Just like with syllogisms conclusions a semantically necessary
consequence of their premises

Semantic Necessity operator: ⊨□

(a) Some expressions of language L are stipulated to have the property
of Boolean true.

(b) Some expressions of language L are a semantically necessary
consequence of others.

True(L,X) means that a semantic connection exists between (a) and X in
L. *Axiom(P) ⊨□ X*

Provable(L,P,X) means that a semantic connection exists between premises
P and X in L. *P ⊨□ X*

The Moon is made from green cheese ⊨□ The Moon is made from cheese

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

On 3/18/23 7:17 PM, olcott wrote:
> Just like with syllogisms conclusions a semantically necessary
> consequence of their premises
>
> Semantic Necessity operator: ⊨□
>
> (a) Some expressions of language L are stipulated to have the property
> of Boolean true.
>
> (b) Some expressions of language L are a semantically necessary
> consequence of others.
>
> True(L,X) means that a semantic connection exists between (a) and X in
> L. *Axiom(P) ⊨□ X*
>
> Provable(L,P,X) means that a semantic connection exists between premises
> P and X in L.   *P ⊨□ X*
>
> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>
>
>

You understand that your "Provable" doesn't match at all the normal
concept of Provable.

In normal logic, Provable is more like your "True" operator, except that
it include the restriction that the chain of semantic connections is
finite in length, i.e. actually expressible.

We talk about a Statement being Provable or not, not with respect to a
given premise, but the logic system as a whole.

On 3/18/2023 6:17 PM, olcott wrote:
> Just like with syllogisms conclusions a semantically necessary
> consequence of their premises
>
> Semantic Necessity operator: ⊨□
>
> (a) Some expressions of language L are stipulated to have the property
> of Boolean true.
>
> (b) Some expressions of language L are a semantically necessary
> consequence of others.
>
> True(L,X) means that a semantic connection exists between (a) and X in
> L. *Axiom(P) ⊨□ X*
>
> Provable(L,P,X) means that a semantic connection exists between premises
> P and X in L.   *P ⊨□ X*
>
> The Moon is made from green cheese ⊨□ The Moon is made from cheese

When this is called the foundation of correct reasoning
*and indeed is the actual foundation of correct reasoning*
that means that every system of logic either derives all of its
operations on the basis of this system or such a system diverges from
correct reasoning into incorrect thus erroneous reasoning.

The kludge of the principle of explosion is eradicated by this
foundation. https://en.wikipedia.org/wiki/Principle_of_explosion

I am not sure what aspect of logic would be changed by this system that
is why I opened up this discussion.

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

On 3/18/23 8:32 PM, olcott wrote:
> On 3/18/2023 6:17 PM, olcott wrote:
>> Just like with syllogisms conclusions a semantically necessary
>> consequence of their premises
>>
>> Semantic Necessity operator: ⊨□
>>
>> (a) Some expressions of language L are stipulated to have the property
>> of Boolean true.
>>
>> (b) Some expressions of language L are a semantically necessary
>> consequence of others.
>>
>> True(L,X) means that a semantic connection exists between (a) and X in
>> L. *Axiom(P) ⊨□ X*
>>
>> Provable(L,P,X) means that a semantic connection exists between
>> premises P and X in L.   *P ⊨□ X*
>>
>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>
> When this is called the foundation of correct reasoning
> *and indeed is the actual foundation of correct reasoning*
> that means that every system of logic either derives all of its
> operations on the basis of this system or such a system diverges from
> correct reasoning into incorrect thus erroneous reasoning.
>
> The kludge of the principle of explosion is eradicated by this
> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>
> I am not sure what aspect of logic would be changed by this system that
> is why I opened up this discussion.
>
>

First, let me clarify, your requirment of "Semantic Connection" isn't
just you "by the meaning of the words" is it, because at that point you
can't prove the Pythagorean theorem since there is nothing about the sm
of the squares of the two sides that would imply that it would
neccesarily be the square of the hypotenuse, so your seem to be using
the classical logic meaning which is connected via a series of logical
inferences.

Next, does you logic system include a "Not" operator. and is it true
that either X or NOT X is true. (I think this is one of your points, but
state it clearly). If your system isn't "Binary", what are all the
logical truth values, and what is the COMPLETE truth table of ALL your
basic operators with inputs of ALL possible Truth Values? (like And, Or,
Not)

That may be one of the issue you are going to need to think about. This
is one of the big points of non-binary logic system.

On 3/18/2023 7:32 PM, olcott wrote:
> On 3/18/2023 6:17 PM, olcott wrote:
>> Just like with syllogisms conclusions a semantically necessary
>> consequence of their premises
>>
>> Semantic Necessity operator: ⊨□
>>
>> (a) Some expressions of language L are stipulated to have the property
>> of Boolean true.
>>
>> (b) Some expressions of language L are a semantically necessary
>> consequence of others.
>>
>> True(L,X) means that a semantic connection exists between (a) and X in
>> L. *Axiom(P) ⊨□ X*
>>
>> Provable(L,P,X) means that a semantic connection exists between
>> premises P and X in L.   *P ⊨□ X*
>>
>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>

L can be any natural or formal language as long as it has the above
interfaces.

> When this is called the foundation of correct reasoning
> *and indeed is the actual foundation of correct reasoning*
> that means that every system of logic either derives all of its
> operations on the basis of this system or such a system diverges from
> correct reasoning into incorrect thus erroneous reasoning.
>
> The kludge of the principle of explosion is eradicated by this
> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>
> I am not sure what aspect of logic would be changed by this system that
> is why I opened up this discussion.
>
>

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

On 3/19/23 2:00 AM, olcott wrote:
> On 3/18/2023 7:32 PM, olcott wrote:
>> On 3/18/2023 6:17 PM, olcott wrote:
>>> Just like with syllogisms conclusions a semantically necessary
>>> consequence of their premises
>>>
>>> Semantic Necessity operator: ⊨□
>>>
>>> (a) Some expressions of language L are stipulated to have the property
>>> of Boolean true.
>>>
>>> (b) Some expressions of language L are a semantically necessary
>>> consequence of others.
>>>
>>> True(L,X) means that a semantic connection exists between (a) and X
>>> in L. *Axiom(P) ⊨□ X*
>>>
>>> Provable(L,P,X) means that a semantic connection exists between
>>> premises P and X in L.   *P ⊨□ X*
>>>
>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>
>
> L can be any natural or formal language as long as it has the above
> interfaces.

???? That seems out of context, maybe if you actually reply to the
message you want to respond to, you might be more understandable.

Of course, that might be the issue, it makes you more understandable and
the errors obvious.

Now, are you talking about "Languages", or "Logic Systems". They are
different you know.

