On 1/14/2023 5:42 PM, Richard Damon wrote:
> On 1/14/23 6:19 PM, olcott wrote:
>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>> On 1/14/23 5:31 PM, olcott wrote:
>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>> How does the formal system know that an expression of language of
>>>>>> this
>>>>>> formal system is true unless this expression of language has a
>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>
>>>>>>
>>>>>
>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>
>>>>
>>>> So PA has no idea that:
>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>
>>>
>>> Why do you say that.
>>>
>>> Just because truth doesn't NEED to be proven for it to be true,
>>> doesn't mean it can't be.
>>>
>>> In fact, your statement just comes out of a simple application of the
>>> addition AXIOMS of PA.
>>>
>>> a + 0 = a
>>> a + Successor(b) = Successor(a + b)
>>>
>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>
>>
>> Unless a formal system has a syntactic connection from an expression of
>> its language to its truth maker axioms the expression is untrue in that
>> formal system.
>
> Right, but the connection can be infinite in length, and thus not provable.

Thus not a connection within the formal system only connection outside
of the formal system.

>>
>> Try and show an expression of language that is true in a formal system
>> (not just true somewhere else) that does not have any connection to
>> truth maker axioms in this formal system. You must show why it is true
>> in this formal system not merely that it is true somewhere else.
>>
>
> The connection might be infinite, and thus not SHOWABLE as a proof
> strictly in the formal system.
>
> If the connection exists as an infinite connection within the system,
> then it is TRUE in the system.
>
> Note, that if there is such an infinite connection, which thus can not
> be proven within the formal system, it is still possible, that another
> system, related to that system, with more knowledge, might be able to
> show that there does exist within the original formal system such an
> infinte connection.
>
> This is what happens to G in F and meta-F
>

This is you fundamental misunderstanding about the way that truth works.
If the original system cannot possibly show that an expression of
language is true then it is not true in that formal system.

True means that there is a connection to truth maker axioms. True in a
formal system means a connection to truth maker axioms in this formal
system.

To do is the way that you are doing it would mean that homeless Bill is
not homeless because some entirely different person is not homeless.

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

On 1/14/23 6:58 PM, olcott wrote:
> On 1/14/2023 5:42 PM, Richard Damon wrote:
>> On 1/14/23 6:19 PM, olcott wrote:
>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>> How does the formal system know that an expression of language of
>>>>>>> this
>>>>>>> formal system is true unless this expression of language has a
>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>
>>>>>
>>>>> So PA has no idea that:
>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>
>>>>
>>>> Why do you say that.
>>>>
>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>> doesn't mean it can't be.
>>>>
>>>> In fact, your statement just comes out of a simple application of
>>>> the addition AXIOMS of PA.
>>>>
>>>> a + 0 = a
>>>> a + Successor(b) = Successor(a + b)
>>>>
>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>
>>>
>>> Unless a formal system has a syntactic connection from an expression of
>>> its language to its truth maker axioms the expression is untrue in that
>>> formal system.
>>
>> Right, but the connection can be infinite in length, and thus not
>> provable.
>
> Thus not a connection within the formal system only connection outside
> of the formal system.

Why? Where does it say "FINITE" connection needed. An infinite set of
connections within the formal system IS a connection.

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

You are just speaking your natural language, the language of LIES.

Do you somehow mistakenly think that Formal Logic systems are limited to
being finite? The difference between a Formal system and a non-Formal
System is that in a Formal Logic System you begin with the
Formalizatioin, the explicit stating of the rules and axioms that it is
built on.

Unless the formal system EXPLICITLY restricts itself to finite linkage,
by adding an axiom that the only things that are true are those that are
provable, such a rule does not exist, and if you add such a rule to a
system, you limit its power or it becomes inconsistent.

>
>>>
>>> Try and show an expression of language that is true in a formal system
>>> (not just true somewhere else) that does not have any connection to
>>> truth maker axioms in this formal system. You must show why it is true
>>> in this formal system not merely that it is true somewhere else.
>>>
>>
>> The connection might be infinite, and thus not SHOWABLE as a proof
>> strictly in the formal system.
>>
>> If the connection exists as an infinite connection within the system,
>> then it is TRUE in the system.
>>
>> Note, that if there is such an infinite connection, which thus can not
>> be proven within the formal system, it is still possible, that another
>> system, related to that system, with more knowledge, might be able to
>> show that there does exist within the original formal system such an
>> infinte connection.
>>
>> This is what happens to G in F and meta-F
>>
>
> This is you fundamental misunderstanding about the way that truth works.
> If the original system cannot possibly show that an expression of
> language is true then it is not true in that formal system.

Nope. SHOWING (as in proving) is different than BEING.

G is true in F because NO Natural Number g does meet the requirment,
thus it is TRUE.

The fact that no finite proof of this exist is irrelevent.

>
> True means that there is a connection to truth maker axioms. True in a
> formal system means a connection to truth maker axioms in this formal
> system.

Right, and there is. Each Natural Number can be individually proven in a
finite number of steps that it does not meet the requirement.

This finite operation needs to be repeated a countable infinite times,
once for each number, thus making the statement TRUE, but not provable.

It is basic operation of logic that if Every element of a set fails to
meet a requirement then NO element of the set meets the requirement.

That is basic categorical logic. That logic holds even for coutable
infinite sets.

>
> To do is the way that you are doing it would mean that homeless Bill is
> not homeless because some entirely different person is not homeless.
>

Nope. Red Herring.

If you claim me wrong, point out the number that meets the requirements.

You are just PROVING you don;'t understand actual logic.

On 1/14/2023 6:30 PM, Richard Damon wrote:
> On 1/14/23 6:58 PM, olcott wrote:
>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>> On 1/14/23 6:19 PM, olcott wrote:
>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>> How does the formal system know that an expression of language
>>>>>>>> of this
>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>
>>>>>>
>>>>>> So PA has no idea that:
>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>
>>>>>
>>>>> Why do you say that.
>>>>>
>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>> doesn't mean it can't be.
>>>>>
>>>>> In fact, your statement just comes out of a simple application of
>>>>> the addition AXIOMS of PA.
>>>>>
>>>>> a + 0 = a
>>>>> a + Successor(b) = Successor(a + b)
>>>>>
>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>
>>>>
>>>> Unless a formal system has a syntactic connection from an expression of
>>>> its language to its truth maker axioms the expression is untrue in that
>>>> formal system.
>>>
>>> Right, but the connection can be infinite in length, and thus not
>>> provable.
>>
>> Thus not a connection within the formal system only connection outside
>> of the formal system.
>
> Why? Where does it say "FINITE" connection needed. An infinite set of
> connections within the formal system IS a connection.
>
> You just don't understand what you are talking about.
>
> You are just speaking your natural language, the language of LIES.
>
> Do you somehow mistakenly think that Formal Logic systems are limited to
> being finite? The difference between a Formal system and a non-Formal
> System is that in a Formal Logic System you begin with the
> Formalizatioin, the explicit stating of the rules and axioms that it is
> built on.
>
> Unless the formal system EXPLICITLY restricts itself to finite linkage,
> by adding an axiom that the only things that are true are those that are
> provable, such a rule does not exist, and if you add such a rule to a
> system, you limit its power or it becomes inconsistent.
>
>>
>>>>
>>>> Try and show an expression of language that is true in a formal system
>>>> (not just true somewhere else) that does not have any connection to
>>>> truth maker axioms in this formal system. You must show why it is true
>>>> in this formal system not merely that it is true somewhere else.
>>>>
>>>
>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>> strictly in the formal system.
>>>
>>> If the connection exists as an infinite connection within the system,
>>> then it is TRUE in the system.
>>>
>>> Note, that if there is such an infinite connection, which thus can
>>> not be proven within the formal system, it is still possible, that
>>> another system, related to that system, with more knowledge, might be
>>> able to show that there does exist within the original formal system
>>> such an infinte connection.
>>>
>>> This is what happens to G in F and meta-F
>>>
>>
>> This is you fundamental misunderstanding about the way that truth works.
>> If the original system cannot possibly show that an expression of
>> language is true then it is not true in that formal system.
>
> Nope. SHOWING (as in proving) is different than BEING.
>

It is not true in PA that "Mary had a little lamb"
Do you understand this ?

Even if we make a Gödel number from the adjacent ASCII characters it is
still not true in PA.

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

On 1/14/23 7:36 PM, olcott wrote:
> On 1/14/2023 6:30 PM, Richard Damon wrote:
>> On 1/14/23 6:58 PM, olcott wrote:
>>> This is you fundamental misunderstanding about the way that truth works.
>>> If the original system cannot possibly show that an expression of
>>> language is true then it is not true in that formal system.
>>
>> Nope. SHOWING (as in proving) is different than BEING.
>>
>
> It is not true in PA that "Mary had a little lamb"
> Do you understand this ?

Right, and I never said it did, so that statement doesn't prove anything
except that you use logcal falicies in your arguments.

>
> Even if we make a Gödel number from the adjacent ASCII characters it is
> still not true in PA.
>

First, by PA do you mean Peano Arithmetic, or the Peano Axioms.

Peano Arithmatic, which is a first order logic system, doesn't meet the
complexity requirements of Godel's proof, as it doesn't express all the
properties of the Natural Numbers. Peano Arithmatic might be complete,
but can not be proved within itself to be consistent.

The Peano Axioms, which use a second order axiom for induction. As I
understand it, the Peano Axioms DO make Godel's statement G true as they
have enough of the properties of the Natural Numbers to support the
Primative Recursive Relationship, and can test all the Natural Numbers
and no g will meet it. This is unprovable, as it requires individually
checking the countably infinite set of numbers.

On 1/14/2023 5:42 PM, Richard Damon wrote:
> On 1/14/23 6:19 PM, olcott wrote:
>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>> On 1/14/23 5:31 PM, olcott wrote:
>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>> How does the formal system know that an expression of language of
>>>>>> this
>>>>>> formal system is true unless this expression of language has a
>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>
>>>>>>
>>>>>
>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>
>>>>
>>>> So PA has no idea that:
>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>
>>>
>>> Why do you say that.
>>>
>>> Just because truth doesn't NEED to be proven for it to be true,
>>> doesn't mean it can't be.
>>>
>>> In fact, your statement just comes out of a simple application of the
>>> addition AXIOMS of PA.
>>>
>>> a + 0 = a
>>> a + Successor(b) = Successor(a + b)
>>>
>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>
>>
>> Unless a formal system has a syntactic connection from an expression of
>> its language to its truth maker axioms the expression is untrue in that
>> formal system.
>
> Right, but the connection can be infinite in length, and thus not provable.
>
>>
>> Try and show an expression of language that is true in a formal system
>> (not just true somewhere else) that does not have any connection to
>> truth maker axioms in this formal system. You must show why it is true
>> in this formal system not merely that it is true somewhere else.
>>
>
> The connection might be infinite, and thus not SHOWABLE as a proof
> strictly in the formal system.
>
> If the connection exists as an infinite connection within the system,
> then it is TRUE in the system.
>
> Note, that if there is such an infinite connection, which thus can not
> be proven within the formal system, it is still possible, that another
> system, related to that system, with more knowledge, might be able to
> show that there does exist within the original formal system such an
> infinte connection.
>
> This is what happens to G in F and meta-F
>
> G states that there does not exist a Natural Number g that meets a
> specific requirement (expressed as a primative recursive relationship).
>
> This statement turns out to be true, because it turns out that no number
> g does meet that requirement, but it can't be proven in F that this is
> true, because in F, to show this we need to test every natuarl number,
> which requires an infinite number of steps (finite for each number, but
> an infinite number of numbers to test).
>
> In meta-F, we can do better, because due to additional knowledge in
> meta-F, we can show that if a number g could be found, then that number
> g could be converted into a proof, in F, of the statement G (which says
> that such a number does not exist).
>
> Thus, in meta-F, we can prove that G is true, and also show that no
> proof of it can exist in F.
>
So your basic line-of-reasoning is that G is true in F even if the truth
of G cannot even be expressed in F as long as the truth of G can be
expressed in meta-F.

