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A new foundation for correct reasoning +++

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  A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-28 16:03 -0600
    Re: A new foundation for correct reasoning +++ Richard Damon <Richard@Damon-Family.org> - 2025-11-28 17:33 -0500
    Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-28 22:54 +0000
      Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-28 17:14 -0600
        Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-29 11:55 +0000
          Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-29 09:18 -0600
            Re: A new foundation for correct reasoning +++ Alan Mackenzie <acm@muc.de> - 2025-11-29 20:48 +0000
              Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-11-29 15:31 -0600
                Re: A new foundation for correct reasoning +++ Richard Damon <Richard@Damon-Family.org> - 2025-11-29 17:04 -0500
          Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-01 06:19 -0600
            Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:56 +0200
              Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-02 08:07 -0600
                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-03 13:17 +0200
                  Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-03 10:13 -0600
                    Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-04 11:29 +0200
                      Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-04 08:18 -0600
                        Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:03 +0200
                          Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-05 11:31 -0600
                            Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:39 +0200
                              Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-06 06:53 -0600
                                Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-07 13:08 +0200
                                  Re: A new foundation for correct reasoning +++ olcott <polcott333@gmail.com> - 2025-12-08 13:56 -0600
                                    Re: A new foundation for correct reasoning +++ Mikko <mikko.levanto@iki.fi> - 2025-12-14 13:05 +0200

Page 1 of 2  [1] 2  Next page →

#641364 — A new foundation for correct reasoning +++

On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
> dart200 <user7160@newsgrouper.org.invalid> wrote:
>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:
>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>> does the logical construction:
> 
>>>> "this sentence is false"
> 
>>>> place a hard limit on our ability to understand truth:
> 
>>>> yes/no???
> 
>>> No, not at all.  Anybody beyond early childhood will recognise it as a
>>> mere frivolous distraction from any seeking after the truth.
> 
>> so why does anyone think such a construct places a meaningful limit in a
>> formal system then?
> 
> People, in general, don't, apart from one or two exceptions.
> 
>> "this sentence has no proof"
> 
> That is a world apart from "This sentence is false.".  It's the kernel
> of Gödel's proof (as you know, of course).  "This sentence has no proof"
> turns out to be true and unprovable (for a precisely defined meaning of
> "unprovable").
> 

*Within A new foundation for correct reasoning*

(a) Every element of the body of knowledge that can
     be expressed in language is entirely composed of
   (1) A finite set of atomic facts
   (2) Every expression of language that is semantically
       entailed by (1)
(b) a formal language based on Rudolf Carnap Meaning
     Postulates combined with The Kurt Gödel definition
     of the "theory of simple types"
     https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
     Where every semantic meaning is fully encoded syntactically
     as one fully integrated whole not needing model theory

We have now totally overcome Gödel Incompleteness
and Tarski Undefinability for the entire body if
knowledge that can be expressed in language. It
is now a giant semantic tautology.

>> "this program loops forever iff it's decided that it halts"
> 
> As you also know, this is the contradiction reached in one of the proofs
> of the Halting Theorem.  This is also not the same as "This sentence is
> false.", though it is inspired by that nonsense.
> 

It is isomorphic.

> None of these sentences/nonsenses limit our ability to understand truth.
> They are part of the truth that we understand.  They delineate
> fundamental boundaries of what can be known and proven, in particular
> that truth is more subtle than provability.
> 

That is bullshit as I have just proven.
Within the giant semantic tautology of knowledge that
can be expressed in language everything is proven or
not an element of this body.

> This opens the possibility that some mathematical conjectures may be
> true but unprovable.  That's just part of existence.
> 
>> -- 
>> a burnt out swe investigating into why our tooling doesn't involve
>> basic semantic proofs like halting analysis
> 
>> please excuse my pseudo-pyscript,
> 
>> ~ nick
> 


-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [next] | [standalone]

#641365

On 11/28/25 5:03 PM, olcott wrote:
> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:
>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>> does the logical construction:
>>
>>>>> "this sentence is false"
>>
>>>>> place a hard limit on our ability to understand truth:
>>
>>>>> yes/no???
>>
>>>> No, not at all.  Anybody beyond early childhood will recognise it as a
>>>> mere frivolous distraction from any seeking after the truth.
>>
>>> so why does anyone think such a construct places a meaningful limit in a
>>> formal system then?
>>
>> People, in general, don't, apart from one or two exceptions.
>>
>>> "this sentence has no proof"
>>
>> That is a world apart from "This sentence is false.".  It's the kernel
>> of Gödel's proof (as you know, of course).  "This sentence has no proof"
>> turns out to be true and unprovable (for a precisely defined meaning of
>> "unprovable").
>>
> 
> *Within A new foundation for correct reasoning*
> 
> (a) Every element of the body of knowledge that can
>      be expressed in language is entirely composed of
>    (1) A finite set of atomic facts
>    (2) Every expression of language that is semantically
>        entailed by (1)
> (b) a formal language based on Rudolf Carnap Meaning
>      Postulates combined with The Kurt Gödel definition
>      of the "theory of simple types"
>      https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>      Where every semantic meaning is fully encoded syntactically
>      as one fully integrated whole not needing model theory

So, your system just can't express statements you don't yet know the 
answer too?

> 
> We have now totally overcome Gödel Incompleteness
> and Tarski Undefinability for the entire body if
> knowledge that can be expressed in language. It
> is now a giant semantic tautology.

Only because you can't ask questions you don't yet know the answer to.

Note, a system that can only talk about knowledge, doesn't need 
"proofs", as anything it can talk about is already established as true.

Incompleteness is about statements that are factually true, even if 
unknown, and the ability to prove them to make them known.

Incompleteness says there are things that are True, but which can't 
become Known, because we can't prove them with a finite proof.

> 
>>> "this program loops forever iff it's decided that it halts"
>>
>> As you also know, this is the contradiction reached in one of the proofs
>> of the Halting Theorem.  This is also not the same as "This sentence is
>> false.", though it is inspired by that nonsense.
>>
> 
> It is isomorphic.
> 
>> None of these sentences/nonsenses limit our ability to understand truth.
>> They are part of the truth that we understand.  They delineate
>> fundamental boundaries of what can be known and proven, in particular
>> that truth is more subtle than provability.
>>
> 
> That is bullshit as I have just proven.
> Within the giant semantic tautology of knowledge that
> can be expressed in language everything is proven or
> not an element of this body.

But the problems you are trying to claim to be talking about are NOT 
about "Knowledge", but about Truth.

Since not all truths end up being knowable, your system just fails to be 
about truth.