>
>> When this is called the foundation of correct reasoning
>> *and indeed is the actual foundation of correct reasoning*
>> that means that every system of logic either derives all of its
>> operations on the basis of this system or such a system diverges from
>> correct reasoning into incorrect thus erroneous reasoning.
>>
>> The kludge of the principle of explosion is eradicated by this
>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> I am not sure what aspect of logic would be changed by this system that
>> is why I opened up this discussion.
>>
>>
>

On 3/19/2023 1:00 AM, olcott wrote:
> On 3/18/2023 7:32 PM, olcott wrote:
>> On 3/18/2023 6:17 PM, olcott wrote:
>>> Just like with syllogisms conclusions a semantically necessary
>>> consequence of their premises
>>>
>>> Semantic Necessity operator: ⊨□
>>>
>>> (a) Some expressions of language L are stipulated to have the property
>>> of Boolean true.
>>>
>>> (b) Some expressions of language L are a semantically necessary
>>> consequence of others.
>>>
>>> True(L,X) means that a semantic connection exists between (a) and X
>>> in L. *Axiom(P) ⊨□ X*
>>>
>>> Provable(L,P,X) means that a semantic connection exists between
>>> premises P and X in L.   *P ⊨□ X*
>>>
>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>
>
> L can be any natural or formal language as long as it has the above
> interfaces.
>
>> When this is called the foundation of correct reasoning
>> *and indeed is the actual foundation of correct reasoning*
>> that means that every system of logic either derives all of its
>> operations on the basis of this system or such a system diverges from
>> correct reasoning into incorrect thus erroneous reasoning.
>>
>> The kludge of the principle of explosion is eradicated by this
>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> I am not sure what aspect of logic would be changed by this system that
>> is why I opened up this discussion.
>>
>>
>

The foundation of correct reasoning is just that and applies to every
element of the entire body of analytical truth, whether it be facts
about the world or mathematical relationships.

(A & ~A) ⊨□ FALSE
FALSE ⊨□ FALSE
TRUE ⊨□ TRUE
A & B ⊨□ A
A & B ⊨□ B
The Moon is made from green cheese ⊨□ The Moon is made from cheese

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

On 3/19/2023 10:45 AM, olcott wrote:
> On 3/19/2023 1:00 AM, olcott wrote:
>> On 3/18/2023 7:32 PM, olcott wrote:
>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>> Just like with syllogisms conclusions a semantically necessary
>>>> consequence of their premises
>>>>
>>>> Semantic Necessity operator: ⊨□
>>>>
>>>> (a) Some expressions of language L are stipulated to have the property
>>>> of Boolean true.
>>>>
>>>> (b) Some expressions of language L are a semantically necessary
>>>> consequence of others.
>>>>
>>>> True(L,X) means that a semantic connection exists between (a) and X
>>>> in L. *Axiom(P) ⊨□ X*
>>>>
>>>> Provable(L,P,X) means that a semantic connection exists between
>>>> premises P and X in L.   *P ⊨□ X*
>>>>
>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>
>>
>> L can be any natural or formal language as long as it has the above
>> interfaces.
>>
>>> When this is called the foundation of correct reasoning
>>> *and indeed is the actual foundation of correct reasoning*
>>> that means that every system of logic either derives all of its
>>> operations on the basis of this system or such a system diverges from
>>> correct reasoning into incorrect thus erroneous reasoning.
>>>
>>> The kludge of the principle of explosion is eradicated by this
>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>
>>> I am not sure what aspect of logic would be changed by this system that
>>> is why I opened up this discussion.
>>>
>>>
>>
>
> The foundation of correct reasoning is just that and applies to every
> element of the entire body of analytical truth, whether it be facts
> about the world or mathematical relationships.
>
> (A & ~A) ⊨□ FALSE
> FALSE ⊨□ FALSE
> TRUE  ⊨□ TRUE
> A & B ⊨□ A
> A & B ⊨□ B
> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>

False(X) ⊨□ True(~X)

X = "this sentence is not true"
(~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)

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

On 3/19/23 11:52 AM, olcott wrote:
> On 3/19/2023 10:45 AM, olcott wrote:
>> On 3/19/2023 1:00 AM, olcott wrote:
>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>> consequence of their premises
>>>>>
>>>>> Semantic Necessity operator: ⊨□
>>>>>
>>>>> (a) Some expressions of language L are stipulated to have the property
>>>>> of Boolean true.
>>>>>
>>>>> (b) Some expressions of language L are a semantically necessary
>>>>> consequence of others.
>>>>>
>>>>> True(L,X) means that a semantic connection exists between (a) and X
>>>>> in L. *Axiom(P) ⊨□ X*
>>>>>
>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>
>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>
>>>
>>> L can be any natural or formal language as long as it has the above
>>> interfaces.
>>>
>>>> When this is called the foundation of correct reasoning
>>>> *and indeed is the actual foundation of correct reasoning*
>>>> that means that every system of logic either derives all of its
>>>> operations on the basis of this system or such a system diverges from
>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>
>>>> The kludge of the principle of explosion is eradicated by this
>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>
>>>> I am not sure what aspect of logic would be changed by this system that
>>>> is why I opened up this discussion.
>>>>
>>>>
>>>
>>
>> The foundation of correct reasoning is just that and applies to every
>> element of the entire body of analytical truth, whether it be facts
>> about the world or mathematical relationships.
>>
>> (A & ~A) ⊨□ FALSE
>> FALSE ⊨□ FALSE
>> TRUE  ⊨□ TRUE
>> A & B ⊨□ A
>> A & B ⊨□ B
>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>
>
> False(X) ⊨□ True(~X)
>
> X = "this sentence is not true"
> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>

So, statements don't actually have "Truth Values" in your system, you
need to use predicates about them?

Is "FALSE" an actual predicate, or is it a logical value?

How about "TRUE".

Your ⊨□ operator was defined on predicates, not values, so how was FALSE
or TRUE used with it?

Seems you don't actually have a system that handles actual logic.

On 3/19/23 11:45 AM, olcott wrote:
> On 3/19/2023 1:00 AM, olcott wrote:
>> On 3/18/2023 7:32 PM, olcott wrote:
>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>> Just like with syllogisms conclusions a semantically necessary
>>>> consequence of their premises
>>>>
>>>> Semantic Necessity operator: ⊨□
>>>>
>>>> (a) Some expressions of language L are stipulated to have the property
>>>> of Boolean true.
>>>>
>>>> (b) Some expressions of language L are a semantically necessary
>>>> consequence of others.
>>>>
>>>> True(L,X) means that a semantic connection exists between (a) and X
>>>> in L. *Axiom(P) ⊨□ X*
>>>>
>>>> Provable(L,P,X) means that a semantic connection exists between
>>>> premises P and X in L.   *P ⊨□ X*
>>>>
>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>
>>
>> L can be any natural or formal language as long as it has the above
>> interfaces.
>>
>>> When this is called the foundation of correct reasoning
>>> *and indeed is the actual foundation of correct reasoning*
>>> that means that every system of logic either derives all of its
>>> operations on the basis of this system or such a system diverges from
>>> correct reasoning into incorrect thus erroneous reasoning.
>>>
>>> The kludge of the principle of explosion is eradicated by this
>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>
>>> I am not sure what aspect of logic would be changed by this system that
>>> is why I opened up this discussion.
>>>
>>>
>>
>
> The foundation of correct reasoning is just that and applies to every
> element of the entire body of analytical truth, whether it be facts
> about the world or mathematical relationships.
>
> (A & ~A) ⊨□ FALSE
> FALSE ⊨□ FALSE
> TRUE  ⊨□ TRUE
> A & B ⊨□ A
> A & B ⊨□ B
> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>

Ok, so you don't understand the question and are acting like a 3-year old.