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

On 1/15/23 11:15 AM, olcott wrote:
> On 1/14/2023 5:42 PM, Richard Damon wrote:
>> On 1/14/23 6:19 PM, olcott wrote:
>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>> How does the formal system know that an expression of language of
>>>>>>> this
>>>>>>> formal system is true unless this expression of language has a
>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>
>>>>>
>>>>> So PA has no idea that:
>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>
>>>>
>>>> Why do you say that.
>>>>
>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>> doesn't mean it can't be.
>>>>
>>>> In fact, your statement just comes out of a simple application of
>>>> the addition AXIOMS of PA.
>>>>
>>>> a + 0 = a
>>>> a + Successor(b) = Successor(a + b)
>>>>
>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>
>>>
>>> Unless a formal system has a syntactic connection from an expression of
>>> its language to its truth maker axioms the expression is untrue in that
>>> formal system.
>>
>> Right, but the connection can be infinite in length, and thus not
>> provable.
>>
>>>
>>> Try and show an expression of language that is true in a formal system
>>> (not just true somewhere else) that does not have any connection to
>>> truth maker axioms in this formal system. You must show why it is true
>>> in this formal system not merely that it is true somewhere else.
>>>
>>
>> The connection might be infinite, and thus not SHOWABLE as a proof
>> strictly in the formal system.
>>
>> If the connection exists as an infinite connection within the system,
>> then it is TRUE in the system.
>>
>> Note, that if there is such an infinite connection, which thus can not
>> be proven within the formal system, it is still possible, that another
>> system, related to that system, with more knowledge, might be able to
>> show that there does exist within the original formal system such an
>> infinte connection.
>>
>> This is what happens to G in F and meta-F
>>
>> G states that there does not exist a Natural Number g that meets a
>> specific requirement (expressed as a primative recursive relationship).
>>
>> This statement turns out to be true, because it turns out that no
>> number g does meet that requirement, but it can't be proven in F that
>> this is true, because in F, to show this we need to test every natuarl
>> number, which requires an infinite number of steps (finite for each
>> number, but an infinite number of numbers to test).
>>
>> In meta-F, we can do better, because due to additional knowledge in
>> meta-F, we can show that if a number g could be found, then that
>> number g could be converted into a proof, in F, of the statement G
>> (which says that such a number does not exist).
>>
>> Thus, in meta-F, we can prove that G is true, and also show that no
>> proof of it can exist in F.
>>
> So your basic line-of-reasoning is that G is true in F even if the truth
> of G cannot even be expressed in F as long as the truth of G can be
> expressed in meta-F.
>

Expect that it CAN be expressed in F, it just is an infinite expression.

In F

G: There is no Natural Number g that satisfies a <specific primative
recurcive relationship> (lets call it f)

To show this, we can show in F that:

f(0) -> false
f(1) -> false
f(2) -> false
....
f(n) -> false
....
for ALL n (one at a time)

The issue is that in F we can not make a proof about all n at once, but
we can for any given n by evaluating f(n) which is a finite operation.

Only in meta-F can we reduce this infinite set to something finite.

Thus, the truth of G is "expressed" in F, but as an infinite set of
relationships, and thus NOT a "Proof" as that needs to be a FINITE set
of relationships.

This is obviously above your head, as it has been explained many times,
but you mind seems to have a short curcuit in it about truth being the
same thing as provable, which just makes your system inconsistent, but
you can't handle that so yo are just closing your eyes to those facts
and saying "I can' hear you so you are just wrong".

You are just PROVING your ignorance and stupidity.

On 1/15/2023 11:05 AM, Richard Damon wrote:
> On 1/15/23 11:15 AM, olcott wrote:
>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>> On 1/14/23 6:19 PM, olcott wrote:
>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>> How does the formal system know that an expression of language
>>>>>>>> of this
>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>
>>>>>>
>>>>>> So PA has no idea that:
>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>
>>>>>
>>>>> Why do you say that.
>>>>>
>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>> doesn't mean it can't be.
>>>>>
>>>>> In fact, your statement just comes out of a simple application of
>>>>> the addition AXIOMS of PA.
>>>>>
>>>>> a + 0 = a
>>>>> a + Successor(b) = Successor(a + b)
>>>>>
>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>
>>>>
>>>> Unless a formal system has a syntactic connection from an expression of
>>>> its language to its truth maker axioms the expression is untrue in that
>>>> formal system.
>>>
>>> Right, but the connection can be infinite in length, and thus not
>>> provable.
>>>
>>>>
>>>> Try and show an expression of language that is true in a formal system
>>>> (not just true somewhere else) that does not have any connection to
>>>> truth maker axioms in this formal system. You must show why it is true
>>>> in this formal system not merely that it is true somewhere else.
>>>>
>>>
>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>> strictly in the formal system.
>>>
>>> If the connection exists as an infinite connection within the system,
>>> then it is TRUE in the system.
>>>
>>> Note, that if there is such an infinite connection, which thus can
>>> not be proven within the formal system, it is still possible, that
>>> another system, related to that system, with more knowledge, might be
>>> able to show that there does exist within the original formal system
>>> such an infinte connection.
>>>
>>> This is what happens to G in F and meta-F
>>>
>>> G states that there does not exist a Natural Number g that meets a
>>> specific requirement (expressed as a primative recursive relationship).
>>>
>>> This statement turns out to be true, because it turns out that no
>>> number g does meet that requirement, but it can't be proven in F that
>>> this is true, because in F, to show this we need to test every
>>> natuarl number, which requires an infinite number of steps (finite
>>> for each number, but an infinite number of numbers to test).
>>>
>>> In meta-F, we can do better, because due to additional knowledge in
>>> meta-F, we can show that if a number g could be found, then that
>>> number g could be converted into a proof, in F, of the statement G
>>> (which says that such a number does not exist).
>>>
>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>> proof of it can exist in F.
>>>
>> So your basic line-of-reasoning is that G is true in F even if the truth
>> of G cannot even be expressed in F as long as the truth of G can be
>> expressed in meta-F.
>>
>
> Expect that it CAN be expressed in F, it just is an infinite expression.
That is false. It is not that G takes an infinite number of steps to
reach its truth maker axioms in F it is that even after an infinite
number of steps it never reaches is truth maker axioms in F because G is
simply untrue in F.

"This sentence is not true"
Not true about what?
Not true about being not true.
Not true about being not true about what?
Not true about being not true about being not true.

Since Gödel said:
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof.

By using the Liar Paradox as a Gödel approved proxy for his proof we
refute his proof by this Gödel approved proxy.

--
Copyright 2023 Olcott

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

On 1/15/23 12:31 PM, olcott wrote:
> On 1/15/2023 11:05 AM, Richard Damon wrote:
>> On 1/15/23 11:15 AM, olcott wrote:
>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>> How does the formal system know that an expression of language
>>>>>>>>> of this
>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>
>>>>>>>
>>>>>>> So PA has no idea that:
>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>
>>>>>>
>>>>>> Why do you say that.
>>>>>>
>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>> doesn't mean it can't be.
>>>>>>
>>>>>> In fact, your statement just comes out of a simple application of
>>>>>> the addition AXIOMS of PA.
>>>>>>
>>>>>> a + 0 = a
>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>
>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>
>>>>>
>>>>> Unless a formal system has a syntactic connection from an
>>>>> expression of
>>>>> its language to its truth maker axioms the expression is untrue in
>>>>> that
>>>>> formal system.
>>>>
>>>> Right, but the connection can be infinite in length, and thus not
>>>> provable.
>>>>
>>>>>
>>>>> Try and show an expression of language that is true in a formal system
>>>>> (not just true somewhere else) that does not have any connection to
>>>>> truth maker axioms in this formal system. You must show why it is true
>>>>> in this formal system not merely that it is true somewhere else.
>>>>>
>>>>
>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>> strictly in the formal system.
>>>>
>>>> If the connection exists as an infinite connection within the
>>>> system, then it is TRUE in the system.
>>>>
>>>> Note, that if there is such an infinite connection, which thus can
>>>> not be proven within the formal system, it is still possible, that
>>>> another system, related to that system, with more knowledge, might
>>>> be able to show that there does exist within the original formal
>>>> system such an infinte connection.
>>>>
>>>> This is what happens to G in F and meta-F
>>>>
>>>> G states that there does not exist a Natural Number g that meets a
>>>> specific requirement (expressed as a primative recursive relationship).
>>>>
>>>> This statement turns out to be true, because it turns out that no
>>>> number g does meet that requirement, but it can't be proven in F
>>>> that this is true, because in F, to show this we need to test every
>>>> natuarl number, which requires an infinite number of steps (finite
>>>> for each number, but an infinite number of numbers to test).
>>>>
>>>> In meta-F, we can do better, because due to additional knowledge in
>>>> meta-F, we can show that if a number g could be found, then that
>>>> number g could be converted into a proof, in F, of the statement G
>>>> (which says that such a number does not exist).
>>>>
>>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>>> proof of it can exist in F.
>>>>
>>> So your basic line-of-reasoning is that G is true in F even if the truth
>>> of G cannot even be expressed in F as long as the truth of G can be
>>> expressed in meta-F.
>>>
>>
>> Expect that it CAN be expressed in F, it just is an infinite expression.
> That is false. It is not that G takes an infinite number of steps to
> reach its truth maker axioms in F it is that even after an infinite
> number of steps it never reaches is truth maker axioms in F because G is
> simply untrue in F.

No, YOUR problem is you aren't actually talking about G in F.

>
> "This sentence is not true"

Which isn't G.

> Not true about what?
> Not true about being not true.
> Not true about being not true about what?
> Not true about being not true about being not true.
>

So you are just a MORON.

> Since Gödel said:
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof.
>
> By using the Liar Paradox as a Gödel approved proxy for his proof we
> refute his proof by this Gödel approved proxy.
>

No, all you have proved is that you are a LYING MORON.

You DON'T know what G actually is, even when it ha been explaine to you,
and it seems you are incapable of learning it.

ince you are just proving that you are a LYING MORON, I can't help you.