Which means you system can't even handle a full theory about the 
mathematics of the Natural Numbers, as that has been proven to be 
"Incomplete"

> 
>> This opens the possibility that some mathematical conjectures may be
>> true but unprovable.  That's just part of existence.
>>
>>> -- 
>>> a burnt out swe investigating into why our tooling doesn't involve
>>> basic semantic proofs like halting analysis
>>
>>> please excuse my pseudo-pyscript,
>>
>>> ~ nick
>>
> 
> 

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#641366

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:
>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>> does the logical construction:

>>>>> "this sentence is false"

>>>>> place a hard limit on our ability to understand truth:

>>>>> yes/no???

>>>> No, not at all.  Anybody beyond early childhood will recognise it as a
>>>> mere frivolous distraction from any seeking after the truth.

>>> so why does anyone think such a construct places a meaningful limit in a
>>> formal system then?

>> People, in general, don't, apart from one or two exceptions.

>>> "this sentence has no proof"

>> That is a world apart from "This sentence is false.".  It's the kernel
>> of Gödel's proof (as you know, of course).  "This sentence has no proof"
>> turns out to be true and unprovable (for a precisely defined meaning of
>> "unprovable").


> *Within A new foundation for correct reasoning*

> (a) Every element of the body of knowledge that can
>     be expressed in language is entirely composed of
>   (1) A finite set of atomic facts
>   (2) Every expression of language that is semantically
>       entailed by (1)
> (b) a formal language based on Rudolf Carnap Meaning
>     Postulates combined with The Kurt Gödel definition
>     of the "theory of simple types"
>     https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>     Where every semantic meaning is fully encoded syntactically
>     as one fully integrated whole not needing model theory

> We have now totally overcome Gödel Incompleteness
> and Tarski Undefinability for the entire body if
> knowledge that can be expressed in language. It
> is now a giant semantic tautology.

You can't "overcome" these theorems, since they're not obstacles.
They're fundamental truths.

>>> "this program loops forever iff it's decided that it halts"

>> As you also know, this is the contradiction reached in one of the proofs
>> of the Halting Theorem.  This is also not the same as "This sentence is
>> false.", though it is inspired by that nonsense.


> It is isomorphic.

Stop using mathematical terms you don't understand.  There is no
isomorphism here.  Your assertion is a category error.

>> None of these sentences/nonsenses limit our ability to understand truth.
>> They are part of the truth that we understand.  They delineate
>> fundamental boundaries of what can be known and proven, in particular
>> that truth is more subtle than provability.


> That is bullshit as I have just proven.

Every time you use the word "proven" you appear to be lying.  I can't
recall any occurrence where you were telling the truth.

> Within the giant semantic tautology of knowledge that
> can be expressed in language everything is proven or
> not an element of this body.

Your scheme is limited indeed, in that it is not powerful enough to
represent unprovable propositions.  I (along with the vast majority of
mathematicians, scientists, philosophers, ....) do not accept such
limitations.  These limitations involve not being able to do arithmetic
at all.

>> This opens the possibility that some mathematical conjectures may be
>> true but unprovable.  That's just part of existence.

>>> -- 
>>> a burnt out swe investigating into why our tooling doesn't involve
>>> basic semantic proofs like halting analysis

>>> please excuse my pseudo-pyscript,

>>> ~ nick

> -- 
> Copyright 2025 Olcott

> My 28 year goal has been to make
> "true on the basis of meaning" computable.

> This required establishing a new foundation
> for correct reasoning.

-- 
Alan Mackenzie (Nuremberg, Germany).

[toc] | [prev] | [next] | [standalone]

#641367

On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
> [ Followup-To: set ]
> 
> In comp.theory olcott <polcott333@gmail.com> wrote:
>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>> On 11/28/25 9:36 AM, Alan Mackenzie wrote:
>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>> does the logical construction:
> 
>>>>>> "this sentence is false"
> 
>>>>>> place a hard limit on our ability to understand truth:
> 
>>>>>> yes/no???
> 
>>>>> No, not at all.  Anybody beyond early childhood will recognise it as a
>>>>> mere frivolous distraction from any seeking after the truth.
> 
>>>> so why does anyone think such a construct places a meaningful limit in a
>>>> formal system then?
> 
>>> People, in general, don't, apart from one or two exceptions.
> 
>>>> "this sentence has no proof"
> 
>>> That is a world apart from "This sentence is false.".  It's the kernel
>>> of Gödel's proof (as you know, of course).  "This sentence has no proof"
>>> turns out to be true and unprovable (for a precisely defined meaning of
>>> "unprovable").
> 
> 
>> *Within A new foundation for correct reasoning*
> 
>> (a) Every element of the body of knowledge that can
>>      be expressed in language is entirely composed of
>>    (1) A finite set of atomic facts
>>    (2) Every expression of language that is semantically
>>        entailed by (1)
>> (b) a formal language based on Rudolf Carnap Meaning
>>      Postulates combined with The Kurt Gödel definition
>>      of the "theory of simple types"
>>      https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>      Where every semantic meaning is fully encoded syntactically
>>      as one fully integrated whole not needing model theory
> 
>> We have now totally overcome Gödel Incompleteness
>> and Tarski Undefinability for the entire body if
>> knowledge that can be expressed in language. It
>> is now a giant semantic tautology.
> 
> You can't "overcome" these theorems, since they're not obstacles.
> They're fundamental truths.
> 

I just showed the detailed steps making both of
them impossible in the system that I just specified.
A counter-example is categorically impossible.

>>>> "this program loops forever iff it's decided that it halts"
> 
>>> As you also know, this is the contradiction reached in one of the proofs
>>> of the Halting Theorem.  This is also not the same as "This sentence is
>>> false.", though it is inspired by that nonsense.
> 
> 
>> It is isomorphic.
> 
> Stop using mathematical terms you don't understand.  There is no
> isomorphism here.  Your assertion is a category error.
> 
I used that term correctly and you cannot actually
show otherwise.

>>> None of these sentences/nonsenses limit our ability to understand truth.
>>> They are part of the truth that we understand.  They delineate
>>> fundamental boundaries of what can be known and proven, in particular
>>> that truth is more subtle than provability.
> 
> 
>> That is bullshit as I have just proven.
> 
> Every time you use the word "proven" you appear to be lying.  I can't
> recall any occurrence where you were telling the truth.
> 

When a counter-example to my claim is categorically
impossible then I have proven this claim even if
you fail to understand that this is the generic
way that all actual proof really works.

>> Within the giant semantic tautology of knowledge that
>> can be expressed in language everything is proven or
>> not an element of this body.
> 
> Your scheme is limited indeed, in that it is not powerful enough to
> represent unprovable propositions. 

In other words "the entire body of knowledge that
can be expressed in language" uses big words that
you cannot understand?

What is left out of:
"the entire body of knowledge that can be expressed in language" ?

What is left out of:
"the entire body of knowledge that can be expressed in language" ?