On 3/19/2023 10:52 AM, olcott wrote:
> On 3/19/2023 10:45 AM, olcott wrote:
>> On 3/19/2023 1:00 AM, olcott wrote:
>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>> consequence of their premises
>>>>>
>>>>> Semantic Necessity operator: ⊨□
>>>>>
>>>>> (a) Some expressions of language L are stipulated to have the property
>>>>> of Boolean true.
>>>>>
>>>>> (b) Some expressions of language L are a semantically necessary
>>>>> consequence of others.
>>>>>
>>>>> True(L,X) means that a semantic connection exists between (a) and X
>>>>> in L. *Axiom(P) ⊨□ X*
>>>>>
>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>
>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>
>>>
>>> L can be any natural or formal language as long as it has the above
>>> interfaces.
>>>
>>>> When this is called the foundation of correct reasoning
>>>> *and indeed is the actual foundation of correct reasoning*
>>>> that means that every system of logic either derives all of its
>>>> operations on the basis of this system or such a system diverges from
>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>
>>>> The kludge of the principle of explosion is eradicated by this
>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>
>>>> I am not sure what aspect of logic would be changed by this system that
>>>> is why I opened up this discussion.
>>>>
>>>>
>>>
>>
>> The foundation of correct reasoning is just that and applies to every
>> element of the entire body of analytical truth, whether it be facts
>> about the world or mathematical relationships.
>>
>> (A & ~A) ⊨□ FALSE
>> FALSE ⊨□ FALSE
>> TRUE  ⊨□ TRUE
>> A & B ⊨□ A
>> A & B ⊨□ B
>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>
>
> False(X) ⊨□ True(~X)
>
> X = "this sentence is not true"
> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>

The predicate True(L,X) is provided to explicitly contradict Tarski's
conclusion that no such predicate can possibly exist.

True(L,X) means that there is a semantic connection from expressions of
language L that are stipulated to be true to X.

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

On 3/19/23 1:30 PM, olcott wrote:
> On 3/19/2023 10:52 AM, olcott wrote:
>> On 3/19/2023 10:45 AM, olcott wrote:
>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>> consequence of their premises
>>>>>>
>>>>>> Semantic Necessity operator: ⊨□
>>>>>>
>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>> property
>>>>>> of Boolean true.
>>>>>>
>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>> consequence of others.
>>>>>>
>>>>>> True(L,X) means that a semantic connection exists between (a) and
>>>>>> X in L. *Axiom(P) ⊨□ X*
>>>>>>
>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>
>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>
>>>>
>>>> L can be any natural or formal language as long as it has the above
>>>> interfaces.
>>>>
>>>>> When this is called the foundation of correct reasoning
>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>> that means that every system of logic either derives all of its
>>>>> operations on the basis of this system or such a system diverges from
>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>
>>>>> The kludge of the principle of explosion is eradicated by this
>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>
>>>>> I am not sure what aspect of logic would be changed by this system
>>>>> that
>>>>> is why I opened up this discussion.
>>>>>
>>>>>
>>>>
>>>
>>> The foundation of correct reasoning is just that and applies to every
>>> element of the entire body of analytical truth, whether it be facts
>>> about the world or mathematical relationships.
>>>
>>> (A & ~A) ⊨□ FALSE
>>> FALSE ⊨□ FALSE
>>> TRUE  ⊨□ TRUE
>>> A & B ⊨□ A
>>> A & B ⊨□ B
>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>
>>
>> False(X) ⊨□ True(~X)
>>
>> X = "this sentence is not true"
>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>
>
> The predicate True(L,X) is provided to explicitly contradict Tarski's
> conclusion that no such predicate can possibly exist.
>
> True(L,X) means that there is a semantic connection from expressions of
> language L that are stipulated to be true to X.
>

Except until you can show how to actually DEFINE true within the system
(so it can be evaluated) you haven't done it.

Your "True" predicate isn't defined IN THE FIELD, but by natural language.

It just makes it clear you don't understand what he is talking about,
which sort of points out the worthlessness of your system.

On 3/19/2023 12:30 PM, olcott wrote:
> On 3/19/2023 10:52 AM, olcott wrote:
>> On 3/19/2023 10:45 AM, olcott wrote:
>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>> consequence of their premises
>>>>>>
>>>>>> Semantic Necessity operator: ⊨□
>>>>>>
>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>> property
>>>>>> of Boolean true.
>>>>>>
>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>> consequence of others.
>>>>>>
>>>>>> True(L,X) means that a semantic connection exists between (a) and
>>>>>> X in L. *Axiom(P) ⊨□ X*
>>>>>>
>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>
>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>
>>>>
>>>> L can be any natural or formal language as long as it has the above
>>>> interfaces.
>>>>
>>>>> When this is called the foundation of correct reasoning
>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>> that means that every system of logic either derives all of its
>>>>> operations on the basis of this system or such a system diverges from
>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>
>>>>> The kludge of the principle of explosion is eradicated by this
>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>
>>>>> I am not sure what aspect of logic would be changed by this system
>>>>> that
>>>>> is why I opened up this discussion.
>>>>>
>>>>>
>>>>
>>>
>>> The foundation of correct reasoning is just that and applies to every
>>> element of the entire body of analytical truth, whether it be facts
>>> about the world or mathematical relationships.
>>>
>>> (A & ~A) ⊨□ FALSE
>>> FALSE ⊨□ FALSE
>>> TRUE  ⊨□ TRUE
>>> A & B ⊨□ A
>>> A & B ⊨□ B
>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>
>>
>> False(X) ⊨□ True(~X)
>>
>> X = "this sentence is not true"
>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>
>
> The predicate True(L,X) is provided to explicitly contradict Tarski's
> conclusion that no such predicate can possibly exist.
>
> True(L,X) means that there is a semantic connection from expressions of
> language L that are stipulated to be true to X.
>

expressions of language L that are stipulated to be true correspond to
Haskell Curry elementary theorems of T.

Let T be such a theory. Then the elementary statements which belong to T
we shall call the elementary theorems of T; we also say that these
elementary statements are true for T. Thus, given T, an elementary
theorem is an elementary statement which is true.
https://www.liarparadox.org/Haskell_Curry_45.pdf

expressions of language L that are stipulated to be true also correspond
to the basic facts of natural language such as cats are animals thus
cats are not ten story office buildings.