On 1/15/2023 11:41 AM, Richard Damon wrote:
> On 1/15/23 12:31 PM, olcott wrote:
>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>> On 1/15/23 11:15 AM, olcott wrote:
>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>> How does the formal system know that an expression of language
>>>>>>>>>> of this
>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> So PA has no idea that:
>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>>
>>>>>>>
>>>>>>> Why do you say that.
>>>>>>>
>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>> doesn't mean it can't be.
>>>>>>>
>>>>>>> In fact, your statement just comes out of a simple application of
>>>>>>> the addition AXIOMS of PA.
>>>>>>>
>>>>>>> a + 0 = a
>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>
>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>>
>>>>>>
>>>>>> Unless a formal system has a syntactic connection from an
>>>>>> expression of
>>>>>> its language to its truth maker axioms the expression is untrue in
>>>>>> that
>>>>>> formal system.
>>>>>
>>>>> Right, but the connection can be infinite in length, and thus not
>>>>> provable.
>>>>>
>>>>>>
>>>>>> Try and show an expression of language that is true in a formal
>>>>>> system
>>>>>> (not just true somewhere else) that does not have any connection to
>>>>>> truth maker axioms in this formal system. You must show why it is
>>>>>> true
>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>
>>>>>
>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>>> strictly in the formal system.
>>>>>
>>>>> If the connection exists as an infinite connection within the
>>>>> system, then it is TRUE in the system.
>>>>>
>>>>> Note, that if there is such an infinite connection, which thus can
>>>>> not be proven within the formal system, it is still possible, that
>>>>> another system, related to that system, with more knowledge, might
>>>>> be able to show that there does exist within the original formal
>>>>> system such an infinte connection.
>>>>>
>>>>> This is what happens to G in F and meta-F
>>>>>
>>>>> G states that there does not exist a Natural Number g that meets a
>>>>> specific requirement (expressed as a primative recursive
>>>>> relationship).
>>>>>
>>>>> This statement turns out to be true, because it turns out that no
>>>>> number g does meet that requirement, but it can't be proven in F
>>>>> that this is true, because in F, to show this we need to test every
>>>>> natuarl number, which requires an infinite number of steps (finite
>>>>> for each number, but an infinite number of numbers to test).
>>>>>
>>>>> In meta-F, we can do better, because due to additional knowledge in
>>>>> meta-F, we can show that if a number g could be found, then that
>>>>> number g could be converted into a proof, in F, of the statement G
>>>>> (which says that such a number does not exist).
>>>>>
>>>>> Thus, in meta-F, we can prove that G is true, and also show that no
>>>>> proof of it can exist in F.
>>>>>
>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>> truth
>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>> expressed in meta-F.
>>>>
>>>
>>> Expect that it CAN be expressed in F, it just is an infinite expression.
>> That is false. It is not that G takes an infinite number of steps to
>> reach its truth maker axioms in F it is that even after an infinite
>> number of steps it never reaches is truth maker axioms in F because G is
>> simply untrue in F.
>
> No, YOUR problem is you aren't actually talking about G in F.
>
>>
>> "This sentence is not true"
>
> Which isn't G.
>
>> Not true about what?
>> Not true about being not true.
>> Not true about being not true about what?
>> Not true about being not true about being not true.
>>
>
> So you are just a MORON.
>
>> Since Gödel said:
>> 14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof.
>>
>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>> refute his proof by this Gödel approved proxy.
>>
>
> No, all you have proved is that you are a LYING MORON.
>

Ad Hominem attacks are the tactic that people having no interest in any
honest dialogue use when they realize that their reasoning has been
utterly defeated.

--
Copyright 2023 Olcott

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

On 1/15/23 12:47 PM, olcott wrote:
> On 1/15/2023 11:41 AM, Richard Damon wrote:
>> On 1/15/23 12:31 PM, olcott wrote:
>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>> language of this
>>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So PA has no idea that:
>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>>>>>>>
>>>>>>>>
>>>>>>>> Why do you say that.
>>>>>>>>
>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>>> doesn't mean it can't be.
>>>>>>>>
>>>>>>>> In fact, your statement just comes out of a simple application
>>>>>>>> of the addition AXIOMS of PA.
>>>>>>>>
>>>>>>>> a + 0 = a
>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>
>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>>>
>>>>>>>
>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>> expression of
>>>>>>> its language to its truth maker axioms the expression is untrue
>>>>>>> in that
>>>>>>> formal system.
>>>>>>
>>>>>> Right, but the connection can be infinite in length, and thus not
>>>>>> provable.
>>>>>>
>>>>>>>
>>>>>>> Try and show an expression of language that is true in a formal
>>>>>>> system
>>>>>>> (not just true somewhere else) that does not have any connection to
>>>>>>> truth maker axioms in this formal system. You must show why it is
>>>>>>> true
>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>
>>>>>>
>>>>>> The connection might be infinite, and thus not SHOWABLE as a proof
>>>>>> strictly in the formal system.
>>>>>>
>>>>>> If the connection exists as an infinite connection within the
>>>>>> system, then it is TRUE in the system.
>>>>>>
>>>>>> Note, that if there is such an infinite connection, which thus can
>>>>>> not be proven within the formal system, it is still possible, that
>>>>>> another system, related to that system, with more knowledge, might
>>>>>> be able to show that there does exist within the original formal
>>>>>> system such an infinte connection.
>>>>>>
>>>>>> This is what happens to G in F and meta-F
>>>>>>
>>>>>> G states that there does not exist a Natural Number g that meets a
>>>>>> specific requirement (expressed as a primative recursive
>>>>>> relationship).
>>>>>>
>>>>>> This statement turns out to be true, because it turns out that no
>>>>>> number g does meet that requirement, but it can't be proven in F
>>>>>> that this is true, because in F, to show this we need to test
>>>>>> every natuarl number, which requires an infinite number of steps
>>>>>> (finite for each number, but an infinite number of numbers to test).
>>>>>>
>>>>>> In meta-F, we can do better, because due to additional knowledge
>>>>>> in meta-F, we can show that if a number g could be found, then
>>>>>> that number g could be converted into a proof, in F, of the
>>>>>> statement G (which says that such a number does not exist).
>>>>>>
>>>>>> Thus, in meta-F, we can prove that G is true, and also show that
>>>>>> no proof of it can exist in F.
>>>>>>
>>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>>> truth
>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>> expressed in meta-F.
>>>>>
>>>>
>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>> expression.
>>> That is false. It is not that G takes an infinite number of steps to
>>> reach its truth maker axioms in F it is that even after an infinite
>>> number of steps it never reaches is truth maker axioms in F because G is
>>> simply untrue in F.
>>
>> No, YOUR problem is you aren't actually talking about G in F.
>>
>>>
>>> "This sentence is not true"
>>
>> Which isn't G.
>>
>>> Not true about what?
>>> Not true about being not true.
>>> Not true about being not true about what?
>>> Not true about being not true about being not true.
>>>
>>
>> So you are just a MORON.
>>
>>> Since Gödel said:
>>> 14 Every epistemological antinomy can likewise be used for a similar
>>> undecidability proof.
>>>
>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>> refute his proof by this Gödel approved proxy.
>>>
>>
>> No, all you have proved is that you are a LYING MORON.
>>
>
> Ad Hominem attacks are the tactic that people having no interest in any
> honest dialogue use when they realize that their reasoning has been
> utterly defeated.
>

And RED HERRING arguements don't work either.

You ARE a LYING MORON as you insist that Godel's G is a sentence that is
actually provably isn't.

You think it is because you are too stupid to actually read any of the
paper, so you take that comment that the statment is "based" on that
statement to mean it IS that statement.

EVERYONE who has read any of this discussion, and bothers to look into
the material, will see who knows what they are saying and who doesn't

You are a LIAR because you state provably untrue statements, and repeat
them even after you have been shown them to be incorrect.

You are a MORON, because you show ZERO signs of being able to do
intelectual reasoning, and for some unknowable reason seem to expect
people to fall for your lies.

IF you honestly can't understand the logic that has been presented to
you, that itself is proof of your lack of intelegence.

Face it, you are destroyed your reputation, and fatally damaged any
actual possible nugget of truth in your ideas.

You are your own worse enemy.

On 1/15/2023 11:58 AM, Richard Damon wrote:
> On 1/15/23 12:47 PM, olcott wrote:
>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>> On 1/15/23 12:31 PM, olcott wrote:
>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>> language of this
>>>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So PA has no idea that:
>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is true
>>>>>>>>>> ???
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Why do you say that.
>>>>>>>>>
>>>>>>>>> Just because truth doesn't NEED to be proven for it to be true,
>>>>>>>>> doesn't mean it can't be.
>>>>>>>>>
>>>>>>>>> In fact, your statement just comes out of a simple application
>>>>>>>>> of the addition AXIOMS of PA.
>>>>>>>>>
>>>>>>>>> a + 0 = a
>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>
>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>> expression of
>>>>>>>> its language to its truth maker axioms the expression is untrue
>>>>>>>> in that
>>>>>>>> formal system.
>>>>>>>
>>>>>>> Right, but the connection can be infinite in length, and thus not
>>>>>>> provable.
>>>>>>>
>>>>>>>>
>>>>>>>> Try and show an expression of language that is true in a formal
>>>>>>>> system
>>>>>>>> (not just true somewhere else) that does not have any connection to
>>>>>>>> truth maker axioms in this formal system. You must show why it
>>>>>>>> is true
>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>
>>>>>>>
>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>> proof strictly in the formal system.
>>>>>>>
>>>>>>> If the connection exists as an infinite connection within the
>>>>>>> system, then it is TRUE in the system.
>>>>>>>
>>>>>>> Note, that if there is such an infinite connection, which thus
>>>>>>> can not be proven within the formal system, it is still possible,
>>>>>>> that another system, related to that system, with more knowledge,
>>>>>>> might be able to show that there does exist within the original
>>>>>>> formal system such an infinte connection.
>>>>>>>
>>>>>>> This is what happens to G in F and meta-F
>>>>>>>
>>>>>>> G states that there does not exist a Natural Number g that meets
>>>>>>> a specific requirement (expressed as a primative recursive
>>>>>>> relationship).
>>>>>>>
>>>>>>> This statement turns out to be true, because it turns out that no
>>>>>>> number g does meet that requirement, but it can't be proven in F
>>>>>>> that this is true, because in F, to show this we need to test
>>>>>>> every natuarl number, which requires an infinite number of steps
>>>>>>> (finite for each number, but an infinite number of numbers to test).
>>>>>>>
>>>>>>> In meta-F, we can do better, because due to additional knowledge
>>>>>>> in meta-F, we can show that if a number g could be found, then
>>>>>>> that number g could be converted into a proof, in F, of the
>>>>>>> statement G (which says that such a number does not exist).
>>>>>>>
>>>>>>> Thus, in meta-F, we can prove that G is true, and also show that
>>>>>>> no proof of it can exist in F.
>>>>>>>
>>>>>> So your basic line-of-reasoning is that G is true in F even if the
>>>>>> truth
>>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>>> expressed in meta-F.
>>>>>>
>>>>>
>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>> expression.
>>>> That is false. It is not that G takes an infinite number of steps to
>>>> reach its truth maker axioms in F it is that even after an infinite
>>>> number of steps it never reaches is truth maker axioms in F because
>>>> G is
>>>> simply untrue in F.
>>>
>>> No, YOUR problem is you aren't actually talking about G in F.
>>>
>>>>
>>>> "This sentence is not true"
>>>
>>> Which isn't G.
>>>
>>>> Not true about what?
>>>> Not true about being not true.
>>>> Not true about being not true about what?
>>>> Not true about being not true about being not true.
>>>>
>>>
>>> So you are just a MORON.
>>>
>>>> Since Gödel said:
>>>> 14 Every epistemological antinomy can likewise be used for a similar
>>>> undecidability proof.
>>>>
>>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>>> refute his proof by this Gödel approved proxy.
>>>>
>>>
>>> No, all you have proved is that you are a LYING MORON.
>>>
>>
>> Ad Hominem attacks are the tactic that people having no interest in any
>> honest dialogue use when they realize that their reasoning has been
>> utterly defeated.
>>
>
> And RED HERRING arguements don't work either.
>
> You ARE a LYING MORON as you insist that Godel's G is a sentence that is
> actually provably isn't.
>
> You think it is because you are too stupid to actually read any of the
> paper, so you take that comment that the statment is "based" on that
> statement to mean it IS that statement.
>
All of your Ad Hominem attacks cannot possibly hide the fact that you
are asserting this counter-factual statement:

when a valid proxy for an argument is defeated this does not defeat the
original argument.