What is left out of:
"the entire body of knowledge that can be expressed in language" ?

What is left out of:
"the entire body of knowledge that can be expressed in language" ?

What is left out of:
"the entire body of knowledge that can be expressed in language" ?

>  I (along with the vast majority of
> mathematicians, scientists, philosophers, ....) do not accept such
> limitations.  These limitations involve not being able to do arithmetic
> at all.
> 
>>> This opens the possibility that some mathematical conjectures may be
>>> true but unprovable.  That's just part of existence.
> 
>>>> -- 
>>>> a burnt out swe investigating into why our tooling doesn't involve
>>>> basic semantic proofs like halting analysis
> 
>>>> please excuse my pseudo-pyscript,
> 
>>>> ~ nick
> 
>> -- 
>> Copyright 2025 Olcott
> 
>> My 28 year goal has been to make
>> "true on the basis of meaning" computable.
> 
>> This required establishing a new foundation
>> for correct reasoning.
> 


-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641396

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:

>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:

[ .... ]

>>> *Within A new foundation for correct reasoning*

>>> (a) Every element of the body of knowledge that can
>>>      be expressed in language is entirely composed of
>>>    (1) A finite set of atomic facts
>>>    (2) Every expression of language that is semantically
>>>        entailed by (1)
>>> (b) a formal language based on Rudolf Carnap Meaning
>>>      Postulates combined with The Kurt Gödel definition
>>>      of the "theory of simple types"
>>>      https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>>      Where every semantic meaning is fully encoded syntactically
>>>      as one fully integrated whole not needing model theory

>>> We have now totally overcome Gödel Incompleteness
>>> and Tarski Undefinability for the entire body if
>>> knowledge that can be expressed in language. It
>>> is now a giant semantic tautology.

>> You can't "overcome" these theorems, since they're not obstacles.
>> They're fundamental truths.

> I just showed the detailed steps making both of
> them impossible in the system that I just specified.
> A counter-example is categorically impossible.

Your construction is impossible, as proven by Gödel's Incompleteness
Theorem.

You didn't "show" anything.  You just waved your hands and expect
everybody to accept your continually repeated falsehoods.

>>>>> "this program loops forever iff it's decided that it halts"

>>>> As you also know, this is the contradiction reached in one of the proofs
>>>> of the Halting Theorem.  This is also not the same as "This sentence is
>>>> false.", though it is inspired by that nonsense.


>>> It is isomorphic.

>> Stop using mathematical terms you don't understand.  There is no
>> isomorphism here.  Your assertion is a category error.

> I used that term correctly and you cannot actually
> show otherwise.

I suggest you look up isomorphism in Wikipedia to find out what it
actually means.

>>>> None of these sentences/nonsenses limit our ability to understand truth.
>>>> They are part of the truth that we understand.  They delineate
>>>> fundamental boundaries of what can be known and proven, in particular
>>>> that truth is more subtle than provability.

>>> That is bullshit as I have just proven.

>> Every time you use the word "proven" you appear to be lying.  I can't
>> recall any occurrence where you were telling the truth.

> When a counter-example to my claim is categorically
> impossible then I have proven this claim even if
> you fail to understand that this is the generic
> way that all actual proof really works.

It has nothing to do with my understanding, and a great deal to do with
your lack of it.  You have not proven that a counter example to whatever
it is you're talking about is "categorically impossible".  You can't,
since you lack the prerequisites to understand what constitutes a proof,
and you lack the mathematical foundations to be able to construct one.

>>> Within the giant semantic tautology of knowledge that
>>> can be expressed in language everything is proven or
>>> not an element of this body.

>> Your scheme is limited indeed, in that it is not powerful enough to
>> represent unprovable propositions. 

> In other words "the entire body of knowledge that
> can be expressed in language" uses big words that
> you cannot understand?

> What is left out of:
> "the entire body of knowledge that can be expressed in language" ?

Arithmetic, for a start.  If that allegedly "entire body of knowledge"
was capable of doing arithmetic, Gödel's Incompleteness Theorem would
apply to it.  That is a proof by contradiction that such a body of
knowledge cannot exist.

[ .... ]

> -- 
> Copyright 2025 Olcott

> My 28 year goal has been to make
> "true on the basis of meaning" computable.

> This required establishing a new foundation
> for correct reasoning.

-- 
Alan Mackenzie (Nuremberg, Germany).

[toc] | [prev] | [next] | [standalone]

#641403

On 11/29/2025 5:55 AM, Alan Mackenzie wrote:
> [ Followup-To: set ]
> 
> In comp.theory olcott <polcott333@gmail.com> wrote:
>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
> 
>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
> 
> [ .... ]
> 
>>>> *Within A new foundation for correct reasoning*
> 
>>>> (a) Every element of the body of knowledge that can
>>>>       be expressed in language is entirely composed of
>>>>     (1) A finite set of atomic facts
>>>>     (2) Every expression of language that is semantically
>>>>         entailed by (1)
>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>       Postulates combined with The Kurt Gödel definition
>>>>       of the "theory of simple types"
>>>>       https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>>>       Where every semantic meaning is fully encoded syntactically
>>>>       as one fully integrated whole not needing model theory
> 
>>>> We have now totally overcome Gödel Incompleteness
>>>> and Tarski Undefinability for the entire body if
>>>> knowledge that can be expressed in language. It
>>>> is now a giant semantic tautology.
> 
>>> You can't "overcome" these theorems, since they're not obstacles.
>>> They're fundamental truths.
> 
>> I just showed the detailed steps making both of
>> them impossible in the system that I just specified.
>> A counter-example is categorically impossible.
> 
> Your construction is impossible, as proven by Gödel's Incompleteness
> Theorem.
> 
> You didn't "show" anything.  You just waved your hands and expect
> everybody to accept your continually repeated falsehoods.
> 

You can claim that my idea is impossible.
It is impossible to show that my idea is impossible.
A mere dogmatic assertion provides zero actual evidence
that I am incorrect.

A consistent finite set of basic facts of the world is possible.
This consistent finite set of basic facts of the world are
encoded in Rudolf Carnap Meaning Postulates thus fully
encoding all of these semantic meaning directly in the formal
language. The Meaning Postulates are arranged in a knowledge
ontology similar to a type hierarchy. The only inference
steps are semantic logical entailment performed syntactically.

You can declare that I must be wrong because it contradicts
what others have said, yet you cannot point out any actual
in any of the steps because there are none.