That it is true in F that G is unprovable in F requires a semantic
connection from elementary theorems of F to G in F, otherwise G is
untrue in 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 3/19/2023 12:55 PM, olcott wrote:
> On 3/19/2023 12:30 PM, olcott wrote:
>> On 3/19/2023 10:52 AM, olcott wrote:
>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>> consequence of their premises
>>>>>>>
>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>
>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>> property
>>>>>>> of Boolean true.
>>>>>>>
>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>> consequence of others.
>>>>>>>
>>>>>>> True(L,X) means that a semantic connection exists between (a) and
>>>>>>> X in L. *Axiom(P) ⊨□ X*
>>>>>>>
>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>
>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>
>>>>>
>>>>> L can be any natural or formal language as long as it has the above
>>>>> interfaces.
>>>>>
>>>>>> When this is called the foundation of correct reasoning
>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>> that means that every system of logic either derives all of its
>>>>>> operations on the basis of this system or such a system diverges from
>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>
>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>
>>>>>> I am not sure what aspect of logic would be changed by this system
>>>>>> that
>>>>>> is why I opened up this discussion.
>>>>>>
>>>>>>
>>>>>
>>>>
>>>> The foundation of correct reasoning is just that and applies to every
>>>> element of the entire body of analytical truth, whether it be facts
>>>> about the world or mathematical relationships.
>>>>
>>>> (A & ~A) ⊨□ FALSE
>>>> FALSE ⊨□ FALSE
>>>> TRUE  ⊨□ TRUE
>>>> A & B ⊨□ A
>>>> A & B ⊨□ B
>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>
>>>
>>> False(X) ⊨□ True(~X)
>>>
>>> X = "this sentence is not true"
>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>
>>
>> The predicate True(L,X) is provided to explicitly contradict Tarski's
>> conclusion that no such predicate can possibly exist.
>>
>> True(L,X) means that there is a semantic connection from expressions
>> of language L that are stipulated to be true to X.
>>
>
> expressions of language L that are stipulated to be true correspond to
> Haskell Curry elementary theorems of T.
>
> Let T be such a theory. Then the elementary statements which belong to T
> we shall call the elementary theorems of T; we also say that these
> elementary statements are true for T. Thus, given T, an elementary
> theorem is an elementary statement which is true.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
>
> expressions of language L that are stipulated to be true also correspond
> to the basic facts of natural language such as cats are animals thus
> cats are not ten story office buildings.
>
> That it is true in F that G is unprovable in F requires a semantic
> connection from elementary theorems of F to G in F, otherwise G is
> untrue in F.

If a semantic connection exists then this semantic connection can be
specified syntactically.

If G states that there is no syntactic connection from the elementary
theorems of F to G in F, then G is stating that G is untrue in 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 3/19/23 2:22 PM, olcott wrote:
> On 3/19/2023 12:55 PM, olcott wrote:
>> On 3/19/2023 12:30 PM, olcott wrote:
>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>> consequence of their premises
>>>>>>>>
>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>
>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>> property
>>>>>>>> of Boolean true.
>>>>>>>>
>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>> consequence of others.
>>>>>>>>
>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>
>>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>>
>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>
>>>>>>
>>>>>> L can be any natural or formal language as long as it has the
>>>>>> above interfaces.
>>>>>>
>>>>>>> When this is called the foundation of correct reasoning
>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>> that means that every system of logic either derives all of its
>>>>>>> operations on the basis of this system or such a system diverges
>>>>>>> from
>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>
>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>
>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>> system that
>>>>>>> is why I opened up this discussion.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>> The foundation of correct reasoning is just that and applies to every
>>>>> element of the entire body of analytical truth, whether it be facts
>>>>> about the world or mathematical relationships.
>>>>>
>>>>> (A & ~A) ⊨□ FALSE
>>>>> FALSE ⊨□ FALSE
>>>>> TRUE  ⊨□ TRUE
>>>>> A & B ⊨□ A
>>>>> A & B ⊨□ B
>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>
>>>>
>>>> False(X) ⊨□ True(~X)
>>>>
>>>> X = "this sentence is not true"
>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>
>>>
>>> The predicate True(L,X) is provided to explicitly contradict Tarski's
>>> conclusion that no such predicate can possibly exist.
>>>
>>> True(L,X) means that there is a semantic connection from expressions
>>> of language L that are stipulated to be true to X.
>>>
>>
>> expressions of language L that are stipulated to be true correspond to
>> Haskell Curry elementary theorems of T.
>>
>> Let T be such a theory. Then the elementary statements which belong to T
>> we shall call the elementary theorems of T; we also say that these
>> elementary statements are true for T. Thus, given T, an elementary
>> theorem is an elementary statement which is true.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>> expressions of language L that are stipulated to be true also correspond
>> to the basic facts of natural language such as cats are animals thus
>> cats are not ten story office buildings.
>>
>> That it is true in F that G is unprovable in F requires a semantic
>> connection from elementary theorems of F to G in F, otherwise G is
>> untrue in F.
>
> If a semantic connection exists then this semantic connection can be
> specified syntactically.
>
> If G states that there is no syntactic connection from the elementary
> theorems of F to G in F, then G is stating that G is untrue in F.
>
>
>

No, G doesn't say there is no semantic connection to G. Just that there
is no FINITE set of connections to G, as required to be a proof.

Part of the problem is you don't understand the requirements for
provability.

Provability requires a FINITE set of steps from the truth makers to the
conclusion, while Truth just requires that a connection, possibly
infinite, exists.

The key point is Proof is about KNOWLEDGE, and as such must be
demonstrable, which, since we are finite, for the proof to involve a
finite number of steps.

Truth, is about existance, not knowledge, and that can be supported by
an infinite set of connections.

You keep on confusing "Knowing Something to be True" (which is Proof)
with "Being True" (which is just reality).

Not everything that is can be knowable, as reality is bigger than
ourselves since we are just a part of it.

On 3/19/23 1:55 PM, olcott wrote:
> On 3/19/2023 12:30 PM, olcott wrote:
>> On 3/19/2023 10:52 AM, olcott wrote:
>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>> consequence of their premises
>>>>>>>
>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>
>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>> property
>>>>>>> of Boolean true.
>>>>>>>
>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>> consequence of others.
>>>>>>>
>>>>>>> True(L,X) means that a semantic connection exists between (a) and
>>>>>>> X in L. *Axiom(P) ⊨□ X*
>>>>>>>
>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>
>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>
>>>>>
>>>>> L can be any natural or formal language as long as it has the above
>>>>> interfaces.
>>>>>
>>>>>> When this is called the foundation of correct reasoning
>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>> that means that every system of logic either derives all of its
>>>>>> operations on the basis of this system or such a system diverges from
>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>
>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>
>>>>>> I am not sure what aspect of logic would be changed by this system
>>>>>> that
>>>>>> is why I opened up this discussion.
>>>>>>
>>>>>>
>>>>>
>>>>
>>>> The foundation of correct reasoning is just that and applies to every
>>>> element of the entire body of analytical truth, whether it be facts
>>>> about the world or mathematical relationships.
>>>>
>>>> (A & ~A) ⊨□ FALSE
>>>> FALSE ⊨□ FALSE
>>>> TRUE  ⊨□ TRUE
>>>> A & B ⊨□ A
>>>> A & B ⊨□ B
>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>
>>>
>>> False(X) ⊨□ True(~X)
>>>
>>> X = "this sentence is not true"
>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>
>>
>> The predicate True(L,X) is provided to explicitly contradict Tarski's
>> conclusion that no such predicate can possibly exist.
>>
>> True(L,X) means that there is a semantic connection from expressions
>> of language L that are stipulated to be true to X.
>>
>
> expressions of language L that are stipulated to be true correspond to
> Haskell Curry elementary theorems of T.
>
> Let T be such a theory. Then the elementary statements which belong to T
> we shall call the elementary theorems of T; we also say that these
> elementary statements are true for T. Thus, given T, an elementary
> theorem is an elementary statement which is true.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
>
> expressions of language L that are stipulated to be true also correspond
> to the basic facts of natural language such as cats are animals thus
> cats are not ten story office buildings.
>
> That it is true in F that G is unprovable in F requires a semantic
> connection from elementary theorems of F to G in F, otherwise G is
> untrue in F.
>
>
>

Unresponsive.
'
Also, shows you don't understand what you are talking about.