--
Copyright 2023 Olcott

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

On 1/15/23 1:23 PM, olcott wrote:
> On 1/15/2023 11:58 AM, Richard Damon wrote:
>> On 1/15/23 12:47 PM, olcott wrote:
>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>> language of this
>>>>>>>>>>>>> formal system is true unless this expression of language has a
>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>> true ???
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Why do you say that.
>>>>>>>>>>
>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>
>>>>>>>>>> In fact, your statement just comes out of a simple application
>>>>>>>>>> of the addition AXIOMS of PA.
>>>>>>>>>>
>>>>>>>>>> a + 0 = a
>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>
>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be
>>>>>>>>>> true.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>> expression of
>>>>>>>>> its language to its truth maker axioms the expression is untrue
>>>>>>>>> in that
>>>>>>>>> formal system.
>>>>>>>>
>>>>>>>> Right, but the connection can be infinite in length, and thus
>>>>>>>> not provable.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Try and show an expression of language that is true in a formal
>>>>>>>>> system
>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>> connection to
>>>>>>>>> truth maker axioms in this formal system. You must show why it
>>>>>>>>> is true
>>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>> proof strictly in the formal system.
>>>>>>>>
>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>
>>>>>>>> Note, that if there is such an infinite connection, which thus
>>>>>>>> can not be proven within the formal system, it is still
>>>>>>>> possible, that another system, related to that system, with more
>>>>>>>> knowledge, might be able to show that there does exist within
>>>>>>>> the original formal system such an infinte connection.
>>>>>>>>
>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>
>>>>>>>> G states that there does not exist a Natural Number g that meets
>>>>>>>> a specific requirement (expressed as a primative recursive
>>>>>>>> relationship).
>>>>>>>>
>>>>>>>> This statement turns out to be true, because it turns out that
>>>>>>>> no number g does meet that requirement, but it can't be proven
>>>>>>>> in F that this is true, because in F, to show this we need to
>>>>>>>> test every natuarl number, which requires an infinite number of
>>>>>>>> steps (finite for each number, but an infinite number of numbers
>>>>>>>> to test).
>>>>>>>>
>>>>>>>> In meta-F, we can do better, because due to additional knowledge
>>>>>>>> in meta-F, we can show that if a number g could be found, then
>>>>>>>> that number g could be converted into a proof, in F, of the
>>>>>>>> statement G (which says that such a number does not exist).
>>>>>>>>
>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show that
>>>>>>>> no proof of it can exist in F.
>>>>>>>>
>>>>>>> So your basic line-of-reasoning is that G is true in F even if
>>>>>>> the truth
>>>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>>>> expressed in meta-F.
>>>>>>>
>>>>>>
>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>> expression.
>>>>> That is false. It is not that G takes an infinite number of steps to
>>>>> reach its truth maker axioms in F it is that even after an infinite
>>>>> number of steps it never reaches is truth maker axioms in F because
>>>>> G is
>>>>> simply untrue in F.
>>>>
>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>
>>>>>
>>>>> "This sentence is not true"
>>>>
>>>> Which isn't G.
>>>>
>>>>> Not true about what?
>>>>> Not true about being not true.
>>>>> Not true about being not true about what?
>>>>> Not true about being not true about being not true.
>>>>>
>>>>
>>>> So you are just a MORON.
>>>>
>>>>> Since Gödel said:
>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof.
>>>>>
>>>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>>>> refute his proof by this Gödel approved proxy.
>>>>>
>>>>
>>>> No, all you have proved is that you are a LYING MORON.
>>>>
>>>
>>> Ad Hominem attacks are the tactic that people having no interest in any
>>> honest dialogue use when they realize that their reasoning has been
>>> utterly defeated.
>>>
>>
>> And RED HERRING arguements don't work either.
>>
>> You ARE a LYING MORON as you insist that Godel's G is a sentence that
>> is actually provably isn't.
>>
>> You think it is because you are too stupid to actually read any of the
>> paper, so you take that comment that the statment is "based" on that
>> statement to mean it IS that statement.
>>
> All of your Ad Hominem attacks cannot possibly hide the fact that you
> are asserting this counter-factual statement:
>
> when a valid proxy for an argument is defeated this does not defeat the
> original argument.
>

On 1/15/2023 12:55 PM, Richard Damon wrote:
> On 1/15/23 1:23 PM, olcott wrote:
>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>> On 1/15/23 12:47 PM, olcott wrote:
>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>> formal system is true unless this expression of language
>>>>>>>>>>>>>> has a
>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>>> true ???
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>
>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>
>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>
>>>>>>>>>>> a + 0 = a
>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>
>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be
>>>>>>>>>>> true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>> expression of
>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>> untrue in that
>>>>>>>>>> formal system.
>>>>>>>>>
>>>>>>>>> Right, but the connection can be infinite in length, and thus
>>>>>>>>> not provable.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>> formal system
>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>> connection to
>>>>>>>>>> truth maker axioms in this formal system. You must show why it
>>>>>>>>>> is true
>>>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>>> proof strictly in the formal system.
>>>>>>>>>
>>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>>
>>>>>>>>> Note, that if there is such an infinite connection, which thus
>>>>>>>>> can not be proven within the formal system, it is still
>>>>>>>>> possible, that another system, related to that system, with
>>>>>>>>> more knowledge, might be able to show that there does exist
>>>>>>>>> within the original formal system such an infinte connection.
>>>>>>>>>
>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>
>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>> recursive relationship).
>>>>>>>>>
>>>>>>>>> This statement turns out to be true, because it turns out that
>>>>>>>>> no number g does meet that requirement, but it can't be proven
>>>>>>>>> in F that this is true, because in F, to show this we need to
>>>>>>>>> test every natuarl number, which requires an infinite number of
>>>>>>>>> steps (finite for each number, but an infinite number of
>>>>>>>>> numbers to test).
>>>>>>>>>
>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>> knowledge in meta-F, we can show that if a number g could be
>>>>>>>>> found, then that number g could be converted into a proof, in
>>>>>>>>> F, of the statement G (which says that such a number does not
>>>>>>>>> exist).
>>>>>>>>>
>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>
>>>>>>>> So your basic line-of-reasoning is that G is true in F even if
>>>>>>>> the truth
>>>>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>>>>> expressed in meta-F.
>>>>>>>>
>>>>>>>
>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>> expression.
>>>>>> That is false. It is not that G takes an infinite number of steps to
>>>>>> reach its truth maker axioms in F it is that even after an infinite
>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>> because G is
>>>>>> simply untrue in F.
>>>>>
>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>
>>>>>>
>>>>>> "This sentence is not true"
>>>>>
>>>>> Which isn't G.
>>>>>
>>>>>> Not true about what?
>>>>>> Not true about being not true.
>>>>>> Not true about being not true about what?
>>>>>> Not true about being not true about being not true.
>>>>>>
>>>>>
>>>>> So you are just a MORON.
>>>>>
>>>>>> Since Gödel said:
>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>> similar undecidability proof.
>>>>>>
>>>>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>
>>>>>
>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>
>>>>
>>>> Ad Hominem attacks are the tactic that people having no interest in any
>>>> honest dialogue use when they realize that their reasoning has been
>>>> utterly defeated.
>>>>
>>>
>>> And RED HERRING arguements don't work either.
>>>
>>> You ARE a LYING MORON as you insist that Godel's G is a sentence that
>>> is actually provably isn't.
>>>
>>> You think it is because you are too stupid to actually read any of
>>> the paper, so you take that comment that the statment is "based" on
>>> that statement to mean it IS that statement.
>>>
>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>> are asserting this counter-factual statement:
>>
>> when a valid proxy for an argument is defeated this does not defeat the
>> original argument.
>>
>
> Right, which is what YOU are doing, showing your arguement is INVALID.
>

On 1/15/23 2:00 PM, olcott wrote:
> On 1/15/2023 12:55 PM, Richard Damon wrote:
>> On 1/15/23 1:23 PM, olcott wrote:
>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>>> formal system is true unless this expression of language
>>>>>>>>>>>>>>> has a
>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>>>> true ???
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>
>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>>
>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>
>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>
>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be
>>>>>>>>>>>> true.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>>> expression of
>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>> untrue in that
>>>>>>>>>>> formal system.
>>>>>>>>>>
>>>>>>>>>> Right, but the connection can be infinite in length, and thus
>>>>>>>>>> not provable.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>> formal system
>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>> connection to
>>>>>>>>>>> truth maker axioms in this formal system. You must show why
>>>>>>>>>>> it is true
>>>>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>>>> proof strictly in the formal system.
>>>>>>>>>>
>>>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>>>
>>>>>>>>>> Note, that if there is such an infinite connection, which thus
>>>>>>>>>> can not be proven within the formal system, it is still
>>>>>>>>>> possible, that another system, related to that system, with
>>>>>>>>>> more knowledge, might be able to show that there does exist
>>>>>>>>>> within the original formal system such an infinte connection.
>>>>>>>>>>
>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>
>>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>>> recursive relationship).
>>>>>>>>>>
>>>>>>>>>> This statement turns out to be true, because it turns out that
>>>>>>>>>> no number g does meet that requirement, but it can't be proven
>>>>>>>>>> in F that this is true, because in F, to show this we need to
>>>>>>>>>> test every natuarl number, which requires an infinite number
>>>>>>>>>> of steps (finite for each number, but an infinite number of
>>>>>>>>>> numbers to test).
>>>>>>>>>>
>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>> knowledge in meta-F, we can show that if a number g could be
>>>>>>>>>> found, then that number g could be converted into a proof, in
>>>>>>>>>> F, of the statement G (which says that such a number does not
>>>>>>>>>> exist).
>>>>>>>>>>
>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>>
>>>>>>>>> So your basic line-of-reasoning is that G is true in F even if
>>>>>>>>> the truth
>>>>>>>>> of G cannot even be expressed in F as long as the truth of G
>>>>>>>>> can be
>>>>>>>>> expressed in meta-F.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>>> expression.
>>>>>>> That is false. It is not that G takes an infinite number of steps to
>>>>>>> reach its truth maker axioms in F it is that even after an infinite
>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>> because G is
>>>>>>> simply untrue in F.
>>>>>>
>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>
>>>>>>>
>>>>>>> "This sentence is not true"
>>>>>>
>>>>>> Which isn't G.
>>>>>>
>>>>>>> Not true about what?
>>>>>>> Not true about being not true.
>>>>>>> Not true about being not true about what?
>>>>>>> Not true about being not true about being not true.
>>>>>>>
>>>>>>
>>>>>> So you are just a MORON.
>>>>>>
>>>>>>> Since Gödel said:
>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>> similar undecidability proof.
>>>>>>>
>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>
>>>>>>
>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>
>>>>>
>>>>> Ad Hominem attacks are the tactic that people having no interest in
>>>>> any
>>>>> honest dialogue use when they realize that their reasoning has been
>>>>> utterly defeated.
>>>>>
>>>>
>>>> And RED HERRING arguements don't work either.
>>>>
>>>> You ARE a LYING MORON as you insist that Godel's G is a sentence
>>>> that is actually provably isn't.
>>>>
>>>> You think it is because you are too stupid to actually read any of
>>>> the paper, so you take that comment that the statment is "based" on
>>>> that statement to mean it IS that statement.
>>>>
>>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>>> are asserting this counter-factual statement:
>>>
>>> when a valid proxy for an argument is defeated this does not defeat the
>>> original argument.
>>>
>>
>> Right, which is what YOU are doing, showing your arguement is INVALID.
>>
>
> In other words you disagree that correctly refuting a valid proxy for an
> argument does correctly refute the original argument?
>
>

