Pythagorean theorem, since the
conclusion isn't "semantically" related to the premises.

>
>>>
>>>> Since it is clear that you want to change some of the basics of how
>>>> logic works, you are not allowed to just use ANY of classical logic
>>>> until you actually show what part of it is still usable under your
>>>> system and what changes happen.
>>>>
>>>
>>> Yes lets apply my ideas to FOL. I have already sketched out many
>>> details.
>>
>> Go ahead, try to fully define your ideas.
>>
>> Remember, until you get to supporting the Higher Order Logics, you
>> can't get to the incompleteness, as that has been only established for
>> systems
>
> I have always been talking about HOL in terms of MTT

Which doesn't work.

>
>> with second order logic, which is also needed for the needed
>> properties of the whole numbers. First Order Peano Arithmatic might be
>> complete, but can't be proved (within itself) to be consistent. Second
>> Order Peaano Arithmatic (which adds the principle of Induction) IS
>> incomplete as it supports enough of the natural number to support
>> Godel's proof.
>>
>>>
>>>> Considering your current status, I would start working hard on that
>>>> right away, as with your current reputation, once you go, NO ONE is
>>>> going to want to look at your ideas, because you have done such a
>>>> good job showing that you don't understand how things work.
>>>>
>>>> I haven't been able to get out of you exactly what you want to do
>>>> with your "Correct Reasoning", and until you show a heart to
>>>> actually try to do something constructive with it, and not just use
>>>> it as an excuse for bad logic, I don't care what it might be able to
>>>> do, because, frankly, I don't think you have the intellect to come
>>>> up with something like that.
>>>>
>>>
>>> I showed how the POE is easily abolished.
>>
>> Nope.
>>
>
> If axioms stipulate that explosion cannot occur then it cannot occur.

Nope. Such an axiom just make your system inconsistant and exploded.

Remember, you never NEED to use a given axiom, so adding an axiom can't
keep you from showing something.

>
>>> I showed how Provable(L,x) and True(L,x) are defined.
>>
>> Note clearly. For instance, A statment x is provable or True in a
>> SYSTEM/THEORY (depending on your terminology) and NOT dependent on
>> some other statement in the system, as you definition seemed to imply.
>> You don't "Prove" something based on a statement, but in a System/Theory.
>>
>
> F ⊢ A is used to express (in the meta-level) that A
> is derivable in F, that is, that there is a proof of
> A in F, or, in other words, that A is a theorem of F.
> https://plato.stanford.edu/entries/goedel-incompleteness/

Right, but you have shown examples where you "L" above was a STATEMENT,
not a FIELD/THEORY.

You also don't understand that the difference between Provable and True
is that Provable requires a finite series of steps, but True can be
satisfied by an infinite series of steps.

>
>>>
>>>> But go ahead and prove me wrong, write an actual paper on the basics
>>>> of your "Correct Reasoning" and show how it actually works, and
>>>> compare it to "Classical Logic" and show what is different. Then
>>>> maybe you can start to work on showing it can actually do something
>>>> useful.
>>>>
>>>
>>> I need a dialogue to vet aspects of my ideas.
>>> The key thing that I have not yet filled in is how to specify the
>>> semantics of every FOL expression.
>>>
>>> This semantics seems fully specified:
>>> ∀n ∈ ℕ ∀m ∈ ℕ ((n > m) ⊨□ (n+1 > m))
>>
>> Nope, you need to actually FULLY DEFINE what you mean by your symbols,
>> you can't just rely on refering to classical meaning since you clearly
>> disagree with some of the classical meanings.
>
> in the above case I can switch to conventional symbols without losing
> anything ∀n ∈ ℕ ∀m ∈ ℕ ((n > m) ⊢ (n+1 > m))

Except that is a domain error, as the ⊢ operator needs a field/theory as
its left operand.

>
> Implication does a poor job of if-then
> p---q---(p ⇒ q)---(if p then q)
> T---T------T------------T
> T---F------F------------F
> F---T------T------------undefined

T
> F---F------T------------undefined
T

Not undefined at all.

From falsity, anything follows.

The statement "If false then B" makes no assertion at all for this case.
Think of your programming languages, a false condition in an if
statement ignores the conditional statements after it.

>
>> You seem to have some disjoint ideas, but seem to be unable to come up
>> with a cohesive whole. You use words that you don't seem to be able to
>> actually fully define.
>>
>> Since you are trying to reject some of the basics of classical logic,
>> you need to FULLY define how your logic works. Name ALL the basic
>> operation that you allow. Do you allow "Not", "Or", "And", "Equals",
>> etc. What are your rules for logical inference. How do you ACTUALLY
>> prove a statement given a set of "Truthmakers".
>>
>
> All of the details that I provided are all of the detail that I know
> right now.