And, as an example, it is shown that Godel's sentence, that there does
not exist any natural number which meets a specific primative recursive
relationship, is True in F (but not provable in F), As we can show that
for ANY number n, it doesn't meet that relationship, and that can be
determine just by running the relationship on the number, all these
steps being in F.

The actual proof that this is the result for all number can't be done in
F, but that doesn't affect the truth of the statement. It IS a fact that
for every natural number n, it can be shown, just within F, that it
doesn't meet the requirements of the relationship.

Thus, G is proved true by a semantic connection from the elementary
theorems of F to the statment G. The set of connection needed just
happens to be infinite, and the definition of a PROOF, is an expressible
finite set of connections with in the Field.

You dont seem to understand that by the definition, it is quite possibe
to prove in meta-F that there exist within the theory F, a connection
within F, from its axioms to the conclusion.

On 3/19/2023 1:22 PM, olcott wrote:
> On 3/19/2023 12:55 PM, olcott wrote:
>> On 3/19/2023 12:30 PM, olcott wrote:
>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>> consequence of their premises
>>>>>>>>
>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>
>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>> property
>>>>>>>> of Boolean true.
>>>>>>>>
>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>> consequence of others.
>>>>>>>>
>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>
>>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>>
>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>
>>>>>>
>>>>>> L can be any natural or formal language as long as it has the
>>>>>> above interfaces.
>>>>>>
>>>>>>> When this is called the foundation of correct reasoning
>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>> that means that every system of logic either derives all of its
>>>>>>> operations on the basis of this system or such a system diverges
>>>>>>> from
>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>
>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>
>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>> system that
>>>>>>> is why I opened up this discussion.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>> The foundation of correct reasoning is just that and applies to every
>>>>> element of the entire body of analytical truth, whether it be facts
>>>>> about the world or mathematical relationships.
>>>>>
>>>>> (A & ~A) ⊨□ FALSE
>>>>> FALSE ⊨□ FALSE
>>>>> TRUE  ⊨□ TRUE
>>>>> A & B ⊨□ A
>>>>> A & B ⊨□ B
>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>
>>>>
>>>> False(X) ⊨□ True(~X)
>>>>
>>>> X = "this sentence is not true"
>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>
>>>
>>> The predicate True(L,X) is provided to explicitly contradict Tarski's
>>> conclusion that no such predicate can possibly exist.
>>>
>>> True(L,X) means that there is a semantic connection from expressions
>>> of language L that are stipulated to be true to X.
>>>
>>
>> expressions of language L that are stipulated to be true correspond to
>> Haskell Curry elementary theorems of T.
>>
>> Let T be such a theory. Then the elementary statements which belong to T
>> we shall call the elementary theorems of T; we also say that these
>> elementary statements are true for T. Thus, given T, an elementary
>> theorem is an elementary statement which is true.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>> expressions of language L that are stipulated to be true also correspond
>> to the basic facts of natural language such as cats are animals thus
>> cats are not ten story office buildings.
>>
>> That it is true in F that G is unprovable in F requires a semantic
>> connection from elementary theorems of F to G in F, otherwise G is
>> untrue in F.
>
> If a semantic connection exists then this semantic connection can be
> specified syntactically.
>
> If G states that there is no syntactic connection from the elementary
> theorems of F to G in F, then G is stating that G is untrue in F.

The conventional proof that G is true is not a proof that G is true in
F, it is a proof that G is true in meta-F.

LP = "This sentence is not true"
is not true because LP is not a truth bearer

This sentence is not true: "This sentence is not true"
is true because LP is not a truth bearer.

G = "this sentence cannot be proven in F"
cannot be proven in F because G has a vacuous truth object.

?- G = not(provable(F, G)).

?- unify_with_occurs_check(G, not(provable(F, G))).
false.

Proves that G has a vacuous truth object.

This sentence cannot be proven: "this sentence cannot be proven in F"
is true because G has a vacuous truth object.

TT = "This sentenced is true"
is not true because TT has a vacuous truth object.

This sentence is true.
What is it true about?
It is true about being true.
What is it true about being true about?
It is true about being true about being true...

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

On 3/19/23 3:21 PM, olcott wrote:
> On 3/19/2023 1:22 PM, olcott wrote:
>> On 3/19/2023 12:55 PM, olcott wrote:
>>> On 3/19/2023 12:30 PM, olcott wrote:
>>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>> consequence of their premises
>>>>>>>>>
>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>
>>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>>> property
>>>>>>>>> of Boolean true.
>>>>>>>>>
>>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>>> consequence of others.
>>>>>>>>>
>>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>>
>>>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>>>
>>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>>
>>>>>>>
>>>>>>> L can be any natural or formal language as long as it has the
>>>>>>> above interfaces.
>>>>>>>
>>>>>>>> When this is called the foundation of correct reasoning
>>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>>> that means that every system of logic either derives all of its
>>>>>>>> operations on the basis of this system or such a system diverges
>>>>>>>> from
>>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>>
>>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>>
>>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>>> system that
>>>>>>>> is why I opened up this discussion.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>> The foundation of correct reasoning is just that and applies to every
>>>>>> element of the entire body of analytical truth, whether it be facts
>>>>>> about the world or mathematical relationships.
>>>>>>
>>>>>> (A & ~A) ⊨□ FALSE
>>>>>> FALSE ⊨□ FALSE
>>>>>> TRUE  ⊨□ TRUE
>>>>>> A & B ⊨□ A
>>>>>> A & B ⊨□ B
>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>
>>>>>
>>>>> False(X) ⊨□ True(~X)
>>>>>
>>>>> X = "this sentence is not true"
>>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>>
>>>>
>>>> The predicate True(L,X) is provided to explicitly contradict
>>>> Tarski's conclusion that no such predicate can possibly exist.
>>>>
>>>> True(L,X) means that there is a semantic connection from expressions
>>>> of language L that are stipulated to be true to X.
>>>>
>>>
>>> expressions of language L that are stipulated to be true correspond to
>>> Haskell Curry elementary theorems of T.
>>>
>>> Let T be such a theory. Then the elementary statements which belong to T
>>> we shall call the elementary theorems of T; we also say that these
>>> elementary statements are true for T. Thus, given T, an elementary
>>> theorem is an elementary statement which is true.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>> expressions of language L that are stipulated to be true also correspond
>>> to the basic facts of natural language such as cats are animals thus
>>> cats are not ten story office buildings.
>>>
>>> That it is true in F that G is unprovable in F requires a semantic
>>> connection from elementary theorems of F to G in F, otherwise G is
>>> untrue in F.
>>
>> If a semantic connection exists then this semantic connection can be
>> specified syntactically.
>>
>> If G states that there is no syntactic connection from the elementary
>> theorems of F to G in F, then G is stating that G is untrue in F.
>
> The conventional proof that G is true is not a proof that G is true in
> F, it is a proof that G is true in meta-F.
>

Which, because of the nature of the statement, also makes it true it F.

if we prove that 2+2 = 4 in one mathematical field, it is also true in
all field with the same mathematics.