>>>>>> "this program loops forever iff it's decided that it halts"
> 
>>>>> As you also know, this is the contradiction reached in one of the proofs
>>>>> of the Halting Theorem.  This is also not the same as "This sentence is
>>>>> false.", though it is inspired by that nonsense.
> 
> 
>>>> It is isomorphic.
> 
>>> Stop using mathematical terms you don't understand.  There is no
>>> isomorphism here.  Your assertion is a category error.
> 
>> I used that term correctly and you cannot actually
>> show otherwise.
> 
> I suggest you look up isomorphism in Wikipedia to find out what it
> actually means.
> 

The object in the Liar Paradox case is the sentence
the object in the halting problem case is the behavior
of the input. In each of these two cases the truth
is the opposite of whatever is said, thus the identical
structure.

They are isomorphic as abstract structures

>>>>> None of these sentences/nonsenses limit our ability to understand truth.
>>>>> They are part of the truth that we understand.  They delineate
>>>>> fundamental boundaries of what can be known and proven, in particular
>>>>> that truth is more subtle than provability.
> 
>>>> That is bullshit as I have just proven.
> 
>>> Every time you use the word "proven" you appear to be lying.  I can't
>>> recall any occurrence where you were telling the truth.
> 
>> When a counter-example to my claim is categorically
>> impossible then I have proven this claim even if
>> you fail to understand that this is the generic
>> way that all actual proof really works.
> 
> It has nothing to do with my understanding, and a great deal to do with
> your lack of it.  You have not proven that a counter example to whatever
> it is you're talking about is "categorically impossible". 

You could not point out any specific error in the
details that I specified. You can only assert mere
baseless dogma that you believe that I am incorrect.

> You can't,
> since you lack the prerequisites to understand what constitutes a proof,
> and you lack the mathematical foundations to be able to construct one.
> 

I don't give a rat's ass about your narrow minded
learned by rote definitions of a proof are.

The most generic form of a proof is essentially
a semantic tautology.

>>>> Within the giant semantic tautology of knowledge that
>>>> can be expressed in language everything is proven or
>>>> not an element of this body.
> 
>>> Your scheme is limited indeed, in that it is not powerful enough to
>>> represent unprovable propositions.
> 
>> In other words "the entire body of knowledge that
>> can be expressed in language" uses big words that
>> you cannot understand?
> 
>> What is left out of:
>> "the entire body of knowledge that can be expressed in language" ?
> 
> Arithmetic, for a start. 

So you are trying to get away with saying that
knowledge of arithmetic cannot be expressed in language?

> If that allegedly "entire body of knowledge"
> was capable of doing arithmetic, Gödel's Incompleteness Theorem would
> apply to it. 

Arithmetic is merely insufficiently expressive,
the body of knowledge that can be expressed in
language knows that.

> That is a proof by contradiction that such a body of
> knowledge cannot exist.
> 

Not at all. Arithmetic is merely insufficiently expressive.
While you attempt to come up with counter-examples know
that dogma does not count.

A counter-example would be an element of knowledge
that can be expressed in language that:
(a) Cannot be expressed in language.
(b) Is not true. (All knowledge is true)

That is what I mean by counter-examples are
categorically impossible

> [ .... ]
> 
>> -- 
>> Copyright 2025 Olcott
> 
>> My 28 year goal has been to make
>> "true on the basis of meaning" computable.
> 
>> This required establishing a new foundation
>> for correct reasoning.
> 


-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641429

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> On 11/29/2025 5:55 AM, Alan Mackenzie wrote:

>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:

>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:

>> [ .... ]

>>>>> *Within A new foundation for correct reasoning*

>>>>> (a) Every element of the body of knowledge that can
>>>>>       be expressed in language is entirely composed of
>>>>>     (1) A finite set of atomic facts
>>>>>     (2) Every expression of language that is semantically
>>>>>         entailed by (1)
>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>       of the "theory of simple types"
>>>>>       https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>       as one fully integrated whole not needing model theory

>>>>> We have now totally overcome Gödel Incompleteness
>>>>> and Tarski Undefinability for the entire body if
>>>>> knowledge that can be expressed in language. It
>>>>> is now a giant semantic tautology.

>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>> They're fundamental truths.

>>> I just showed the detailed steps making both of
>>> them impossible in the system that I just specified.
>>> A counter-example is categorically impossible.

>> Your construction is impossible, as proven by Gödel's Incompleteness
>> Theorem.

>> You didn't "show" anything.  You just waved your hands and expect
>> everybody to accept your continually repeated falsehoods.


> You can claim that my idea is impossible.

I no longer remember which idea that is.

> It is impossible to show that my idea is impossible.

Given that your ideas strongly tend to violate firmly established
mathematical results, there is no such impossibility as you assert.  Note
that if you hold established results to be false, you have the burden of
proof.  At no time in this newsgroup have you met this obligation.

> A mere dogmatic assertion provides zero actual evidence
> that I am incorrect.

I don't need to provide evidence.  As just written, the burden of proof
is on your side.

> A consistent finite set of basic facts of the world is possible.

There are many such finite sets, but none of them are complete, and they
cannot be complete.  This was demonstrated by mathematicians in the early
20th century.

> This consistent finite set of basic facts of the world are
> encoded in Rudolf Carnap Meaning Postulates thus fully
> encoding all of these semantic meaning directly in the formal
> language. The Meaning Postulates are arranged in a knowledge
> ontology similar to a type hierarchy. The only inference
> steps are semantic logical entailment performed syntactically.

This is a will o' the wisp, as much as Frege's or Russell and Whitehead's
much more modest attempts to formalise all of mathematics were.

> You can declare that I must be wrong because it contradicts
> what others have said, yet you cannot point out any actual
> in any of the steps because there are none.

As I keep saying, the burden of proof is on your side.  The three
mathematicians just mentioned failed because what they were attempting
was fundamentally impossible.  That was not yet understood in the early
years of the twentieth century, but it is firm knowledge now.  What you
are insisting can be done is a superset of these impossibilities.

There is a lot of hubris involved here, and seemingly not a little
personal insecurity, in someone who cannot accept reality as it is.

>>>>>>> "this program loops forever iff it's decided that it halts"

>>>>>> As you also know, this is the contradiction reached in one of the proofs
>>>>>> of the Halting Theorem.  This is also not the same as "This sentence is
>>>>>> false.", though it is inspired by that nonsense.

[ .... ]

>>>>>> None of these sentences/nonsenses limit our ability to understand
>>>>>> truth.  They are part of the truth that we understand.  They
>>>>>> delineate fundamental boundaries of what can be known and proven,
>>>>>> in particular that truth is more subtle than provability.

>>>>> That is bullshit as I have just proven.

>>>> Every time you use the word "proven" you appear to be lying.  I can't
>>>> recall any occurrence where you were telling the truth.

>>> When a counter-example to my claim is categorically
>>> impossible then I have proven this claim even if
>>> you fail to understand that this is the generic
>>> way that all actual proof really works.