Which is your problem. You seem incapable of understanding how the
changes you want to make affect the whole system, because you don't know
it well enough,

>
>> Remember, if you want to reject classical logic, you can't use it to
>> define your system.
>
> I can take it as a basis and add and subtract things from it
>

And if you change it at all, you need to go back and see what all the
effects are. You can't assume the tree remains the same if you change
its roots.

Richard Damon

unread,

Apr 25, 2023, 7:56:29 AM4/25/23

to

The aren't, by DEFINITION. It is a basic piece of Knowledge theory. You
can only know something showable in finite steps since we are only finite.

> When you understood rather than ignore that a proof of G in F requires a
> sequence of inference steps in F that prove that they themselves don't
> exist then and only then is it possible to understand that a proof of G
> in F cannot be done only because it is self-contradictory.
>
> Ignoring this doesn't make it go away. Assuming this it is not needed
> requires another way of proving in F that G cannot be proved in F.
> An infinite proof is always impossible so that way is out.

And you seem to not understand how knowledge works.

G can not be proven in F, because F doesn't have the tools to allow us
to construct the needed finite proof.

G can be TRUE in F, as Truth doesn't require that it be knowable in the
field, just that its truth is established by a, possible infinite, set
of connections to the truth makers.

G can be KNOWN True in F, because it can be proven in Meta-F, which has
additional knowledge about F, that allows us to perform in finite steps
in Meta-F things that take an infinte number of steps in F. Because
Meta-F knows about F, it can show what knowledge in Meta-F can be
transfered to include in F.

By the same token, we can show in Meta-F that G can not be proven in F,
and that this Knowledge can be transfered to include in F

>
>>
>> With a finite number of steps in Meta-F, we can prove that the
>> infinite number of steps in F exist and are true.
>>
>
> That is cheating. The purpose here is to see WHY rather than merely THAT
> G is unprovable in F.
>

G is unprovable, because if you could prove it, then it couldn't be true.

WHY is a much harder questing that IS.

>> In particular, in F, we need to check every number individual to see
>> if it satisfies the relationship, and we have no short cut to make
>> this operation finite,
>
> Then it doesn't count for jack shit. You might as well resort to a magic
> fairy waving a magic wand.

Why? We have shown in Meta-F that an infinite sequence of steps exist in
F to show that G is true.

You just are too stupid to understand it.

>
>> so we can't prove it. But in Meta-F, we know something about the
>> relationship, and are able to prove that no number can satisfy the
>> relationship, and do so in a finite number of steps.
>>
>
> When we write G in Meta-F to begin with then Meta-F can recognize the
> contradiction and report the non-sequitur error.

Nope, we find that G is True in F and Meta-F, not provable in F, but
provable in Meta-F.

>
>> Thus, we can prove in Meta-F that G must be true in F.
>>
>> The sequence of steps in F is infinite, so not a proof in F.
>>
>> In fact, in Meta-F we are also able to prove that there CAN'T be a
>> finite sequence set of steps that prove G true in F.
>>
>> Thus, with logic in Meta-F, we can prove that, G is True in F and can
>> not be proven in F.
>>
>> You just don't seem to understand how Meta-Logic works. And, it turns
>> out, that meta-logic is a very important tool for proving things, so
>> this is one of your Kryponites.
>>
>
> Actually I understand how Meta-F works better than most. We need no F
> and Meta-F we write G in Meta-F to begin with and it rejects G as
> semantically erroneous.
>

Which shows you don't understand Meta-F.

PERIOD.

A wise man knows what he doesn't know.

A fool thinks he knows what he doesn't know.

olcott

unread,

Apr 26, 2023, 12:39:01 AM4/26/23

to

Infinite proof are not allowed: Because they can't possibly ever occur.

>>
>> We can imagine an Oracle machine that can complete these proofs in the
>> same sort of way that we can imagine a magic fairy that waves a magic
>> wand.
>>
>>> You are just showing you don't understand what you talking about and
>>> just spouting word (or symbol) salad.
>>>
>>> You are oriving you are an IDIOT.
>>
>> I am seeing these things at a deeper philosophical level than you are.
>> I know that is hard to believe.
>
> But not according to the rules of the system you are talking about.
>
> You don't get to change the rules on a system.
>

YES I DO !!!
My whole purpose to provide the *correct reasoning* foundation such that
formal systems can be defined without undecidability or undefinability,
or inconsistently.