> LP = "This sentence is not true"
> is not true because LP is not a truth bearer

But that isn't the Statment of G.

>
> This sentence is not true: "This sentence is not true"
> is true because LP is not a truth bearer.

So?

>
> G = "this sentence cannot be proven in F"
> cannot be proven in F because G has a vacuous truth object.

Which isn't the statement of G, but only a statement provable in Meta-F
to have the same truth value as G.

G IS a truth bearer, as it asks about the existance of a natural number
matching a computable result.

>
> ?- G = not(provable(F, G)).
>
> ?- unify_with_occurs_check(G, not(provable(F, G))).
> false.
>
> Proves that G has a vacuous truth object.

Nope, proves you are a LIAR.

Since that isn't G.
>
> This sentence cannot be proven: "this sentence cannot be proven in F"
> is true because G has a vacuous truth object.

Not G, so just proving your ignorance.

>
> TT = "This sentenced is true"
> is not true because TT has a vacuous truth object.

Irrelevent

>
> This sentence is true.
> What is it true about?
> It is true about being true.
> What is it true about being true about?
> It is true about being true about being true...
>
>
>

Just prove that you don;t know what you are talking about.

And, have the emotional level of a three-year old.

On 3/19/2023 2:21 PM, olcott wrote:
> On 3/19/2023 1:22 PM, olcott wrote:
>> On 3/19/2023 12:55 PM, olcott wrote:
>>> On 3/19/2023 12:30 PM, olcott wrote:
>>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>> consequence of their premises
>>>>>>>>>
>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>
>>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>>> property
>>>>>>>>> of Boolean true.
>>>>>>>>>
>>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>>> consequence of others.
>>>>>>>>>
>>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>>
>>>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>>>
>>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>>
>>>>>>>
>>>>>>> L can be any natural or formal language as long as it has the
>>>>>>> above interfaces.
>>>>>>>
>>>>>>>> When this is called the foundation of correct reasoning
>>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>>> that means that every system of logic either derives all of its
>>>>>>>> operations on the basis of this system or such a system diverges
>>>>>>>> from
>>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>>
>>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>>
>>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>>> system that
>>>>>>>> is why I opened up this discussion.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>> The foundation of correct reasoning is just that and applies to every
>>>>>> element of the entire body of analytical truth, whether it be facts
>>>>>> about the world or mathematical relationships.
>>>>>>
>>>>>> (A & ~A) ⊨□ FALSE
>>>>>> FALSE ⊨□ FALSE
>>>>>> TRUE  ⊨□ TRUE
>>>>>> A & B ⊨□ A
>>>>>> A & B ⊨□ B
>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>
>>>>>
>>>>> False(X) ⊨□ True(~X)
>>>>>
>>>>> X = "this sentence is not true"
>>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>>
>>>>
>>>> The predicate True(L,X) is provided to explicitly contradict
>>>> Tarski's conclusion that no such predicate can possibly exist.
>>>>
>>>> True(L,X) means that there is a semantic connection from expressions
>>>> of language L that are stipulated to be true to X.
>>>>
>>>
>>> expressions of language L that are stipulated to be true correspond to
>>> Haskell Curry elementary theorems of T.
>>>
>>> Let T be such a theory. Then the elementary statements which belong to T
>>> we shall call the elementary theorems of T; we also say that these
>>> elementary statements are true for T. Thus, given T, an elementary
>>> theorem is an elementary statement which is true.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>> expressions of language L that are stipulated to be true also correspond
>>> to the basic facts of natural language such as cats are animals thus
>>> cats are not ten story office buildings.
>>>
>>> That it is true in F that G is unprovable in F requires a semantic
>>> connection from elementary theorems of F to G in F, otherwise G is
>>> untrue in F.
>>
>> If a semantic connection exists then this semantic connection can be
>> specified syntactically.
>>
>> If G states that there is no syntactic connection from the elementary
>> theorems of F to G in F, then G is stating that G is untrue in F.
>
> The conventional proof that G is true is not a proof that G is true in
> F, it is a proof that G is true in meta-F.
>
> LP = "This sentence is not true"
> is not true because LP is not a truth bearer
>
> This sentence is not true: "This sentence is not true"
> is true because LP is not a truth bearer.
>
> G = "this sentence cannot be proven in F"
> cannot be proven in F because G has a vacuous truth object.
>
> ?- G = not(provable(F, G)).
>
> ?- unify_with_occurs_check(G, not(provable(F, G))).
> false.
>
> Proves that G has a vacuous truth object.
>
> This sentence cannot be proven: "this sentence cannot be proven in F"
> is true because G has a vacuous truth object.

G has a vacuous truth object
G has a vacuous truth object
G has a vacuous truth object
G has a vacuous truth object

>
> TT = "This sentenced is true"
> is not true because TT has a vacuous truth object.
>
> This sentence is true.
> What is it true about?
> It is true about being true.
> What is it true about being true about?
> It is true about being true about being true...
>
>
>

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

On 3/22/23 1:05 AM, olcott wrote:
> On 3/19/2023 2:21 PM, olcott wrote:
>> On 3/19/2023 1:22 PM, olcott wrote:
>>> On 3/19/2023 12:55 PM, olcott wrote:
>>>> On 3/19/2023 12:30 PM, olcott wrote:
>>>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>>> consequence of their premises
>>>>>>>>>>
>>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>>
>>>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>>>> property
>>>>>>>>>> of Boolean true.
>>>>>>>>>>
>>>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>>>> consequence of others.
>>>>>>>>>>
>>>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>>>
>>>>>>>>>> Provable(L,P,X) means that a semantic connection exists
>>>>>>>>>> between premises P and X in L.   *P ⊨□ X*
>>>>>>>>>>
>>>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from
>>>>>>>>>> cheese
>>>>>>>>>
>>>>>>>>
>>>>>>>> L can be any natural or formal language as long as it has the
>>>>>>>> above interfaces.
>>>>>>>>
>>>>>>>>> When this is called the foundation of correct reasoning
>>>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>>>> that means that every system of logic either derives all of its
>>>>>>>>> operations on the basis of this system or such a system
>>>>>>>>> diverges from
>>>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>>>
>>>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>>>
>>>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>>>> system that
>>>>>>>>> is why I opened up this discussion.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> The foundation of correct reasoning is just that and applies to
>>>>>>> every
>>>>>>> element of the entire body of analytical truth, whether it be facts
>>>>>>> about the world or mathematical relationships.
>>>>>>>
>>>>>>> (A & ~A) ⊨□ FALSE
>>>>>>> FALSE ⊨□ FALSE
>>>>>>> TRUE  ⊨□ TRUE
>>>>>>> A & B ⊨□ A
>>>>>>> A & B ⊨□ B
>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>
>>>>>>
>>>>>> False(X) ⊨□ True(~X)
>>>>>>
>>>>>> X = "this sentence is not true"
>>>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>>>
>>>>>
>>>>> The predicate True(L,X) is provided to explicitly contradict
>>>>> Tarski's conclusion that no such predicate can possibly exist.
>>>>>
>>>>> True(L,X) means that there is a semantic connection from
>>>>> expressions of language L that are stipulated to be true to X.
>>>>>
>>>>
>>>> expressions of language L that are stipulated to be true correspond to
>>>> Haskell Curry elementary theorems of T.
>>>>
>>>> Let T be such a theory. Then the elementary statements which belong
>>>> to T
>>>> we shall call the elementary theorems of T; we also say that these
>>>> elementary statements are true for T. Thus, given T, an elementary
>>>> theorem is an elementary statement which is true.
>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>
>>>> expressions of language L that are stipulated to be true also
>>>> correspond
>>>> to the basic facts of natural language such as cats are animals thus
>>>> cats are not ten story office buildings.
>>>>
>>>> That it is true in F that G is unprovable in F requires a semantic
>>>> connection from elementary theorems of F to G in F, otherwise G is
>>>> untrue in F.
>>>
>>> If a semantic connection exists then this semantic connection can be
>>> specified syntactically.
>>>
>>> If G states that there is no syntactic connection from the elementary
>>> theorems of F to G in F, then G is stating that G is untrue in F.
>>
>> The conventional proof that G is true is not a proof that G is true in
>> F, it is a proof that G is true in meta-F.
>>
>> LP = "This sentence is not true"
>> is not true because LP is not a truth bearer
>>
>> This sentence is not true: "This sentence is not true"
>> is true because LP is not a truth bearer.
>>
>> G = "this sentence cannot be proven in F"
>> cannot be proven in F because G has a vacuous truth object.
>>
>> ?- G = not(provable(F, G)).
>>
>> ?- unify_with_occurs_check(G, not(provable(F, G))).
>> false.
>>
>> Proves that G has a vacuous truth object.
>>
>> This sentence cannot be proven: "this sentence cannot be proven in F"
>> is true because G has a vacuous truth object.
>
> G has a vacuous truth object
> G has a vacuous truth object
> G has a vacuous truth object
> G has a vacuous truth object