>> It has nothing to do with my understanding, and a great deal to do with
>> your lack of it.  You have not proven that a counter example to whatever
>> it is you're talking about is "categorically impossible". 

> You could not point out any specific error in the
> details that I specified. You can only assert mere
> baseless dogma that you believe that I am incorrect.

The "details" you "specified" were just hand-waving nonsense, not based
on any firm logical or mathematical results.  Therefore they can be
justifiably disregarded.

>> You can't, since you lack the prerequisites to understand what
>> constitutes a proof, and you lack the mathematical foundations to be
>> able to construct one.

> I don't give a rat's ass about your narrow minded learned by rote
> definitions of a proof are.

Neither do I.  Not relevant, since I don't have any such learned by rote
definitions of a proof.

> The most generic form of a proof is essentially a semantic tautology.

That's neither here not there, being too abstract to be of use.

>>>>> Within the giant semantic tautology of knowledge that
>>>>> can be expressed in language everything is proven or
>>>>> not an element of this body.

>>>> Your scheme is limited indeed, in that it is not powerful enough to
>>>> represent unprovable propositions.

>>> In other words "the entire body of knowledge that
>>> can be expressed in language" uses big words that
>>> you cannot understand?

>>> What is left out of:
>>> "the entire body of knowledge that can be expressed in language" ?

>> Arithmetic, for a start. 

> So you are trying to get away with saying that
> knowledge of arithmetic cannot be expressed in language?

I'm saying that any system of knowledge in which Gödel's Incompleteness
Theorem doesn't apply is either inconsistent or incapable of doing
arithmetic.

>> If that allegedly "entire body of knowledge"
>> was capable of doing arithmetic, Gödel's Incompleteness Theorem would
>> apply to it. 

> Arithmetic is merely insufficiently expressive, the body of knowledge
> that can be expressed in language knows that.

No, the body of knowledge that can be represented as you envisage
wouldn't come up to the level of a stone-age person.

>> That is a proof by contradiction that such a body of
>> knowledge cannot exist.

> Not at all.

How can you say that?  You don't understand proof by contradiction,
remember?

> Arithmetic is merely insufficiently expressive.
> While you attempt to come up with counter-examples know
> that dogma does not count.

I don't know what you mean by dogma.  I'm talking about proven results
like 2 + 2 = 4.  You're just ignorant, because you don't have the
background needed to test these results, but you reject them just because
you don't like them.  You're an idiot, in other words.

> A counter-example would be an element of knowledge
> that can be expressed in language that:
> (a) Cannot be expressed in language.
> (b) Is not true. (All knowledge is true)

That would indeed be a counter example.  But given there is no suspicion
that such a construct of knowledge could be complete, no proof, no
attempt at a proof, there is nothing to give a counter example to.

> That is what I mean by counter-examples are
> categorically impossible

Your complete system of knowledge is categorically impossible.

> -- 
> Copyright 2025 Olcott

> My 28 year goal has been to make
> "true on the basis of meaning" computable.

> This required establishing a new foundation
> for correct reasoning.

-- 
Alan Mackenzie (Nuremberg, Germany).

[toc] | [prev] | [next] | [standalone]

#641433

On 11/29/2025 2:48 PM, Alan Mackenzie wrote:
> [ Followup-To: set ]
> 
> In comp.theory olcott <polcott333@gmail.com> wrote:
>> On 11/29/2025 5:55 AM, Alan Mackenzie wrote:
> 
>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
> 
>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
> 
>>> [ .... ]
> 
>>>>>> *Within A new foundation for correct reasoning*
> 
>>>>>> (a) Every element of the body of knowledge that can
>>>>>>        be expressed in language is entirely composed of
>>>>>>      (1) A finite set of atomic facts
>>>>>>      (2) Every expression of language that is semantically
>>>>>>          entailed by (1)
>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>        Postulates combined with The Kurt Gödel definition
>>>>>>        of the "theory of simple types"
>>>>>>        https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>>>>>        Where every semantic meaning is fully encoded syntactically
>>>>>>        as one fully integrated whole not needing model theory
> 
>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>> and Tarski Undefinability for the entire body if
>>>>>> knowledge that can be expressed in language. It
>>>>>> is now a giant semantic tautology.
> 
>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>> They're fundamental truths.
> 
>>>> I just showed the detailed steps making both of
>>>> them impossible in the system that I just specified.
>>>> A counter-example is categorically impossible.
> 
>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>> Theorem.
> 
>>> You didn't "show" anything.  You just waved your hands and expect
>>> everybody to accept your continually repeated falsehoods.
> 
> 
>> You can claim that my idea is impossible.
> 
> I no longer remember which idea that is.
> 
>> It is impossible to show that my idea is impossible.
> 
> Given that your ideas strongly tend to violate firmly established
> mathematical results, there is no such impossibility as you assert.  Note
> that if you hold established results to be false, you have the burden of
> proof.  At no time in this newsgroup have you met this obligation.
> 
>> A mere dogmatic assertion provides zero actual evidence
>> that I am incorrect.
> 
> I don't need to provide evidence.  As just written, the burden of proof
> is on your side.
> 
>> A consistent finite set of basic facts of the world is possible.
> 
> There are many such finite sets, but none of them are complete, and they
> cannot be complete.  This was demonstrated by mathematicians in the early
> 20th century.
> 

The current complete finite set of atomic facts
of general knowledge that can be expressed in
language exist right now. They just aren't written
does all in the same place.

>> This consistent finite set of basic facts of the world are
>> encoded in Rudolf Carnap Meaning Postulates thus fully
>> encoding all of these semantic meaning directly in the formal
>> language. The Meaning Postulates are arranged in a knowledge
>> ontology similar to a type hierarchy. The only inference
>> steps are semantic logical entailment performed syntactically.
> 
> This is a will o' the wisp, as much as Frege's or Russell and Whitehead's
> much more modest attempts to formalise all of mathematics were.
> 

So you can't even begin to imagine the body of general knowledge
that can be expressed in language.

>> You can declare that I must be wrong because it contradicts
>> what others have said, yet you cannot point out any actual
>> in any of the steps because there are none.
> 
> As I keep saying, the burden of proof is on your side. 

I cannot prove that every element of an infinite set
has a certain property exception by proving that it
it categorically impossible that these elements do
not have that property.

For example every element of the set of general
knowledge that can be expressed in symbolic language
can be written down.

>  The three
> mathematicians just mentioned failed because what they were attempting
> was fundamentally impossible.  That was not yet understood in the early
> years of the twentieth century, but it is firm knowledge now.  What you
> are insisting can be done is a superset of these impossibilities.
> 

Every element of the set of general knowledge that
can be expressed in symbolic language is a semantic
tautology thus can be proven true entirely on the
basis of relations between finite strings.