On 1/15/2023 12:55 PM, Richard Damon wrote:
> On 1/15/23 1:23 PM, olcott wrote:
>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>> On 1/15/23 12:47 PM, olcott wrote:
>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>> formal system is true unless this expression of language
>>>>>>>>>>>>>> has a
>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>>> true ???
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>
>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>
>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>
>>>>>>>>>>> a + 0 = a
>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>
>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be
>>>>>>>>>>> true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>> expression of
>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>> untrue in that
>>>>>>>>>> formal system.
>>>>>>>>>
>>>>>>>>> Right, but the connection can be infinite in length, and thus
>>>>>>>>> not provable.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>> formal system
>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>> connection to
>>>>>>>>>> truth maker axioms in this formal system. You must show why it
>>>>>>>>>> is true
>>>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>>> proof strictly in the formal system.
>>>>>>>>>
>>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>>
>>>>>>>>> Note, that if there is such an infinite connection, which thus
>>>>>>>>> can not be proven within the formal system, it is still
>>>>>>>>> possible, that another system, related to that system, with
>>>>>>>>> more knowledge, might be able to show that there does exist
>>>>>>>>> within the original formal system such an infinte connection.
>>>>>>>>>
>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>
>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>> recursive relationship).
>>>>>>>>>
>>>>>>>>> This statement turns out to be true, because it turns out that
>>>>>>>>> no number g does meet that requirement, but it can't be proven
>>>>>>>>> in F that this is true, because in F, to show this we need to
>>>>>>>>> test every natuarl number, which requires an infinite number of
>>>>>>>>> steps (finite for each number, but an infinite number of
>>>>>>>>> numbers to test).
>>>>>>>>>
>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>> knowledge in meta-F, we can show that if a number g could be
>>>>>>>>> found, then that number g could be converted into a proof, in
>>>>>>>>> F, of the statement G (which says that such a number does not
>>>>>>>>> exist).
>>>>>>>>>
>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>
>>>>>>>> So your basic line-of-reasoning is that G is true in F even if
>>>>>>>> the truth
>>>>>>>> of G cannot even be expressed in F as long as the truth of G can be
>>>>>>>> expressed in meta-F.
>>>>>>>>
>>>>>>>
>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>> expression.
>>>>>> That is false. It is not that G takes an infinite number of steps to
>>>>>> reach its truth maker axioms in F it is that even after an infinite
>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>> because G is
>>>>>> simply untrue in F.
>>>>>
>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>
>>>>>>
>>>>>> "This sentence is not true"
>>>>>
>>>>> Which isn't G.
>>>>>
>>>>>> Not true about what?
>>>>>> Not true about being not true.
>>>>>> Not true about being not true about what?
>>>>>> Not true about being not true about being not true.
>>>>>>
>>>>>
>>>>> So you are just a MORON.
>>>>>
>>>>>> Since Gödel said:
>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>> similar undecidability proof.
>>>>>>
>>>>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>
>>>>>
>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>
>>>>
>>>> Ad Hominem attacks are the tactic that people having no interest in any
>>>> honest dialogue use when they realize that their reasoning has been
>>>> utterly defeated.
>>>>
>>>
>>> And RED HERRING arguements don't work either.
>>>
>>> You ARE a LYING MORON as you insist that Godel's G is a sentence that
>>> is actually provably isn't.
>>>
>>> You think it is because you are too stupid to actually read any of
>>> the paper, so you take that comment that the statment is "based" on
>>> that statement to mean it IS that statement.
>>>
>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>> are asserting this counter-factual statement:
>>
>> when a valid proxy for an argument is defeated this does not defeat the
>> original argument.
>>
>
> Right, which is what YOU are doing, showing your arguement is INVALID.
>
In other words you disagree that correctly refuting a valid proxy for an
argument does correctly refute the original argument?

On 1/15/2023 1:06 PM, Richard Damon wrote:
> On 1/15/23 2:00 PM, olcott wrote:
>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>> On 1/15/23 1:23 PM, olcott wrote:
>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>>>> formal system is true unless this expression of language
>>>>>>>>>>>>>>>> has a
>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM*
>>>>>>>>>>>>>>>> ???
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>>>>> true ???
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>>>
>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>
>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>
>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to
>>>>>>>>>>>>> be true.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>>>> expression of
>>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>>> untrue in that
>>>>>>>>>>>> formal system.
>>>>>>>>>>>
>>>>>>>>>>> Right, but the connection can be infinite in length, and thus
>>>>>>>>>>> not provable.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>>> formal system
>>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>>> connection to
>>>>>>>>>>>> truth maker axioms in this formal system. You must show why
>>>>>>>>>>>> it is true
>>>>>>>>>>>> in this formal system not merely that it is true somewhere
>>>>>>>>>>>> else.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>>>>> proof strictly in the formal system.
>>>>>>>>>>>
>>>>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>>>>
>>>>>>>>>>> Note, that if there is such an infinite connection, which
>>>>>>>>>>> thus can not be proven within the formal system, it is still
>>>>>>>>>>> possible, that another system, related to that system, with
>>>>>>>>>>> more knowledge, might be able to show that there does exist
>>>>>>>>>>> within the original formal system such an infinte connection.
>>>>>>>>>>>
>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>
>>>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>>>> recursive relationship).
>>>>>>>>>>>
>>>>>>>>>>> This statement turns out to be true, because it turns out
>>>>>>>>>>> that no number g does meet that requirement, but it can't be
>>>>>>>>>>> proven in F that this is true, because in F, to show this we
>>>>>>>>>>> need to test every natuarl number, which requires an infinite
>>>>>>>>>>> number of steps (finite for each number, but an infinite
>>>>>>>>>>> number of numbers to test).
>>>>>>>>>>>
>>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>>> knowledge in meta-F, we can show that if a number g could be
>>>>>>>>>>> found, then that number g could be converted into a proof, in
>>>>>>>>>>> F, of the statement G (which says that such a number does not
>>>>>>>>>>> exist).
>>>>>>>>>>>
>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>>>
>>>>>>>>>> So your basic line-of-reasoning is that G is true in F even if
>>>>>>>>>> the truth
>>>>>>>>>> of G cannot even be expressed in F as long as the truth of G
>>>>>>>>>> can be
>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>>>> expression.
>>>>>>>> That is false. It is not that G takes an infinite number of
>>>>>>>> steps to
>>>>>>>> reach its truth maker axioms in F it is that even after an infinite
>>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>>> because G is
>>>>>>>> simply untrue in F.
>>>>>>>
>>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>>
>>>>>>>>
>>>>>>>> "This sentence is not true"
>>>>>>>
>>>>>>> Which isn't G.
>>>>>>>
>>>>>>>> Not true about what?
>>>>>>>> Not true about being not true.
>>>>>>>> Not true about being not true about what?
>>>>>>>> Not true about being not true about being not true.
>>>>>>>>
>>>>>>>
>>>>>>> So you are just a MORON.
>>>>>>>
>>>>>>>> Since Gödel said:
>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>> similar undecidability proof.
>>>>>>>>
>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his
>>>>>>>> proof we
>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>
>>>>>>>
>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>
>>>>>>
>>>>>> Ad Hominem attacks are the tactic that people having no interest
>>>>>> in any
>>>>>> honest dialogue use when they realize that their reasoning has been
>>>>>> utterly defeated.
>>>>>>
>>>>>
>>>>> And RED HERRING arguements don't work either.
>>>>>
>>>>> You ARE a LYING MORON as you insist that Godel's G is a sentence
>>>>> that is actually provably isn't.
>>>>>
>>>>> You think it is because you are too stupid to actually read any of
>>>>> the paper, so you take that comment that the statment is "based" on
>>>>> that statement to mean it IS that statement.
>>>>>
>>>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>>>> are asserting this counter-factual statement:
>>>>
>>>> when a valid proxy for an argument is defeated this does not defeat the
>>>> original argument.
>>>>
>>>
>>> Right, which is what YOU are doing, showing your arguement is INVALID.
>>>
>>
>> In other words you disagree that correctly refuting a valid proxy for an
>> argument does correctly refute the original argument?
>>
>>
>
> VALID is the key word,
>
> Yours isn't (I don't think you actually know the meaning of the words)
>
> And you are an IDIOT to claim it is.
So Gödel is wrong when he says:

On 1/15/23 2:29 PM, olcott wrote:
> On 1/15/2023 1:06 PM, Richard Damon wrote:
>> On 1/15/23 2:00 PM, olcott wrote:
>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL
>>>>>>>>>>>>>>>>> SYSTEM* ???
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>>>>>> true ???
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to
>>>>>>>>>>>>>> be true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>>>>> expression of
>>>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>>>> untrue in that
>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>
>>>>>>>>>>>> Right, but the connection can be infinite in length, and
>>>>>>>>>>>> thus not provable.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>>>> formal system
>>>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>>>> connection to
>>>>>>>>>>>>> truth maker axioms in this formal system. You must show why
>>>>>>>>>>>>> it is true
>>>>>>>>>>>>> in this formal system not merely that it is true somewhere
>>>>>>>>>>>>> else.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>>>>>> proof strictly in the formal system.
>>>>>>>>>>>>
>>>>>>>>>>>> If the connection exists as an infinite connection within
>>>>>>>>>>>> the system, then it is TRUE in the system.
>>>>>>>>>>>>
>>>>>>>>>>>> Note, that if there is such an infinite connection, which
>>>>>>>>>>>> thus can not be proven within the formal system, it is still
>>>>>>>>>>>> possible, that another system, related to that system, with
>>>>>>>>>>>> more knowledge, might be able to show that there does exist
>>>>>>>>>>>> within the original formal system such an infinte connection.
>>>>>>>>>>>>
>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>
>>>>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>>>>> recursive relationship).
>>>>>>>>>>>>
>>>>>>>>>>>> This statement turns out to be true, because it turns out
>>>>>>>>>>>> that no number g does meet that requirement, but it can't be
>>>>>>>>>>>> proven in F that this is true, because in F, to show this we
>>>>>>>>>>>> need to test every natuarl number, which requires an
>>>>>>>>>>>> infinite number of steps (finite for each number, but an
>>>>>>>>>>>> infinite number of numbers to test).
>>>>>>>>>>>>
>>>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>>>> knowledge in meta-F, we can show that if a number g could be
>>>>>>>>>>>> found, then that number g could be converted into a proof,
>>>>>>>>>>>> in F, of the statement G (which says that such a number does
>>>>>>>>>>>> not exist).
>>>>>>>>>>>>
>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>>>>
>>>>>>>>>>> So your basic line-of-reasoning is that G is true in F even
>>>>>>>>>>> if the truth
>>>>>>>>>>> of G cannot even be expressed in F as long as the truth of G
>>>>>>>>>>> can be
>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>>>>> expression.
>>>>>>>>> That is false. It is not that G takes an infinite number of
>>>>>>>>> steps to
>>>>>>>>> reach its truth maker axioms in F it is that even after an
>>>>>>>>> infinite
>>>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>>>> because G is
>>>>>>>>> simply untrue in F.
>>>>>>>>
>>>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> "This sentence is not true"
>>>>>>>>
>>>>>>>> Which isn't G.
>>>>>>>>
>>>>>>>>> Not true about what?
>>>>>>>>> Not true about being not true.
>>>>>>>>> Not true about being not true about what?
>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>
>>>>>>>>
>>>>>>>> So you are just a MORON.
>>>>>>>>
>>>>>>>>> Since Gödel said:
>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>> similar undecidability proof.
>>>>>>>>>
>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his
>>>>>>>>> proof we
>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>
>>>>>>>>
>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>
>>>>>>>
>>>>>>> Ad Hominem attacks are the tactic that people having no interest
>>>>>>> in any
>>>>>>> honest dialogue use when they realize that their reasoning has been
>>>>>>> utterly defeated.
>>>>>>>
>>>>>>
>>>>>> And RED HERRING arguements don't work either.
>>>>>>
>>>>>> You ARE a LYING MORON as you insist that Godel's G is a sentence
>>>>>> that is actually provably isn't.
>>>>>>
>>>>>> You think it is because you are too stupid to actually read any of
>>>>>> the paper, so you take that comment that the statment is "based"
>>>>>> on that statement to mean it IS that statement.
>>>>>>
>>>>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>>>>> are asserting this counter-factual statement:
>>>>>
>>>>> when a valid proxy for an argument is defeated this does not defeat
>>>>> the
>>>>> original argument.
>>>>>
>>>>
>>>> Right, which is what YOU are doing, showing your arguement is INVALID.
>>>>
>>>
>>> In other words you disagree that correctly refuting a valid proxy for an
>>> argument does correctly refute the original argument?
>>>
>>>
>>
>> VALID is the key word,
>>
>> Yours isn't (I don't think you actually know the meaning of the words)
>>
>> And you are an IDIOT to claim it is.
> So Gödel is wrong when he says:
>
> 14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof.
>
>

On 1/15/23 2:28 PM, olcott wrote:
> On 1/15/2023 12:55 PM, Richard Damon wrote:
>> On 1/15/23 1:23 PM, olcott wrote:
>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>>> formal system is true unless this expression of language
>>>>>>>>>>>>>>> has a
>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0) is
>>>>>>>>>>>>> true ???
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>
>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>>
>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>
>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>
>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to be
>>>>>>>>>>>> true.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>>> expression of
>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>> untrue in that
>>>>>>>>>>> formal system.
>>>>>>>>>>
>>>>>>>>>> Right, but the connection can be infinite in length, and thus
>>>>>>>>>> not provable.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>> formal system
>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>> connection to
>>>>>>>>>>> truth maker axioms in this formal system. You must show why
>>>>>>>>>>> it is true
>>>>>>>>>>> in this formal system not merely that it is true somewhere else.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as a
>>>>>>>>>> proof strictly in the formal system.
>>>>>>>>>>
>>>>>>>>>> If the connection exists as an infinite connection within the
>>>>>>>>>> system, then it is TRUE in the system.
>>>>>>>>>>
>>>>>>>>>> Note, that if there is such an infinite connection, which thus
>>>>>>>>>> can not be proven within the formal system, it is still
>>>>>>>>>> possible, that another system, related to that system, with
>>>>>>>>>> more knowledge, might be able to show that there does exist
>>>>>>>>>> within the original formal system such an infinte connection.
>>>>>>>>>>
>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>
>>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>>> recursive relationship).
>>>>>>>>>>
>>>>>>>>>> This statement turns out to be true, because it turns out that
>>>>>>>>>> no number g does meet that requirement, but it can't be proven
>>>>>>>>>> in F that this is true, because in F, to show this we need to
>>>>>>>>>> test every natuarl number, which requires an infinite number
>>>>>>>>>> of steps (finite for each number, but an infinite number of
>>>>>>>>>> numbers to test).
>>>>>>>>>>
>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>> knowledge in meta-F, we can show that if a number g could be
>>>>>>>>>> found, then that number g could be converted into a proof, in
>>>>>>>>>> F, of the statement G (which says that such a number does not
>>>>>>>>>> exist).
>>>>>>>>>>
>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>>
>>>>>>>>> So your basic line-of-reasoning is that G is true in F even if
>>>>>>>>> the truth
>>>>>>>>> of G cannot even be expressed in F as long as the truth of G
>>>>>>>>> can be
>>>>>>>>> expressed in meta-F.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>>> expression.
>>>>>>> That is false. It is not that G takes an infinite number of steps to
>>>>>>> reach its truth maker axioms in F it is that even after an infinite
>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>> because G is
>>>>>>> simply untrue in F.
>>>>>>
>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>
>>>>>>>
>>>>>>> "This sentence is not true"
>>>>>>
>>>>>> Which isn't G.
>>>>>>
>>>>>>> Not true about what?
>>>>>>> Not true about being not true.
>>>>>>> Not true about being not true about what?
>>>>>>> Not true about being not true about being not true.
>>>>>>>
>>>>>>
>>>>>> So you are just a MORON.
>>>>>>
>>>>>>> Since Gödel said:
>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>> similar undecidability proof.
>>>>>>>
>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his proof we
>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>
>>>>>>
>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>
>>>>>
>>>>> Ad Hominem attacks are the tactic that people having no interest in
>>>>> any
>>>>> honest dialogue use when they realize that their reasoning has been
>>>>> utterly defeated.
>>>>>
>>>>
>>>> And RED HERRING arguements don't work either.
>>>>
>>>> You ARE a LYING MORON as you insist that Godel's G is a sentence
>>>> that is actually provably isn't.
>>>>
>>>> You think it is because you are too stupid to actually read any of
>>>> the paper, so you take that comment that the statment is "based" on
>>>> that statement to mean it IS that statement.
>>>>
>>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>>> are asserting this counter-factual statement:
>>>
>>> when a valid proxy for an argument is defeated this does not defeat the
>>> original argument.
>>>
>>
>> Right, which is what YOU are doing, showing your arguement is INVALID.
>>
> In other words you disagree that correctly refuting a valid proxy for an
> argument does correctly refute the original argument?
>

On 1/15/2023 1:46 PM, Richard Damon wrote:
> On 1/15/23 2:29 PM, olcott wrote:
>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>> On 1/15/23 2:00 PM, olcott wrote:
>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL
>>>>>>>>>>>>>>>>>> SYSTEM* ???
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is
>>>>>>>>>>>>>>>>> true.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0)
>>>>>>>>>>>>>>>> is true ???
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to be
>>>>>>>>>>>>>>> true, doesn't mean it can't be.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN to
>>>>>>>>>>>>>>> be true.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>>>>>> expression of
>>>>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>>>>> untrue in that
>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Right, but the connection can be infinite in length, and
>>>>>>>>>>>>> thus not provable.
>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>>>>> formal system
>>>>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>>>>> connection to
>>>>>>>>>>>>>> truth maker axioms in this formal system. You must show
>>>>>>>>>>>>>> why it is true
>>>>>>>>>>>>>> in this formal system not merely that it is true somewhere
>>>>>>>>>>>>>> else.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as
>>>>>>>>>>>>> a proof strictly in the formal system.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If the connection exists as an infinite connection within
>>>>>>>>>>>>> the system, then it is TRUE in the system.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Note, that if there is such an infinite connection, which
>>>>>>>>>>>>> thus can not be proven within the formal system, it is
>>>>>>>>>>>>> still possible, that another system, related to that
>>>>>>>>>>>>> system, with more knowledge, might be able to show that
>>>>>>>>>>>>> there does exist within the original formal system such an
>>>>>>>>>>>>> infinte connection.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>
>>>>>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>>>>>> recursive relationship).
>>>>>>>>>>>>>
>>>>>>>>>>>>> This statement turns out to be true, because it turns out
>>>>>>>>>>>>> that no number g does meet that requirement, but it can't
>>>>>>>>>>>>> be proven in F that this is true, because in F, to show
>>>>>>>>>>>>> this we need to test every natuarl number, which requires
>>>>>>>>>>>>> an infinite number of steps (finite for each number, but an
>>>>>>>>>>>>> infinite number of numbers to test).
>>>>>>>>>>>>>
>>>>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>>>>> knowledge in meta-F, we can show that if a number g could
>>>>>>>>>>>>> be found, then that number g could be converted into a
>>>>>>>>>>>>> proof, in F, of the statement G (which says that such a
>>>>>>>>>>>>> number does not exist).
>>>>>>>>>>>>>
>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also show
>>>>>>>>>>>>> that no proof of it can exist in F.
>>>>>>>>>>>>>
>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in F even
>>>>>>>>>>>> if the truth
>>>>>>>>>>>> of G cannot even be expressed in F as long as the truth of G
>>>>>>>>>>>> can be
>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>>>>>> expression.
>>>>>>>>>> That is false. It is not that G takes an infinite number of
>>>>>>>>>> steps to
>>>>>>>>>> reach its truth maker axioms in F it is that even after an
>>>>>>>>>> infinite
>>>>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>>>>> because G is
>>>>>>>>>> simply untrue in F.
>>>>>>>>>
>>>>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> "This sentence is not true"
>>>>>>>>>
>>>>>>>>> Which isn't G.
>>>>>>>>>
>>>>>>>>>> Not true about what?
>>>>>>>>>> Not true about being not true.
>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So you are just a MORON.
>>>>>>>>>
>>>>>>>>>> Since Gödel said:
>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>
>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his
>>>>>>>>>> proof we
>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Ad Hominem attacks are the tactic that people having no interest
>>>>>>>> in any
>>>>>>>> honest dialogue use when they realize that their reasoning has been
>>>>>>>> utterly defeated.
>>>>>>>>
>>>>>>>
>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>
>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a sentence
>>>>>>> that is actually provably isn't.
>>>>>>>
>>>>>>> You think it is because you are too stupid to actually read any
>>>>>>> of the paper, so you take that comment that the statment is
>>>>>>> "based" on that statement to mean it IS that statement.
>>>>>>>
>>>>>> All of your Ad Hominem attacks cannot possibly hide the fact that you
>>>>>> are asserting this counter-factual statement:
>>>>>>
>>>>>> when a valid proxy for an argument is defeated this does not
>>>>>> defeat the
>>>>>> original argument.
>>>>>>
>>>>>
>>>>> Right, which is what YOU are doing, showing your arguement is INVALID.
>>>>>
>>>>
>>>> In other words you disagree that correctly refuting a valid proxy
>>>> for an
>>>> argument does correctly refute the original argument?
>>>>
>>>>
>>>
>>> VALID is the key word,
>>>
>>> Yours isn't (I don't think you actually know the meaning of the words)
>>>
>>> And you are an IDIOT to claim it is.
>> So Gödel is wrong when he says:
>>
>> 14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof.
>>
>>
>
> No, but you don't understand what he is saying.
>
He is saying that every epistemological antinomy is a valid proxy for
his proof. He is not saying that his expression is not an
epistemological antinomy.