>>
>> You are so sure that I must be wrong that you don't bother to understand
>> what I am saying.
>
> No, I understand what you are saying and see where you are WRONG.
>

Yet will continue to dodge this because you are only bluffing.
You cannot even begin to show that I am wrong.

>>
>> It seem that the time has come for me to spend the little time that it
>> takes to understand the technical details of Gödel's proof.
>>
>> I am estimating that have very good understanding of the preface to
>> the proof and the SEP article should provide this.
>>
>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>
>>
>

olcott

unread,

Apr 26, 2023, 2:07:53 AM4/26/23

to

FALSE Proves that Donald Trump is the Christ

It is jack ass nonsense like this that proves the
principle of explosion is nothing even kludge

> False -> Donald Trump is the Christ
>
>

Semantic Necessity operator: ⊨□

FALSE ⊨□ FALSE // POE abolished
(P ∧ ¬P) ⊨□ FALSE // POE abolished

From False only False follows.
From Contradiction only False follows.

> Is the statement that this is implying.
>

I reject implication and replace it with this
Semantic Necessity operator: ⊨□

Or this Archimedes Plutonium's:
If--> then
T --> T = T
T --> F = F
F --> T = U (unknown or uncertain)
F --> F = U (unknown or uncertain)

> You seem to have a confusion between the implication operator and the
> proves operator.
>

I meant the stronger meaning The best hing to use might be :
Archimedes Plutonium's: If--> then (see above).

The whole idea is to formalize the notion of correct reasoning and use
this model to correct the issues with formal logic.

>>
>>> Right now, I would say you are to ignorant on that basics of logic to
>>> be able to explain, even in basic terms, how it works, you have shown
>>> yourself to be that stupid.
>>>
>>>
>>>>
>>>> *Correction abolishing the POE nonsense*
>>>> Semantic Necessity operator: ⊨□
>>>> FALSE ⊨□ FALSE
>>>> (P ∧ ¬P) ⊨□ FALSE
>>>>
>>>
>>> So, FULLY define what you mean by that.
>>>
>>
>> The two logic symbols already say semantic necessity, model theory may
>> have screwed up the idea of semantics by allowing vacuous truth.
>> I must become a master expert of at least basic model theory.
>
> So, you don't understand what it means to DEFINE something.
>
> I guess your theory is dead them.
>

Vacuous truth is eliminated by requiring every variable to be quantified.

> By your examples, your logical necessisty operator can only establish a
> falsehood. Seems about right for the arguments you have been making.
>

Try and explain what you mean by that.

The big picture of what I am doing is defining the foundation of the
formalization of correct reasoning.

I am doing this on the basis of existing systems, then adding, removing
or changing things as needed to conform the system to correct reasoning.

When I am redefining current systems so that they conform to correct
reasoning I make minimal changes to existing notions.

>>
>> The connection between elements of the proof must be at least as good as
>> relevance logic.
>
> So, your logic system is WEAKER than stadard logic. Have you gone back
> to the formal proofs that establish fields like Computability Theory and
> see what still remains after the requirement of relevance logic?
>

No it is not and you cannot show that it is.

>
>>
>>> because, conventional logic defines semantic consequence as the
>>> conclusion must be true if the premise is true.
>>>
>>> You seem to mean something diffent, but haven't explained what you
>>> mean by that.
>>>
>>
>> You never heard of ordinary sound deductive inference?
>
> Yes, I have, but you aren't using it. for instance, you allow a logical
> conclusion to be made from an false premise.

False does Derive False, Please try to back up all of your assertions
with reasoning. For statements like the one above you need a time
stamped quote of exactly what I said.

> You seem to want to remove
> parts of the logic, but can't actually define what you mean.
>
>

I have defined many key aspects many times: True/False/Non Sequitur
abolishes incompleteness and undefinability while maintaining consistency.

>>
>>>>
>>>> sound inference expression X of language L must be a semantic
>>>> consequence of the axioms of L.
>>>>
>>>> For formal systems such as FOL the semantics is mostly the meaning
>>>> of the logic symbols.
>>>>
>>>> These two logic symbols are abolished ⇒ → and replaced with this:
>>>> Semantic Necessity operator: ⊨□
>>>
>>> Why do you need to abolish shows symbols?
>>
>> They seem to lead to the principle of explosion.
>
> No, they are often used in the proof, but the mere ability to assert
> simple logic.
>
> Allowing the following sort of logic is enough:
>
> IT is True that A
> Therefore it is True that A | B
>
> and
>
> It is True that A | B
> It is False that A
> Therefore B must be True.
>
> You can build the principle of explosion from simple logic like that, so
> unless you eliminate the "and" and the "or" predicate, you get the
> principle of explosion.
>

Show me how and I will point out how it is fixed.