> There is a lot of hubris involved here, and seemingly not a little
> personal insecurity, in someone who cannot accept reality as it is.
> 
>>>>>>>> "this program loops forever iff it's decided that it halts"
> 
>>>>>>> As you also know, this is the contradiction reached in one of the proofs
>>>>>>> of the Halting Theorem.  This is also not the same as "This sentence is
>>>>>>> false.", though it is inspired by that nonsense.
> 
> [ .... ]
> 
>>>>>>> None of these sentences/nonsenses limit our ability to understand
>>>>>>> truth.  They are part of the truth that we understand.  They
>>>>>>> delineate fundamental boundaries of what can be known and proven,
>>>>>>> in particular that truth is more subtle than provability.
> 
>>>>>> That is bullshit as I have just proven.
> 
>>>>> Every time you use the word "proven" you appear to be lying.  I can't
>>>>> recall any occurrence where you were telling the truth.
> 
>>>> When a counter-example to my claim is categorically
>>>> impossible then I have proven this claim even if
>>>> you fail to understand that this is the generic
>>>> way that all actual proof really works.
> 
>>> It has nothing to do with my understanding, and a great deal to do with
>>> your lack of it.  You have not proven that a counter example to whatever
>>> it is you're talking about is "categorically impossible".
> 
>> You could not point out any specific error in the
>> details that I specified. You can only assert mere
>> baseless dogma that you believe that I am incorrect.
> 
> The "details" you "specified" were just hand-waving nonsense, not based
> on any firm logical or mathematical results.  Therefore they can be
> justifiably disregarded.
> 

*This is a new foundation for semantics*
Every element of the set of general knowledge that
can be expressed in symbolic language is a semantic
tautology thus can be proven true entirely on the
basis of relations between finite strings.

>>> You can't, since you lack the prerequisites to understand what
>>> constitutes a proof, and you lack the mathematical foundations to be
>>> able to construct one.
> 
>> I don't give a rat's ass about your narrow minded learned by rote
>> definitions of a proof are.
> 
> Neither do I.  Not relevant, since I don't have any such learned by rote
> definitions of a proof.
> 

I make sure to never have such.
I only know things on the basis that they are proven
to be inherently true.

>> The most generic form of a proof is essentially a semantic tautology.
> 
> That's neither here not there, being too abstract to be of use.
> 

It shows that natural preexisting order of all knowledge.

>>>>>> Within the giant semantic tautology of knowledge that
>>>>>> can be expressed in language everything is proven or
>>>>>> not an element of this body.
> 
>>>>> Your scheme is limited indeed, in that it is not powerful enough to
>>>>> represent unprovable propositions.
> 
>>>> In other words "the entire body of knowledge that
>>>> can be expressed in language" uses big words that
>>>> you cannot understand?
> 
>>>> What is left out of:
>>>> "the entire body of knowledge that can be expressed in language" ?
> 
>>> Arithmetic, for a start.
> 
>> So you are trying to get away with saying that
>> knowledge of arithmetic cannot be expressed in language?
> 
> I'm saying that any system of knowledge in which Gödel's Incompleteness
> Theorem doesn't apply is either inconsistent or incapable of doing
> arithmetic.
> 

You are merely spouting off dogma with no understanding
of how I showed that this does not work.

He used Gödel numbers to hide the underlying
semantics in a language that could not directly
specify either provability or self-reference.

G says of itself that it is unprovable in F
G := (F ⊬ G)

>>> If that allegedly "entire body of knowledge"
>>> was capable of doing arithmetic, Gödel's Incompleteness Theorem would
>>> apply to it.
> 
>> Arithmetic is merely insufficiently expressive, the body of knowledge
>> that can be expressed in language knows that.
> 
> No, the body of knowledge that can be represented as you envisage
> wouldn't come up to the level of a stone-age person.
> 

Since it directly formalizes the semantics of anything
that anyone can possible ever say how can this be true?

>>> That is a proof by contradiction that such a body of
>>> knowledge cannot exist.
> 
>> Not at all.
> 
> How can you say that?  You don't understand proof by contradiction,
> remember?
> 
>> Arithmetic is merely insufficiently expressive.
>> While you attempt to come up with counter-examples know
>> that dogma does not count.
> 
> I don't know what you mean by dogma.  I'm talking about proven results
> like 2 + 2 = 4.  You're just ignorant, because you don't have the
> background needed to test these results, but you reject them just because
> you don't like them.  You're an idiot, in other words.
> 
>> A counter-example would be an element of knowledge
>> that can be expressed in language that:
>> (a) Cannot be expressed in language.
>> (b) Is not true. (All knowledge is true)
> 
> That would indeed be a counter example.  But given there is no suspicion
> that such a construct of knowledge could be complete, no proof, no
> attempt at a proof, there is nothing to give a counter example to.
> 

G := (F ⊬ G) // G says of itself that it cannot be proved in F
Gödel says the same thing so verbosely that no one has any
idea that it all boils down to this: G := (F ⊬ G)

>> That is what I mean by counter-examples are
>> categorically impossible
> 
> Your complete system of knowledge is categorically impossible.
> 
>> -- 
>> Copyright 2025 Olcott
> 
>> My 28 year goal has been to make
>> "true on the basis of meaning" computable.
> 
>> This required establishing a new foundation
>> for correct reasoning.
> 


-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641440

On 11/29/25 4:31 PM, olcott wrote:
> On 11/29/2025 2:48 PM, Alan Mackenzie wrote:
>> [ Followup-To: set ]
>>
>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>> On 11/29/2025 5:55 AM, Alan Mackenzie wrote:
>>
>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>
>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>
>>>> [ .... ]
>>
>>>>>>> *Within A new foundation for correct reasoning*
>>
>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>        be expressed in language is entirely composed of
>>>>>>>      (1) A finite set of atomic facts
>>>>>>>      (2) Every expression of language that is semantically
>>>>>>>          entailed by (1)
>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>        Postulates combined with The Kurt Gödel definition
>>>>>>>        of the "theory of simple types"
>>>>>>>        https://en.wikipedia.org/wiki/ 
>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>        Where every semantic meaning is fully encoded syntactically
>>>>>>>        as one fully integrated whole not needing model theory
>>
>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>> knowledge that can be expressed in language. It
>>>>>>> is now a giant semantic tautology.
>>
>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>> They're fundamental truths.
>>
>>>>> I just showed the detailed steps making both of
>>>>> them impossible in the system that I just specified.
>>>>> A counter-example is categorically impossible.
>>
>>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>>> Theorem.
>>
>>>> You didn't "show" anything.  You just waved your hands and expect
>>>> everybody to accept your continually repeated falsehoods.
>>
>>
>>> You can claim that my idea is impossible.
>>
>> I no longer remember which idea that is.
>>
>>> It is impossible to show that my idea is impossible.
>>
>> Given that your ideas strongly tend to violate firmly established
>> mathematical results, there is no such impossibility as you assert.  Note
>> that if you hold established results to be false, you have the burden of
>> proof.  At no time in this newsgroup have you met this obligation.
>>
>>> A mere dogmatic assertion provides zero actual evidence
>>> that I am incorrect.
>>
>> I don't need to provide evidence.  As just written, the burden of proof
>> is on your side.
>>
>>> A consistent finite set of basic facts of the world is possible.
>>
>> There are many such finite sets, but none of them are complete, and they
>> cannot be complete.  This was demonstrated by mathematicians in the early
>> 20th century.
>>
> 
> The current complete finite set of atomic facts
> of general knowledge that can be expressed in
> language exist right now. They just aren't written
> does all in the same place.