On 1/15/23 3:12 PM, olcott wrote:
> On 1/15/2023 1:46 PM, Richard Damon wrote:
>> On 1/15/23 2:29 PM, olcott wrote:
>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> How does the formal system know that an expression of
>>>>>>>>>>>>>>>>>>> language of this
>>>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL
>>>>>>>>>>>>>>>>>>> SYSTEM* ???
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is
>>>>>>>>>>>>>>>>>> true.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0)
>>>>>>>>>>>>>>>>> is true ???
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to
>>>>>>>>>>>>>>>> be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN
>>>>>>>>>>>>>>>> to be true.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection from an
>>>>>>>>>>>>>>> expression of
>>>>>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>>>>>> untrue in that
>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Right, but the connection can be infinite in length, and
>>>>>>>>>>>>>> thus not provable.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>>>>>> formal system
>>>>>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>>>>>> connection to
>>>>>>>>>>>>>>> truth maker axioms in this formal system. You must show
>>>>>>>>>>>>>>> why it is true
>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE as
>>>>>>>>>>>>>> a proof strictly in the formal system.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> If the connection exists as an infinite connection within
>>>>>>>>>>>>>> the system, then it is TRUE in the system.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Note, that if there is such an infinite connection, which
>>>>>>>>>>>>>> thus can not be proven within the formal system, it is
>>>>>>>>>>>>>> still possible, that another system, related to that
>>>>>>>>>>>>>> system, with more knowledge, might be able to show that
>>>>>>>>>>>>>> there does exist within the original formal system such an
>>>>>>>>>>>>>> infinte connection.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> G states that there does not exist a Natural Number g that
>>>>>>>>>>>>>> meets a specific requirement (expressed as a primative
>>>>>>>>>>>>>> recursive relationship).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> This statement turns out to be true, because it turns out
>>>>>>>>>>>>>> that no number g does meet that requirement, but it can't
>>>>>>>>>>>>>> be proven in F that this is true, because in F, to show
>>>>>>>>>>>>>> this we need to test every natuarl number, which requires
>>>>>>>>>>>>>> an infinite number of steps (finite for each number, but
>>>>>>>>>>>>>> an infinite number of numbers to test).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>>>>>> knowledge in meta-F, we can show that if a number g could
>>>>>>>>>>>>>> be found, then that number g could be converted into a
>>>>>>>>>>>>>> proof, in F, of the statement G (which says that such a
>>>>>>>>>>>>>> number does not exist).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also
>>>>>>>>>>>>>> show that no proof of it can exist in F.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in F even
>>>>>>>>>>>>> if the truth
>>>>>>>>>>>>> of G cannot even be expressed in F as long as the truth of
>>>>>>>>>>>>> G can be
>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an infinite
>>>>>>>>>>>> expression.
>>>>>>>>>>> That is false. It is not that G takes an infinite number of
>>>>>>>>>>> steps to
>>>>>>>>>>> reach its truth maker axioms in F it is that even after an
>>>>>>>>>>> infinite
>>>>>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>>>>>> because G is
>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>
>>>>>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>
>>>>>>>>>> Which isn't G.
>>>>>>>>>>
>>>>>>>>>>> Not true about what?
>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>
>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>>
>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his
>>>>>>>>>>> proof we
>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>> interest in any
>>>>>>>>> honest dialogue use when they realize that their reasoning has
>>>>>>>>> been
>>>>>>>>> utterly defeated.
>>>>>>>>>
>>>>>>>>
>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>
>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a sentence
>>>>>>>> that is actually provably isn't.
>>>>>>>>
>>>>>>>> You think it is because you are too stupid to actually read any
>>>>>>>> of the paper, so you take that comment that the statment is
>>>>>>>> "based" on that statement to mean it IS that statement.
>>>>>>>>
>>>>>>> All of your Ad Hominem attacks cannot possibly hide the fact that
>>>>>>> you
>>>>>>> are asserting this counter-factual statement:
>>>>>>>
>>>>>>> when a valid proxy for an argument is defeated this does not
>>>>>>> defeat the
>>>>>>> original argument.
>>>>>>>
>>>>>>
>>>>>> Right, which is what YOU are doing, showing your arguement is
>>>>>> INVALID.
>>>>>>
>>>>>
>>>>> In other words you disagree that correctly refuting a valid proxy
>>>>> for an
>>>>> argument does correctly refute the original argument?
>>>>>
>>>>>
>>>>
>>>> VALID is the key word,
>>>>
>>>> Yours isn't (I don't think you actually know the meaning of the words)
>>>>
>>>> And you are an IDIOT to claim it is.
>>> So Gödel is wrong when he says:
>>>
>>> 14 Every epistemological antinomy can likewise be used for a
>>> similar undecidability proof.
>>>
>>>
>>
>> No, but you don't understand what he is saying.
>>
> He is saying that every epistemological antinomy is a valid proxy for
> his proof. He is not saying that his expression is not an
> epistemological antinomy.
>

On 1/15/2023 2:23 PM, Richard Damon wrote:
> On 1/15/23 3:12 PM, olcott wrote:
>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>> On 1/15/23 2:29 PM, olcott wrote:
>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> How does the formal system know that an expression
>>>>>>>>>>>>>>>>>>>> of language of this
>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL
>>>>>>>>>>>>>>>>>>>> SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what is
>>>>>>>>>>>>>>>>>>> true.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) + successor(0)
>>>>>>>>>>>>>>>>>> is true ???
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to
>>>>>>>>>>>>>>>>> be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN
>>>>>>>>>>>>>>>>> to be true.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection from
>>>>>>>>>>>>>>>> an expression of
>>>>>>>>>>>>>>>> its language to its truth maker axioms the expression is
>>>>>>>>>>>>>>>> untrue in that
>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Right, but the connection can be infinite in length, and
>>>>>>>>>>>>>>> thus not provable.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Try and show an expression of language that is true in a
>>>>>>>>>>>>>>>> formal system
>>>>>>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>>>>>>> connection to
>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You must show
>>>>>>>>>>>>>>>> why it is true
>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE
>>>>>>>>>>>>>>> as a proof strictly in the formal system.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If the connection exists as an infinite connection within
>>>>>>>>>>>>>>> the system, then it is TRUE in the system.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Note, that if there is such an infinite connection, which
>>>>>>>>>>>>>>> thus can not be proven within the formal system, it is
>>>>>>>>>>>>>>> still possible, that another system, related to that
>>>>>>>>>>>>>>> system, with more knowledge, might be able to show that
>>>>>>>>>>>>>>> there does exist within the original formal system such
>>>>>>>>>>>>>>> an infinte connection.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> G states that there does not exist a Natural Number g
>>>>>>>>>>>>>>> that meets a specific requirement (expressed as a
>>>>>>>>>>>>>>> primative recursive relationship).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> This statement turns out to be true, because it turns out
>>>>>>>>>>>>>>> that no number g does meet that requirement, but it can't
>>>>>>>>>>>>>>> be proven in F that this is true, because in F, to show
>>>>>>>>>>>>>>> this we need to test every natuarl number, which requires
>>>>>>>>>>>>>>> an infinite number of steps (finite for each number, but
>>>>>>>>>>>>>>> an infinite number of numbers to test).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>>>>>>> knowledge in meta-F, we can show that if a number g could
>>>>>>>>>>>>>>> be found, then that number g could be converted into a
>>>>>>>>>>>>>>> proof, in F, of the statement G (which says that such a
>>>>>>>>>>>>>>> number does not exist).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also
>>>>>>>>>>>>>>> show that no proof of it can exist in F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in F
>>>>>>>>>>>>>> even if the truth
>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the truth of
>>>>>>>>>>>>>> G can be
>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>> That is false. It is not that G takes an infinite number of
>>>>>>>>>>>> steps to
>>>>>>>>>>>> reach its truth maker axioms in F it is that even after an
>>>>>>>>>>>> infinite
>>>>>>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>>>>>>> because G is
>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>
>>>>>>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>
>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>
>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>
>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>>>> similar undecidability proof.
>>>>>>>>>>>>
>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his
>>>>>>>>>>>> proof we
>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>>> interest in any
>>>>>>>>>> honest dialogue use when they realize that their reasoning has
>>>>>>>>>> been
>>>>>>>>>> utterly defeated.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>
>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>
>>>>>>>>> You think it is because you are too stupid to actually read any
>>>>>>>>> of the paper, so you take that comment that the statment is
>>>>>>>>> "based" on that statement to mean it IS that statement.
>>>>>>>>>
>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the fact
>>>>>>>> that you
>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>
>>>>>>>> when a valid proxy for an argument is defeated this does not
>>>>>>>> defeat the
>>>>>>>> original argument.
>>>>>>>>
>>>>>>>
>>>>>>> Right, which is what YOU are doing, showing your arguement is
>>>>>>> INVALID.
>>>>>>>
>>>>>>
>>>>>> In other words you disagree that correctly refuting a valid proxy
>>>>>> for an
>>>>>> argument does correctly refute the original argument?
>>>>>>
>>>>>>
>>>>>
>>>>> VALID is the key word,
>>>>>
>>>>> Yours isn't (I don't think you actually know the meaning of the words)
>>>>>
>>>>> And you are an IDIOT to claim it is.
>>>> So Gödel is wrong when he says:
>>>>
>>>> 14 Every epistemological antinomy can likewise be used for a
>>>> similar undecidability proof.
>>>>
>>>>
>>>
>>> No, but you don't understand what he is saying.
>>>
>> He is saying that every epistemological antinomy is a valid proxy for
>> his proof. He is not saying that his expression is not an
>> epistemological antinomy.
>>
>
> Nope, that isn't what he is saying. How could it be, the ACTUAL G is a
> proven Truth Bearer, while the Liar's Paradox isn't
>
> Your arguement just shows its inconsistency.
>
> In part, because you don't actually understand what the sentence
> actually is.
>
>
>> The analogy between this result and Richard’s antinomy leaps to the eye;
>> there is also a close relationship with the “liar” antinomy,14 since the
>> undecidable proposition [R(q); q] states precisely that q belongs to K,
>> i.e. according to (1), that [R(q); q] is not provable. We are therefore
>> confronted with a proposition which asserts its own unprovability.
>> (Gödel 1931:43)
>>
>> This <is> an isomorphism to a proposition that asserts its own untruth.
>>
>>
>
> Nope, unless you erroneously think that statements about Truth ARE
> statements about provability, that isn't an isomoprhism.
>
> Note, you have even stated that *ALL* statements of the form "statement
> x is provable" or "Statment x is not provable" are Truth Bearers,