>
>>
>>> You do understand that the statment that A -> B is equivalent to the
>>> asserting of (~A | B) is ALWAYS TRUE (which might be part of your
>>> problem, as you don't seem to understand that categorical meaning of
>>> ALL and NO), so either you need to outlaw the negation operator, or
>>> the or operator to do this.
>>>
>>> Again, what does "Semantic Necessity" operator mean?
>>
>> A ⊨□ B the meaning of B is an aspect of the meaning of A.
>>
>
> So, you seem to be saying that you will not be able to prove the
> pythogrean theorem, since the conclusion doesn't have a "meaning" that
> is an aspect of the "meaning" of the conditions.
>

It has plenty of geometric meaning.

>>
>>>
>>> Note, one issue with your use of symbols, so many of the symbols can
>>> have slightly diffferent meanings based on the context and system you
>>> are working in.
>>>
>>
>> I don't see this can you provide examples?
>> I am stipulating standard meanings.
>
> WHICH standard meaning.
>

All of the logic symbols have their standard meaning.

> That is your problem, you don't seem to know enough to understand that
> there are shades of meaning in things.
>
>>
>>>>
>>>>
>>>>> To just try to change things at the end is just PROOF that your
>>>>> "Correct Reasoning" has to not be based on any real principles of
>>>>> logic.
>>>>>
>>>>
>>>> No logic must be based on correct reasoning any logic that prove
>>>> Donal Trump is the Christ is incorrect reasoning, thus the POE is
>>>> abolished
>>>
>>> You CAN'T abolish the Principle of Explosion unless you greatly
>>> restrict the power of your logic.
>>>
>>
>> My two axioms abolish it neatly. All that I am getting rid of is
>> incompleteness and undecidability and I am gaining a universal True(L,x)
>> predicate.
>
> Nope, you don't understand how the Principle of Explosion works.
>

These are stipulated

FALSE ⊨□ FALSE
(P ∧ ¬P) ⊨□ FALSE

> No AXIOMS can affect it,

That sounds ridiculous to me. Can you show what you mean?

> as it comes out of a couple of simple logical
> rules.
>
>>
>>>>
>>>> These two logic symbols are abolished ⇒ → and replaced with this:
>>>> Semantic Necessity operator: ⊨□
>>>>
>>>> Explosions have been abolished
>>>
>>> Nope.
>>>
>>>> FALSE ⊨□ FALSE
>>>> (P ∧ ¬P) ⊨□ FALSE
>>>
>>> Again DEFINE this operator, and the words you use to define it.
>>>
>>
>> The semantic meaning of B is necessitated by the semantic meaning of A.
>> If I have a dog then I have an animal because a dog is an animal.
>
> So you seem to be limited to categorical logic only. As I have pointed
> out, this means you can't prove the Pythagorean theorem, since the
> conclusion isn't "semantically" related to the premises.
>

I am simply using that as a concrete starting point to show one example
of how it works.

>>
>>>>
>>>>> Since it is clear that you want to change some of the basics of how
>>>>> logic works, you are not allowed to just use ANY of classical logic
>>>>> until you actually show what part of it is still usable under your
>>>>> system and what changes happen.
>>>>>
>>>>
>>>> Yes lets apply my ideas to FOL. I have already sketched out many
>>>> details.
>>>
>>> Go ahead, try to fully define your ideas.
>>>
>>> Remember, until you get to supporting the Higher Order Logics, you
>>> can't get to the incompleteness, as that has been only established
>>> for systems
>>
>> I have always been talking about HOL in terms of MTT
>
> Which doesn't work.

MTT does work. The earlier version translated even very complex logic
expressions into the equivalent direct graph.

I think that the current version only does a parse tree.

Richard Damon

unread,

Apr 26, 2023, 8:07:38 AM4/26/23

to

That isn't what the statment actually means, so you are just stupid.

>
> It is jack ass nonsense like this that proves the
> principle of explosion is nothing even kludge

Right, false doesn't PROVE anything, but implies anything,

The difference is "Proves" takes a Field as its input, so "False" isn't
a field.

Implication takes a statement as its input, so can take false.

Since False implies eithert true or false, as false statement can imply
anything,.

>
>
>> False -> Donald Trump is the Christ
>>
>>
>
> Semantic Necessity operator: ⊨□
> FALSE ⊨□ FALSE // POE abolished

So, what do you actually mean by that?

> (P ∧ ¬P) ⊨□ FALSE // POE abolished
>
> From False only False follows.
> From Contradiction only False follows.
>
>> Is the statement that this is implying.
>>
>
> I reject implication and replace it with this
> Semantic Necessity operator: ⊨□
>
> Or this Archimedes Plutonium's:
> If--> then
> T --> T = T
> T --> F = F
> F --> T = U (unknown or uncertain)
> F --> F = U (unknown or uncertain)

So, you don't understand how a truth table works or how logic works with
them.