What is an "atomic fact"? Sounds like double speak.

One problem is that when talking about the physical universe, the number 
of "exact" facts is essentially 0, at best we have that a given 
measurement of something gave a given reading representing some range of 
possible values.

When we talk about logical theories, we end up with an infinite set of 
possible axioms to work from, even if we try to limit them to things 
that seem to be reasonable approximations to the physical universe.

And then we get that you seem to like to talk about "general knowledge" 
as if that is actually a domain subject to logic.

> 
>>> This consistent finite set of basic facts of the world are
>>> encoded in Rudolf Carnap Meaning Postulates thus fully
>>> encoding all of these semantic meaning directly in the formal
>>> language. The Meaning Postulates are arranged in a knowledge
>>> ontology similar to a type hierarchy. The only inference
>>> steps are semantic logical entailment performed syntactically.
>>
>> This is a will o' the wisp, as much as Frege's or Russell and Whitehead's
>> much more modest attempts to formalise all of mathematics were.
>>
> 
> So you can't even begin to imagine the body of general knowledge
> that can be expressed in language.

The problem is that such a thing doesn't affect what LOGIC says. You are 
just confusing the Known with the Truth.

> 
>>> You can declare that I must be wrong because it contradicts
>>> what others have said, yet you cannot point out any actual
>>> in any of the steps because there are none.
>>
>> As I keep saying, the burden of proof is on your side. 
> 
> I cannot prove that every element of an infinite set
> has a certain property exception by proving that it
> it categorically impossible that these elements do
> not have that property.

Which is a problem with you limited logic.

> 
> For example every element of the set of general
> knowledge that can be expressed in symbolic language
> can be written down.

WHich isn't a fixed set, as general knowledge keeps changing, so it 
can't be used as the basis of a formal system.

> 
>>  The three
>> mathematicians just mentioned failed because what they were attempting
>> was fundamentally impossible.  That was not yet understood in the early
>> years of the twentieth century, but it is firm knowledge now.  What you
>> are insisting can be done is a superset of these impossibilities.
>>
> 
> Every element of the set of general knowledge that
> can be expressed in symbolic language is a semantic
> tautology thus can be proven true entirely on the
> basis of relations between finite strings.

Which is a worthless statement, as it just boils down to we know what we 
know, which tells us nothing about what we don't know but might be true 
(or false).

> 
>> There is a lot of hubris involved here, and seemingly not a little
>> personal insecurity, in someone who cannot accept reality as it is.
>>
>>>>>>>>> "this program loops forever iff it's decided that it halts"
>>
>>>>>>>> As you also know, this is the contradiction reached in one of 
>>>>>>>> the proofs
>>>>>>>> of the Halting Theorem.  This is also not the same as "This 
>>>>>>>> sentence is
>>>>>>>> false.", though it is inspired by that nonsense.
>>
>> [ .... ]
>>
>>>>>>>> None of these sentences/nonsenses limit our ability to understand
>>>>>>>> truth.  They are part of the truth that we understand.  They
>>>>>>>> delineate fundamental boundaries of what can be known and proven,
>>>>>>>> in particular that truth is more subtle than provability.
>>
>>>>>>> That is bullshit as I have just proven.
>>
>>>>>> Every time you use the word "proven" you appear to be lying.  I can't
>>>>>> recall any occurrence where you were telling the truth.
>>
>>>>> When a counter-example to my claim is categorically
>>>>> impossible then I have proven this claim even if
>>>>> you fail to understand that this is the generic
>>>>> way that all actual proof really works.
>>
>>>> It has nothing to do with my understanding, and a great deal to do with
>>>> your lack of it.  You have not proven that a counter example to 
>>>> whatever
>>>> it is you're talking about is "categorically impossible".
>>
>>> You could not point out any specific error in the
>>> details that I specified. You can only assert mere
>>> baseless dogma that you believe that I am incorrect.
>>
>> The "details" you "specified" were just hand-waving nonsense, not based
>> on any firm logical or mathematical results.  Therefore they can be
>> justifiably disregarded.
>>
> 
> *This is a new foundation for semantics*
> Every element of the set of general knowledge that
> can be expressed in symbolic language is a semantic
> tautology thus can be proven true entirely on the
> basis of relations between finite strings.

No, it is a worthless foundation, as it can't be used to expand that 
knowledge, as you restrict the system to just what is already know.

> 
>>>> You can't, since you lack the prerequisites to understand what
>>>> constitutes a proof, and you lack the mathematical foundations to be
>>>> able to construct one.
>>
>>> I don't give a rat's ass about your narrow minded learned by rote
>>> definitions of a proof are.
>>
>> Neither do I.  Not relevant, since I don't have any such learned by rote
>> definitions of a proof.
>>
> 
> I make sure to never have such.
> I only know things on the basis that they are proven
> to be inherently true.

Your problem is you have never-learned but used by rote statements.

Your second statement is just a lie, as you claim many things that are 
just not true in the actual system you claim to be in.

> 
>>> The most generic form of a proof is essentially a semantic tautology.
>>
>> That's neither here not there, being too abstract to be of use.
>>
> 
> It shows that natural preexisting order of all knowledge.

Double-Talk.