SO you think that the existance of a Natural Number that satisfies a
computable relationship can br vacuoud?

That is like saying if we are asked if 2 + 2 = 4, there is no answer.

Of course, your problem is you don't undertand what G actually is, just
what FROM G can be proved in Meta-F, namely that any number that
satisfies the relationship proves that G is true (that there is no
number that satisfies it), and the lack of such a number means that G
can't be proved within F.

>
>>
>> TT = "This sentenced is true"
>> is not true because TT has a vacuous truth object.
>>
>> This sentence is true.
>> What is it true about?
>> It is true about being true.
>> What is it true about being true about?
>> It is true about being true about being true...
>>
>>
>>
>

On 3/19/2023 2:21 PM, olcott wrote:
> On 3/19/2023 1:22 PM, olcott wrote:
>> On 3/19/2023 12:55 PM, olcott wrote:
>>> On 3/19/2023 12:30 PM, olcott wrote:
>>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>> consequence of their premises
>>>>>>>>>
>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>
>>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>>> property
>>>>>>>>> of Boolean true.
>>>>>>>>>
>>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>>> consequence of others.
>>>>>>>>>
>>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>>
>>>>>>>>> Provable(L,P,X) means that a semantic connection exists between
>>>>>>>>> premises P and X in L.   *P ⊨□ X*
>>>>>>>>>
>>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>>
>>>>>>>
>>>>>>> L can be any natural or formal language as long as it has the
>>>>>>> above interfaces.
>>>>>>>
>>>>>>>> When this is called the foundation of correct reasoning
>>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>>> that means that every system of logic either derives all of its
>>>>>>>> operations on the basis of this system or such a system diverges
>>>>>>>> from
>>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>>
>>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>>
>>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>>> system that
>>>>>>>> is why I opened up this discussion.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>> The foundation of correct reasoning is just that and applies to every
>>>>>> element of the entire body of analytical truth, whether it be facts
>>>>>> about the world or mathematical relationships.
>>>>>>
>>>>>> (A & ~A) ⊨□ FALSE
>>>>>> FALSE ⊨□ FALSE
>>>>>> TRUE  ⊨□ TRUE
>>>>>> A & B ⊨□ A
>>>>>> A & B ⊨□ B
>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>
>>>>>
>>>>> False(X) ⊨□ True(~X)
>>>>>
>>>>> X = "this sentence is not true"
>>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>>
>>>>
>>>> The predicate True(L,X) is provided to explicitly contradict
>>>> Tarski's conclusion that no such predicate can possibly exist.
>>>>
>>>> True(L,X) means that there is a semantic connection from expressions
>>>> of language L that are stipulated to be true to X.
>>>>
>>>
>>> expressions of language L that are stipulated to be true correspond to
>>> Haskell Curry elementary theorems of T.
>>>
>>> Let T be such a theory. Then the elementary statements which belong to T
>>> we shall call the elementary theorems of T; we also say that these
>>> elementary statements are true for T. Thus, given T, an elementary
>>> theorem is an elementary statement which is true.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>> expressions of language L that are stipulated to be true also correspond
>>> to the basic facts of natural language such as cats are animals thus
>>> cats are not ten story office buildings.
>>>
>>> That it is true in F that G is unprovable in F requires a semantic
>>> connection from elementary theorems of F to G in F, otherwise G is
>>> untrue in F.
>>
>> If a semantic connection exists then this semantic connection can be
>> specified syntactically.
>>
>> If G states that there is no syntactic connection from the elementary
>> theorems of F to G in F, then G is stating that G is untrue in F.
>
> The conventional proof that G is true is not a proof that G is true in
> F, it is a proof that G is true in meta-F.
>
> LP = "This sentence is not true"
> is not true because LP is not a truth bearer
>
> This sentence is not true: "This sentence is not true"
> is true because LP is not a truth bearer.
>
> G = "this sentence cannot be proven in F"
> cannot be proven in F because G has a vacuous truth object.
>
> ?- G = not(provable(F, G)).
>
> ?- unify_with_occurs_check(G, not(provable(F, G))).
> false.
>
> Proves that G has a vacuous truth object.
>

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

Thus Gödel's G is simplified to this:
G = ¬(F ⊢ G)

Translated into Prolog like this:
?- G = not(provable(F, G)).

Found to be incorrect by this:
?- unify_with_occurs_check(G, not(provable(F, G))).
false

Because the Prolog G has an “uninstantiated subterm of itself” we can
know that unification will fail because it specifies “some kind of
infinite structure.”The quotes come from: (Clocksin and Mellish 2003:255)

So G is unprovable in F because G is incorrect, thus not because F is
incomplete.