If that WAS the truth table for implication, then no implication would
be valid unless its premise was a tautology, something true in all the
models of the system, so if its own truth is 'uncertain' for some cases,
it can't be taken as true.

Note, A -> B, with A false, just means that we are uncertain about the
truth of B, as by the truth table, B could be either True or False.

>
>> You seem to have a confusion between the implication operator and the
>> proves operator.
>>
>
> I meant the stronger meaning The best hing to use might be :
> Archimedes Plutonium's: If--> then (see above).

So, you ARE confused about the meaning of the implication operator.

>
> The whole idea is to formalize the notion of correct reasoning and use
> this model to correct the issues with formal logic.
>

And if you want to do that, you need to go to the beginning and start there.

You can't change it later down the chain.

>>>
>>>> Right now, I would say you are to ignorant on that basics of logic
>>>> to be able to explain, even in basic terms, how it works, you have
>>>> shown yourself to be that stupid.
>>>>
>>>>
>>>>>
>>>>> *Correction abolishing the POE nonsense*
>>>>> Semantic Necessity operator: ⊨□
>>>>> FALSE ⊨□ FALSE
>>>>> (P ∧ ¬P) ⊨□ FALSE
>>>>>
>>>>
>>>> So, FULLY define what you mean by that.
>>>>
>>>
>>> The two logic symbols already say semantic necessity, model theory may
>>> have screwed up the idea of semantics by allowing vacuous truth.
>>> I must become a master expert of at least basic model theory.
>>
>> So, you don't understand what it means to DEFINE something.
>>
>> I guess your theory is dead them.
>>
>
> Vacuous truth is eliminated by requiring every variable to be quantified.

So, since you can't actually define any of your terms, your whole system
is eliminated.

>
>> By your examples, your logical necessisty operator can only establish
>> a falsehood. Seems about right for the arguments you have been making.
>>
>
> Try and explain what you mean by that.

You have only defined it for case where the input is FALSE.

>
> The big picture of what I am doing is defining the foundation of the
> formalization of correct reasoning.

So DEFINE it, not just talk about it.

>
> I am doing this on the basis of existing systems, then adding, removing
> or changing things as needed to conform the system to correct reasoning.

Which doesn't work, as everything that you take might (and likely has
been) established by rules you reject.

You have no idea what you can actually use are being derived from your
logic system, as you have never actually applied it to the base.

But claim to make major changes to their operation, so you have no idea
what parts of the curret system are still valid.

You are just building your argument on a lie, the lie that you are
working in a logic system build on your rules.

>
>>>
>>> The connection between elements of the proof must be at least as good as
>>> relevance logic.
>>
>> So, your logic system is WEAKER than stadard logic. Have you gone back
>> to the formal proofs that establish fields like Computability Theory
>> and see what still remains after the requirement of relevance logic?
>>
>
> No it is not and you cannot show that it is.

You are disallowing proofs that are currently allowed.

That makes it weaker.

>
>>
>>>
>>>> because, conventional logic defines semantic consequence as the
>>>> conclusion must be true if the premise is true.
>>>>
>>>> You seem to mean something diffent, but haven't explained what you
>>>> mean by that.
>>>>
>>>
>>> You never heard of ordinary sound deductive inference?
>>
>> Yes, I have, but you aren't using it. for instance, you allow a
>> logical conclusion to be made from an false premise.
>
> False does Derive False, Please try to back up all of your assertions
> with reasoning. For statements like the one above you need a time
> stamped quote of exactly what I said.

But you claim something to be TRUE based on a false preise.

Maybe you don't even understand your own arguement.

>
>
>> You seem to want to remove parts of the logic, but can't actually
>> define what you mean.
>>
>>
>
> I have defined many key aspects many times: True/False/Non Sequitur
> abolishes incompleteness and undefinability while maintaining consistency.

Nope, you have scattered ideas, but not actually establish how to
actually build and use your system.

The likely issue is you just don't understand how logic works well
enough to understand what you need to define.