On 1/15/23 7:26 PM, olcott wrote:
> On 1/15/2023 2:23 PM, Richard Damon wrote:
>> On 1/15/23 3:12 PM, olcott wrote:
>>> On 1/15/2023 1:46 PM, Richard Damon wrote:
>>>> On 1/15/23 2:29 PM, olcott wrote:
>>>>> On 1/15/2023 1:06 PM, Richard Damon wrote:
>>>>>> On 1/15/23 2:00 PM, olcott wrote:
>>>>>>> On 1/15/2023 12:55 PM, Richard Damon wrote:
>>>>>>>> On 1/15/23 1:23 PM, olcott wrote:
>>>>>>>>> On 1/15/2023 11:58 AM, Richard Damon wrote:
>>>>>>>>>> On 1/15/23 12:47 PM, olcott wrote:
>>>>>>>>>>> On 1/15/2023 11:41 AM, Richard Damon wrote:
>>>>>>>>>>>> On 1/15/23 12:31 PM, olcott wrote:
>>>>>>>>>>>>> On 1/15/2023 11:05 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/15/23 11:15 AM, olcott wrote:
>>>>>>>>>>>>>>> On 1/14/2023 5:42 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/14/23 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/14/2023 4:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 1/14/23 5:31 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> How does the formal system know that an expression
>>>>>>>>>>>>>>>>>>>>> of language of this
>>>>>>>>>>>>>>>>>>>>> formal system is true unless this expression of
>>>>>>>>>>>>>>>>>>>>> language has a
>>>>>>>>>>>>>>>>>>>>> connection to truth maker axioms *IN THIS FORMAL
>>>>>>>>>>>>>>>>>>>>> SYSTEM* ???
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Becaue the formal system doesn't need to KNOW what
>>>>>>>>>>>>>>>>>>>> is true.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> So PA has no idea that:
>>>>>>>>>>>>>>>>>>> successor(successor(0)) == successor(0) +
>>>>>>>>>>>>>>>>>>> successor(0) is true ???
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Why do you say that.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Just because truth doesn't NEED to be proven for it to
>>>>>>>>>>>>>>>>>> be true, doesn't mean it can't be.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> In fact, your statement just comes out of a simple
>>>>>>>>>>>>>>>>>> application of the addition AXIOMS of PA.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> a + 0 = a
>>>>>>>>>>>>>>>>>> a + Successor(b) = Successor(a + b)
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> So it is a PROVABLE statement, and thus actually KNOWN
>>>>>>>>>>>>>>>>>> to be true.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Unless a formal system has a syntactic connection from
>>>>>>>>>>>>>>>>> an expression of
>>>>>>>>>>>>>>>>> its language to its truth maker axioms the expression
>>>>>>>>>>>>>>>>> is untrue in that
>>>>>>>>>>>>>>>>> formal system.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Right, but the connection can be infinite in length, and
>>>>>>>>>>>>>>>> thus not provable.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Try and show an expression of language that is true in
>>>>>>>>>>>>>>>>> a formal system
>>>>>>>>>>>>>>>>> (not just true somewhere else) that does not have any
>>>>>>>>>>>>>>>>> connection to
>>>>>>>>>>>>>>>>> truth maker axioms in this formal system. You must show
>>>>>>>>>>>>>>>>> why it is true
>>>>>>>>>>>>>>>>> in this formal system not merely that it is true
>>>>>>>>>>>>>>>>> somewhere else.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The connection might be infinite, and thus not SHOWABLE
>>>>>>>>>>>>>>>> as a proof strictly in the formal system.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If the connection exists as an infinite connection
>>>>>>>>>>>>>>>> within the system, then it is TRUE in the system.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Note, that if there is such an infinite connection,
>>>>>>>>>>>>>>>> which thus can not be proven within the formal system,
>>>>>>>>>>>>>>>> it is still possible, that another system, related to
>>>>>>>>>>>>>>>> that system, with more knowledge, might be able to show
>>>>>>>>>>>>>>>> that there does exist within the original formal system
>>>>>>>>>>>>>>>> such an infinte connection.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> This is what happens to G in F and meta-F
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> G states that there does not exist a Natural Number g
>>>>>>>>>>>>>>>> that meets a specific requirement (expressed as a
>>>>>>>>>>>>>>>> primative recursive relationship).
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> This statement turns out to be true, because it turns
>>>>>>>>>>>>>>>> out that no number g does meet that requirement, but it
>>>>>>>>>>>>>>>> can't be proven in F that this is true, because in F, to
>>>>>>>>>>>>>>>> show this we need to test every natuarl number, which
>>>>>>>>>>>>>>>> requires an infinite number of steps (finite for each
>>>>>>>>>>>>>>>> number, but an infinite number of numbers to test).
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> In meta-F, we can do better, because due to additional
>>>>>>>>>>>>>>>> knowledge in meta-F, we can show that if a number g
>>>>>>>>>>>>>>>> could be found, then that number g could be converted
>>>>>>>>>>>>>>>> into a proof, in F, of the statement G (which says that
>>>>>>>>>>>>>>>> such a number does not exist).
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Thus, in meta-F, we can prove that G is true, and also
>>>>>>>>>>>>>>>> show that no proof of it can exist in F.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So your basic line-of-reasoning is that G is true in F
>>>>>>>>>>>>>>> even if the truth
>>>>>>>>>>>>>>> of G cannot even be expressed in F as long as the truth
>>>>>>>>>>>>>>> of G can be
>>>>>>>>>>>>>>> expressed in meta-F.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Expect that it CAN be expressed in F, it just is an
>>>>>>>>>>>>>> infinite expression.
>>>>>>>>>>>>> That is false. It is not that G takes an infinite number of
>>>>>>>>>>>>> steps to
>>>>>>>>>>>>> reach its truth maker axioms in F it is that even after an
>>>>>>>>>>>>> infinite
>>>>>>>>>>>>> number of steps it never reaches is truth maker axioms in F
>>>>>>>>>>>>> because G is
>>>>>>>>>>>>> simply untrue in F.
>>>>>>>>>>>>
>>>>>>>>>>>> No, YOUR problem is you aren't actually talking about G in F.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> "This sentence is not true"
>>>>>>>>>>>>
>>>>>>>>>>>> Which isn't G.
>>>>>>>>>>>>
>>>>>>>>>>>>> Not true about what?
>>>>>>>>>>>>> Not true about being not true.
>>>>>>>>>>>>> Not true about being not true about what?
>>>>>>>>>>>>> Not true about being not true about being not true.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> So you are just a MORON.
>>>>>>>>>>>>
>>>>>>>>>>>>> Since Gödel said:
>>>>>>>>>>>>> 14 Every epistemological antinomy can likewise be used for
>>>>>>>>>>>>> a similar undecidability proof.
>>>>>>>>>>>>>
>>>>>>>>>>>>> By using the Liar Paradox as a Gödel approved proxy for his
>>>>>>>>>>>>> proof we
>>>>>>>>>>>>> refute his proof by this Gödel approved proxy.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> No, all you have proved is that you are a LYING MORON.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Ad Hominem attacks are the tactic that people having no
>>>>>>>>>>> interest in any
>>>>>>>>>>> honest dialogue use when they realize that their reasoning
>>>>>>>>>>> has been
>>>>>>>>>>> utterly defeated.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> And RED HERRING arguements don't work either.
>>>>>>>>>>
>>>>>>>>>> You ARE a LYING MORON as you insist that Godel's G is a
>>>>>>>>>> sentence that is actually provably isn't.
>>>>>>>>>>
>>>>>>>>>> You think it is because you are too stupid to actually read
>>>>>>>>>> any of the paper, so you take that comment that the statment
>>>>>>>>>> is "based" on that statement to mean it IS that statement.
>>>>>>>>>>
>>>>>>>>> All of your Ad Hominem attacks cannot possibly hide the fact
>>>>>>>>> that you
>>>>>>>>> are asserting this counter-factual statement:
>>>>>>>>>
>>>>>>>>> when a valid proxy for an argument is defeated this does not
>>>>>>>>> defeat the
>>>>>>>>> original argument.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Right, which is what YOU are doing, showing your arguement is
>>>>>>>> INVALID.
>>>>>>>>
>>>>>>>
>>>>>>> In other words you disagree that correctly refuting a valid proxy
>>>>>>> for an
>>>>>>> argument does correctly refute the original argument?
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> VALID is the key word,
>>>>>>
>>>>>> Yours isn't (I don't think you actually know the meaning of the
>>>>>> words)
>>>>>>
>>>>>> And you are an IDIOT to claim it is.
>>>>> So Gödel is wrong when he says:
>>>>>
>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof.
>>>>>
>>>>>
>>>>
>>>> No, but you don't understand what he is saying.
>>>>
>>> He is saying that every epistemological antinomy is a valid proxy for
>>> his proof. He is not saying that his expression is not an
>>> epistemological antinomy.
>>>
>>
>> Nope, that isn't what he is saying. How could it be, the ACTUAL G is a
>> proven Truth Bearer, while the Liar's Paradox isn't
>>
>> Your arguement just shows its inconsistency.
>>
>> In part, because you don't actually understand what the sentence
>> actually is.
>>
>>
>>> The analogy between this result and Richard’s antinomy leaps to the eye;
>>> there is also a close relationship with the “liar” antinomy,14 since the
>>> undecidable proposition [R(q); q] states precisely that q belongs to K,
>>> i.e. according to (1), that [R(q); q] is not provable. We are therefore
>>> confronted with a proposition which asserts its own unprovability.
>>> (Gödel 1931:43)
>>>
>>> This <is> an isomorphism to a proposition that asserts its own untruth.
>>>
>>>
>>
>> Nope, unless you erroneously think that statements about Truth ARE
>> statements about provability, that isn't an isomoprhism.
>>
>> Note, you have even stated that *ALL* statements of the form
>> "statement x is provable" or "Statment x is not provable" are Truth
>> Bearers,
>
> I have most definitely never said this or anything that could be
> unintentionally misconstrued to mean this.
>
> It is always the case that when-so-ever any expression of language only
> refers to its own truth or provability that this expression is not a
> truth bearer, thus not a member of any formal system of logic.
>