> This sentence cannot be proven: "this sentence cannot be proven in F"
> is true because G has a vacuous truth object.
>
> TT = "This sentenced is true"
> is not true because TT has a vacuous truth object.
>
> This sentence is true.
> What is it true about?
> It is true about being true.
> What is it true about being true about?
> It is true about being true about being true...
>
>
>

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

On 3/22/23 3:25 PM, olcott wrote:
> On 3/19/2023 2:21 PM, olcott wrote:
>> On 3/19/2023 1:22 PM, olcott wrote:
>>> On 3/19/2023 12:55 PM, olcott wrote:
>>>> On 3/19/2023 12:30 PM, olcott wrote:
>>>>> On 3/19/2023 10:52 AM, olcott wrote:
>>>>>> On 3/19/2023 10:45 AM, olcott wrote:
>>>>>>> On 3/19/2023 1:00 AM, olcott wrote:
>>>>>>>> On 3/18/2023 7:32 PM, olcott wrote:
>>>>>>>>> On 3/18/2023 6:17 PM, olcott wrote:
>>>>>>>>>> Just like with syllogisms conclusions a semantically necessary
>>>>>>>>>> consequence of their premises
>>>>>>>>>>
>>>>>>>>>> Semantic Necessity operator: ⊨□
>>>>>>>>>>
>>>>>>>>>> (a) Some expressions of language L are stipulated to have the
>>>>>>>>>> property
>>>>>>>>>> of Boolean true.
>>>>>>>>>>
>>>>>>>>>> (b) Some expressions of language L are a semantically necessary
>>>>>>>>>> consequence of others.
>>>>>>>>>>
>>>>>>>>>> True(L,X) means that a semantic connection exists between (a)
>>>>>>>>>> and X in L. *Axiom(P) ⊨□ X*
>>>>>>>>>>
>>>>>>>>>> Provable(L,P,X) means that a semantic connection exists
>>>>>>>>>> between premises P and X in L.   *P ⊨□ X*
>>>>>>>>>>
>>>>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from
>>>>>>>>>> cheese
>>>>>>>>>
>>>>>>>>
>>>>>>>> L can be any natural or formal language as long as it has the
>>>>>>>> above interfaces.
>>>>>>>>
>>>>>>>>> When this is called the foundation of correct reasoning
>>>>>>>>> *and indeed is the actual foundation of correct reasoning*
>>>>>>>>> that means that every system of logic either derives all of its
>>>>>>>>> operations on the basis of this system or such a system
>>>>>>>>> diverges from
>>>>>>>>> correct reasoning into incorrect thus erroneous reasoning.
>>>>>>>>>
>>>>>>>>> The kludge of the principle of explosion is eradicated by this
>>>>>>>>> foundation. https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>>>>
>>>>>>>>> I am not sure what aspect of logic would be changed by this
>>>>>>>>> system that
>>>>>>>>> is why I opened up this discussion.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> The foundation of correct reasoning is just that and applies to
>>>>>>> every
>>>>>>> element of the entire body of analytical truth, whether it be facts
>>>>>>> about the world or mathematical relationships.
>>>>>>>
>>>>>>> (A & ~A) ⊨□ FALSE
>>>>>>> FALSE ⊨□ FALSE
>>>>>>> TRUE  ⊨□ TRUE
>>>>>>> A & B ⊨□ A
>>>>>>> A & B ⊨□ B
>>>>>>> The Moon is made from green cheese ⊨□ The Moon is made from cheese
>>>>>>>
>>>>>>
>>>>>> False(X) ⊨□ True(~X)
>>>>>>
>>>>>> X = "this sentence is not true"
>>>>>> (~True(X) & ~False(X)) ⊨□ ~Truth_Bearer(X)
>>>>>>
>>>>>
>>>>> The predicate True(L,X) is provided to explicitly contradict
>>>>> Tarski's conclusion that no such predicate can possibly exist.
>>>>>
>>>>> True(L,X) means that there is a semantic connection from
>>>>> expressions of language L that are stipulated to be true to X.
>>>>>
>>>>
>>>> expressions of language L that are stipulated to be true correspond to
>>>> Haskell Curry elementary theorems of T.
>>>>
>>>> Let T be such a theory. Then the elementary statements which belong
>>>> to T
>>>> we shall call the elementary theorems of T; we also say that these
>>>> elementary statements are true for T. Thus, given T, an elementary
>>>> theorem is an elementary statement which is true.
>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>
>>>> expressions of language L that are stipulated to be true also
>>>> correspond
>>>> to the basic facts of natural language such as cats are animals thus
>>>> cats are not ten story office buildings.
>>>>
>>>> That it is true in F that G is unprovable in F requires a semantic
>>>> connection from elementary theorems of F to G in F, otherwise G is
>>>> untrue in F.
>>>
>>> If a semantic connection exists then this semantic connection can be
>>> specified syntactically.
>>>
>>> If G states that there is no syntactic connection from the elementary
>>> theorems of F to G in F, then G is stating that G is untrue in F.
>>
>> The conventional proof that G is true is not a proof that G is true in
>> F, it is a proof that G is true in meta-F.
>>
>> LP = "This sentence is not true"
>> is not true because LP is not a truth bearer
>>
>> This sentence is not true: "This sentence is not true"
>> is true because LP is not a truth bearer.
>>
>> G = "this sentence cannot be proven in F"
>> cannot be proven in F because G has a vacuous truth object.
>>
>> ?- G = not(provable(F, G)).
>>
>> ?- unify_with_occurs_check(G, not(provable(F, G))).
>> false.
>>
>> Proves that G has a vacuous truth object.
>>
>
>
> We are therefore confronted with a proposition which asserts its own
> unprovability. (Gödel 1931:39-41)

Right, which isn't G itself, but something derived from it in Meta-F

Read the proof you have posted, keep track of what system he is talking
about.

Your just PROVING that you don't actually understand what the proof is
about.

>
> Thus Gödel's G is simplified to this:
> G = ¬(F ⊢ G)

Nope, it says that G is true if and only if it is not true that F proves
G, as proven in Meta-F

>
> Translated into Prolog like this:
> ?- G = not(provable(F, G)).

Nop,e as that ISN'T G, only the statment PROVEN to have and equivalent
truth value ot G.

Note, Prolog is incapable of handling this level of Logic.

Can you use Prolog to prove the Pythagorean Theorem?

>
> Found to be incorrect by this:
> ?- unify_with_occurs_check(G, not(provable(F, G))).
> false

Which just means that it is beyond Prolog

Also, since you LIED to Prolog, doesn't mean anything.

>
> Because the Prolog G has an “uninstantiated subterm of itself” we can
> know that unification will fail because it specifies “some kind of
> infinite structure.”The quotes come from: (Clocksin and Mellish 2003:255)

Right, because the logic of the system exceeds the capabilities of Prolog.

>
> So G is unprovable in F because G is incorrect, thus not because F is
> incomplete.

Nope, Since you have shown you don't understand what G actually is, your
logic is incorret.

IF G is incorrect, then there must exist a number that matches the
Primative Recursive Relationship, and thus from the proof in Meta-F, we
know that G is provable, so by your logic, you logic system can prove an
incorrect statement, and thus is shown to be inconsistent.

Of course, since you don't understand what G is, even though you have
presented the paper (translated) of the proof, you are showing that this
is above your head, just shows how little you understand about logic.

>
>> This sentence cannot be proven: "this sentence cannot be proven in F"
>> is true because G has a vacuous truth object.
>>
>> TT = "This sentenced is true"
>> is not true because TT has a vacuous truth object.
>>
>> This sentence is true.
>> What is it true about?
>> It is true about being true.
>> What is it true about being true about?
>> It is true about being true about being true...
>>
>>
>>
>