>
>>>
>>>>>
>>>>> sound inference expression X of language L must be a semantic
>>>>> consequence of the axioms of L.
>>>>>
>>>>> For formal systems such as FOL the semantics is mostly the meaning
>>>>> of the logic symbols.
>>>>>
>>>>> These two logic symbols are abolished ⇒ → and replaced with this:
>>>>> Semantic Necessity operator: ⊨□
>>>>
>>>> Why do you need to abolish shows symbols?
>>>
>>> They seem to lead to the principle of explosion.
>>
>> No, they are often used in the proof, but the mere ability to assert
>> simple logic.
>>
>> Allowing the following sort of logic is enough:
>>
>> IT is True that A
>> Therefore it is True that A | B
>>
>> and
>>
>> It is True that A | B
>> It is False that A
>> Therefore B must be True.
>>
>> You can build the principle of explosion from simple logic like that,
>> so unless you eliminate the "and" and the "or" predicate, you get the
>> principle of explosion.
>>
>
> Show me how and I will point out how it is fixed.

So, you can't see it from the above. If we can prove that statement A is
both True and False, which is the meaning of proving a contradiction, we
can use the above logic to prove B is true, no matter what it is.

Having proved A, we can prove that A | B is true, and if A | B is true,
and A is false, B must be True.

Either you can't have compound terms using "and" or "or", or you can't
allow contradictions.

>
>>
>>>
>>>> You do understand that the statment that A -> B is equivalent to the
>>>> asserting of (~A | B) is ALWAYS TRUE (which might be part of your
>>>> problem, as you don't seem to understand that categorical meaning of
>>>> ALL and NO), so either you need to outlaw the negation operator, or
>>>> the or operator to do this.
>>>>
>>>> Again, what does "Semantic Necessity" operator mean?
>>>
>>> A ⊨□ B the meaning of B is an aspect of the meaning of A.
>>>
>>
>> So, you seem to be saying that you will not be able to prove the
>> pythogrean theorem, since the conclusion doesn't have a "meaning" that
>> is an aspect of the "meaning" of the conditions.
>>
>
> It has plenty of geometric meaning.

Nothing from the definitions of the terms. Yes, from what can be derived
from it, but not from itself.

>
>>>
>>>>
>>>> Note, one issue with your use of symbols, so many of the symbols can
>>>> have slightly diffferent meanings based on the context and system
>>>> you are working in.
>>>>
>>>
>>> I don't see this can you provide examples?
>>> I am stipulating standard meanings.
>>
>> WHICH standard meaning.
>>
>
> All of the logic symbols have their standard meaning.

WHICH standard meaning.

>
>> That is your problem, you don't seem to know enough to understand that
>> there are shades of meaning in things.
>>
>>>
>>>>>
>>>>>
>>>>>> To just try to change things at the end is just PROOF that your
>>>>>> "Correct Reasoning" has to not be based on any real principles of
>>>>>> logic.
>>>>>>
>>>>>
>>>>> No logic must be based on correct reasoning any logic that prove
>>>>> Donal Trump is the Christ is incorrect reasoning, thus the POE is
>>>>> abolished
>>>>
>>>> You CAN'T abolish the Principle of Explosion unless you greatly
>>>> restrict the power of your logic.
>>>>
>>>
>>> My two axioms abolish it neatly. All that I am getting rid of is
>>> incompleteness and undecidability and I am gaining a universal True(L,x)
>>> predicate.
>>
>> Nope, you don't understand how the Principle of Explosion works.
>>
>
> These are stipulated
> FALSE ⊨□ FALSE
> (P ∧ ¬P) ⊨□ FALSE

SO you don't understand how the principle of Explosion works.

>
>> No AXIOMS can affect it,
>
>
> That sounds ridiculous to me. Can you show what you mean?

A proof only uses the axioms it uses. Adding another axiom has no affect
on that proof.

So, trying to add as a axiom that POE doesn't exist, doesn't affect the
proof that POE exists.

Thus, adding the axiom just makes the system inconsistent, and thus POE
is in full affect on the system.

>
>> as it comes out of a couple of simple logical rules.
>>
>>>
>>>>>
>>>>> These two logic symbols are abolished ⇒ → and replaced with this:
>>>>> Semantic Necessity operator: ⊨□
>>>>>
>>>>> Explosions have been abolished
>>>>
>>>> Nope.
>>>>
>>>>> FALSE ⊨□ FALSE
>>>>> (P ∧ ¬P) ⊨□ FALSE
>>>>
>>>> Again DEFINE this operator, and the words you use to define it.
>>>>
>>>
>>> The semantic meaning of B is necessitated by the semantic meaning of A.
>>> If I have a dog then I have an animal because a dog is an animal.
>>
>> So you seem to be limited to categorical logic only. As I have pointed
>> out, this means you can't prove the Pythagorean theorem, since the
>> conclusion isn't "semantically" related to the premises.
>>
>
> I am simply using that as a concrete starting point to show one example
> of how it works.

SO develop it there, but realize that categorical logic is weaker that
even frist order logic, so can't handle concepts used in systems with
higher order logic, like where Halting and Incompleteness live.

>
>>>
>>>>>
>>>>>> Since it is clear that you want to change some of the basics of
>>>>>> how logic works, you are not allowed to just use ANY of classical
>>>>>> logic until you actually show what part of it is still usable
>>>>>> under your system and what changes happen.
>>>>>>
>>>>>
>>>>> Yes lets apply my ideas to FOL. I have already sketched out many
>>>>> details.
>>>>
>>>> Go ahead, try to fully define your ideas.
>>>>
>>>> Remember, until you get to supporting the Higher Order Logics, you
>>>> can't get to the incompleteness, as that has been only established
>>>> for systems
>>>
>>> I have always been talking about HOL in terms of MTT
>>
>> Which doesn't work.
>
> MTT does work. The earlier version translated even very complex logic
> expressions into the equivalent direct graph.
>
> I think that the current version only does a parse tree.

Nope, it doesn't work, because it violates the basic rules. You don't
see it because you don't understand how logic works.

Richard Damon

unread,

Apr 26, 2023, 8:07:44 AM4/26/23

How about this one?
Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))

>>
>> Requires formal systems to do the logically impossible:
>> to prove self-contradictory expressions of language.
>
> Nope. You don't understand what the words mean.

That part I have correctly and Gödel acknowledged the self-contradictory
expressions ... can likewise be used for a similar undecidability proof...

...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...
(Gödel 1931:40)

Antinomy
...term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy

> Remember, incompleteness only happens if a TRUE statement can't be
> proven, an actual "self-contradictory" statment won't be true.
>

You have that incorrectly too.
When G asserts its own unprovability in F the proof of G in F requires a

sequence of inference steps in F that prove that they themselves do not

exist.

Gödel’s Theorem, as a simple corollary of Proposition VI (p. 57) is
frequently called, proves that there are arithmetical propositions which
are undecidable (i.e. neither provable nor disprovable) within their
arithmetical system, and the proof proceeds by actually specifying such
a proposition, namely the proposition g expressed by the formula to
which “17 Gen r” refers (p. 58). g is an arithmetical proposition; but
the proposition that g is undecidable within the system is not an
arithmetical proposition, since it is concerned with provability within
an arithmetical system, and this is a meta-arithmetical and not an
arithmetical notion. Gödel’s Theorem is thus a result which belongs not
to mathematics but to metamathematics, the name given by Hilbert to the
study of rigorous proof in mathematics and symbolic logic

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

> (or is FALSE and can't be proven to be false, which is basically the
> same thing).
>
>>
>> So formal systems are "incomplete" in the same sense that we determine
>> that a baker that cannot bake a proper angel food cake using ordinary
>> red house bricks as the only ingredient lacks sufficient baking skill.
>>
>
> Nope, becuase they are only inclomplete if a statement that is TRUE
> can't be proven.
>

The liar paradox is self contradictory when applied to itself is not
self-contradictory when applied to another different instance of itself.

This sentence is not true: "This sentence is not true"

inner one is neither true nor false
outer one is true because the inner one is neither true nor false

When G asserts its own unprovability in F the proof of G in F requires a

sequence of inference steps in F that prove that they themselves do not

exist. metamathematics, can see that G cannot be proved in F.

> You just don't understand that,
>

Richard Damon

unread,

Apr 28, 2023, 7:40:35 AM4/28/23

to

On 4/28/23 12:23 AM, olcott wrote:
> On 4/27/2023 9:41 PM, Richard Damon wrote:
>> On 4/27/23 9:07 PM, olcott wrote:
>>
>>> The standard definition of mathematical incompleteness:
>>> Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>
>> Remember, that if φ ∈ F then φ has a defined truth value in F, it is
>> either True of False, and thus can't be the "Liar's Paradox".
>>
>>
>
> How about this one?
> Incomplete(T) ↔ ∃φ ∈ WFF(F) ((T ⊬ φ) ∧ (T ⊬ ¬φ))

You use of terms that you do not define doesn't help you.

Incomplete means, in actual words, that there exists a true statement in
F that can not be proven in F, or similarly a False statement in F that
can not be disproven (proven to be false).

Incompleteness is NOT about statements that meet the "syntax" of F, but
might not actually be Truthbearers. Of course you can't prove or refute
a non-truthbearer (at best you might be able to show it is a
non-truthbearer).

Trying to use ANY other definition that isn't actually equivalent is
just proof that you don't understand the rules of logic and have fallen
to a strawman.

>
>>>
>>> Requires formal systems to do the logically impossible:
>>> to prove self-contradictory expressions of language.
>>
>> Nope. You don't understand what the words mean.
>
> That part I have correctly and Gödel acknowledged the self-contradictory
> expressions ... can likewise be used for a similar undecidability proof...

And none of those are directly about G in F.

>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...
> (Gödel 1931:40)

Yep, you can use the FORM of any epistemolgoical antinomy, converting it
from a statement about its own truth to being about its own provability,
to get a similar proof.

>
> Antinomy
> ...term often used in logic and epistemology, when describing a paradox
> or unresolvable contradiction.
> https://www.newworldencyclopedia.org/entry/Antinomy
>
>> Remember, incompleteness only happens if a TRUE statement can't be
>> proven, an actual "self-contradictory" statment won't be true.
>>
>
> You have that incorrectly too.
> When G asserts its own unprovability in F the proof of G in F requires a
> sequence of inference steps in F that prove that they themselves do not
> exist.

But G DOESN'T "asserts its own unprovability in F", and G is not proven
"in F".

You statement just shows that you don't understand the proof and are
totally missing that almost all of the paper is written from the aspect
of Meta-F.

>
> Gödel’s Theorem, as a simple corollary of Proposition VI (p. 57) is
> frequently called, proves that there are arithmetical propositions which
> are undecidable (i.e. neither provable nor disprovable) within their
> arithmetical system, and the proof proceeds by actually specifying such
> a proposition, namely the proposition g expressed by the formula to
> which “17 Gen r” refers (p. 58). g is an arithmetical proposition; but
> the proposition that g is undecidable within the system is not an
> arithmetical proposition, since it is concerned with provability within
> an arithmetical system, and this is a meta-arithmetical and not an
> arithmetical notion. Gödel’s Theorem is thus a result which belongs not
> to mathematics but to metamathematics, the name given by Hilbert to the
> study of rigorous proof in mathematics and symbolic logic
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Yes, Hilbert had simillar errors in logic, which he, I believe,
eventaully realized. Yes, much of Godel's proof could be described as
"meta-mathematics", but that meta- shows that IN MATHEMATICS ITSELF,
there exist propositions that are true but can not be proven within
mathematics. Thus, mathematics meets the requirements to be called
"incomplete"

>
>> (or is FALSE and can't be proven to be false, which is basically the
>> same thing).
>>
>>>
>>> So formal systems are "incomplete" in the same sense that we determine
>>> that a baker that cannot bake a proper angel food cake using ordinary
>>> red house bricks as the only ingredient lacks sufficient baking skill.
>>>
>>
>> Nope, becuase they are only inclomplete if a statement that is TRUE
>> can't be proven.
>>
>
> The liar paradox is self contradictory when applied to itself is not
> self-contradictory when applied to another different instance of itself.

So, you don't understand what the "Liar Paradox" actually is. It is, and
only is, a statement that asserts ITS OWN falsehood. It can't refer to a
"different instance" as either that other isn't "itself", so refering to
it makes this statement not the liar's paradox, or it actually IS
itself, and thus must have the same truth value. You don't seem to
understand the fundamental rule that if a copy of the statement is
considered to be "the same statement", that all those copies must. by
definition. have the same truth value.

>
> This sentence is not true: "This sentence is not true"
> inner one is neither true nor false
> outer one is true because the inner one is neither true nor false

But isn't the liar's paradox.

Again, you show you don't understand the actual meaning of the words.

>
> When G asserts its own unprovability in F the proof of G in F requires a
> sequence of inference steps in F that prove that they themselves do not
> exist. metamathematics, can see that G cannot be proved in F.

Exept that Godel's G doesn't "assert is own unprovability in F" nor is
"G proved in F" (in fact, Godel shows such a proof is impossible).

metamathematics can PROVE that Godel's statement G is TRUE IN
MATHEMATICS, but not provable there.

You don't seem to understand how meta-systems work and how they can
actaully prove things about the system they are a meta- for.

If you "Correct Reasoning" can't handle meta-logic, then you aren't
going to be able to prove much in it, as most major proofs actually use
meta-logic.

Richard Damon

unread,

Apr 28, 2023, 7:40:38 AM4/28/23

to

So, you still don't understand the statement because you are just using
(never actually) learned by rote transformations.

Just shows your ignorance.

Richard Damon

unread,

Apr 28, 2023, 7:40:38 AM4/28/23

to

On 4/28/23 12:00 AM, olcott wrote:

Nope, in this case ⊥ means contradiction (which is actually what falsum
implies, not just "false")

As I have pointed out, you need to be careful with symbols because you
don't seem to understand the actual breadth of their meaning.

Note, it seems you don't even understand the English, because a
"falsehood" isn't just the value of "false".