> 
>>>>>>> Within the giant semantic tautology of knowledge that
>>>>>>> can be expressed in language everything is proven or
>>>>>>> not an element of this body.
>>
>>>>>> Your scheme is limited indeed, in that it is not powerful enough to
>>>>>> represent unprovable propositions.
>>
>>>>> In other words "the entire body of knowledge that
>>>>> can be expressed in language" uses big words that
>>>>> you cannot understand?
>>
>>>>> What is left out of:
>>>>> "the entire body of knowledge that can be expressed in language" ?
>>
>>>> Arithmetic, for a start.
>>
>>> So you are trying to get away with saying that
>>> knowledge of arithmetic cannot be expressed in language?
>>
>> I'm saying that any system of knowledge in which Gödel's Incompleteness
>> Theorem doesn't apply is either inconsistent or incapable of doing
>> arithmetic.
>>
> 
> You are merely spouting off dogma with no understanding
> of how I showed that this does not work.
> 
> He used Gödel numbers to hide the underlying
> semantics in a language that could not directly
> specify either provability or self-reference.
> 
> G says of itself that it is unprovable in F
> G := (F ⊬ G)
> 
>>>> If that allegedly "entire body of knowledge"
>>>> was capable of doing arithmetic, Gödel's Incompleteness Theorem would
>>>> apply to it.
>>
>>> Arithmetic is merely insufficiently expressive, the body of knowledge
>>> that can be expressed in language knows that.
>>
>> No, the body of knowledge that can be represented as you envisage
>> wouldn't come up to the level of a stone-age person.
>>
> 
> Since it directly formalizes the semantics of anything
> that anyone can possible ever say how can this be true?
> 
>>>> That is a proof by contradiction that such a body of
>>>> knowledge cannot exist.
>>
>>> Not at all.
>>
>> How can you say that?  You don't understand proof by contradiction,
>> remember?
>>
>>> Arithmetic is merely insufficiently expressive.
>>> While you attempt to come up with counter-examples know
>>> that dogma does not count.
>>
>> I don't know what you mean by dogma.  I'm talking about proven results
>> like 2 + 2 = 4.  You're just ignorant, because you don't have the
>> background needed to test these results, but you reject them just because
>> you don't like them.  You're an idiot, in other words.
>>
>>> A counter-example would be an element of knowledge
>>> that can be expressed in language that:
>>> (a) Cannot be expressed in language.
>>> (b) Is not true. (All knowledge is true)
>>
>> That would indeed be a counter example.  But given there is no suspicion
>> that such a construct of knowledge could be complete, no proof, no
>> attempt at a proof, there is nothing to give a counter example to.
>>
> 
> G := (F ⊬ G) // G says of itself that it cannot be proved in F
> Gödel says the same thing so verbosely that no one has any
> idea that it all boils down to this: G := (F ⊬ G)
> 
>>> That is what I mean by counter-examples are
>>> categorically impossible
>>
>> Your complete system of knowledge is categorically impossible.
>>
>>> -- 
>>> Copyright 2025 Olcott
>>
>>> My 28 year goal has been to make
>>> "true on the basis of meaning" computable.
>>
>>> This required establishing a new foundation
>>> for correct reasoning.
>>
> 
> 

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#641506

On 12/1/2025 4:31 AM, Mikko wrote:
> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>> [ Followup-To: set ]
>>
>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>
>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>
>> [ .... ]
>>
>>>>> *Within A new foundation for correct reasoning*
>>
>>>>> (a) Every element of the body of knowledge that can
>>>>>       be expressed in language is entirely composed of
>>>>>     (1) A finite set of atomic facts
>>>>>     (2) Every expression of language that is semantically
>>>>>         entailed by (1)
>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>       of the "theory of simple types"
>>>>>       https://en.wikipedia.org/wiki/ 
>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>       as one fully integrated whole not needing model theory
>>
>>>>> We have now totally overcome Gödel Incompleteness
>>>>> and Tarski Undefinability for the entire body if
>>>>> knowledge that can be expressed in language. It
>>>>> is now a giant semantic tautology.
>>
>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>> They're fundamental truths.
>>
>>> I just showed the detailed steps making both of
>>> them impossible in the system that I just specified.
>>> A counter-example is categorically impossible.
>>
>> Your construction is impossible, as proven by Gödel's Incompleteness
>> Theorem.
> 
> Doesn't a theory that has no theorems satisfy all above stated
> requriements?
> 

Every element of the body of knowledge
is not such a formal system.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641563

olcott kirjoitti 1.12.2025 klo 14.19:
> On 12/1/2025 4:31 AM, Mikko wrote:
>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>> [ Followup-To: set ]
>>>
>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>
>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>
>>> [ .... ]
>>>
>>>>>> *Within A new foundation for correct reasoning*
>>>
>>>>>> (a) Every element of the body of knowledge that can
>>>>>>       be expressed in language is entirely composed of
>>>>>>     (1) A finite set of atomic facts
>>>>>>     (2) Every expression of language that is semantically
>>>>>>         entailed by (1)
>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>       of the "theory of simple types"
>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>>       as one fully integrated whole not needing model theory
>>>
>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>> and Tarski Undefinability for the entire body if
>>>>>> knowledge that can be expressed in language. It
>>>>>> is now a giant semantic tautology.
>>>
>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>> They're fundamental truths.
>>>
>>>> I just showed the detailed steps making both of
>>>> them impossible in the system that I just specified.
>>>> A counter-example is categorically impossible.
>>>
>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>> Theorem.
>>
>> Doesn't a theory that has no theorems satisfy all above stated
>> requriements?
> 
> Every element of the body of knowledge
> is not such a formal system.

That's right, the body of knowledge is irrelevant here.


-- 
Mikko

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#641567

On 12/2/2025 3:56 AM, Mikko wrote:
> olcott kirjoitti 1.12.2025 klo 14.19:
>> On 12/1/2025 4:31 AM, Mikko wrote:
>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>> [ Followup-To: set ]
>>>>
>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>
>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>
>>>> [ .... ]
>>>>
>>>>>>> *Within A new foundation for correct reasoning*
>>>>
>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>       be expressed in language is entirely composed of
>>>>>>>     (1) A finite set of atomic facts
>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>         entailed by (1)
>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>       of the "theory of simple types"
>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>>>       as one fully integrated whole not needing model theory
>>>>
>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>> knowledge that can be expressed in language. It
>>>>>>> is now a giant semantic tautology.
>>>>
>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>> They're fundamental truths.
>>>>
>>>>> I just showed the detailed steps making both of
>>>>> them impossible in the system that I just specified.
>>>>> A counter-example is categorically impossible.
>>>>
>>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>>> Theorem.
>>>
>>> Doesn't a theory that has no theorems satisfy all above stated
>>> requriements?
>>
>> Every element of the body of knowledge
>> is not such a formal system.
> 
> That's right, the body of knowledge is irrelevant here.
> 
> 

If we are not talking about elements of the body
of knowledge that are missing or unknown truths
then there is no notion of actual incompleteness
that remains.

The problem here is that technical fields tend to
overload conventional terms with terms-of-the-art
meanings that are incompatible with their base meaning.

Undecidable decision problem have literally nothing
to do with any inability to make a decision.

They are actually merely yes/no questions such that
both yes and no are the wrong answer.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641581

olcott kirjoitti 2.12.2025 klo 16.07:
> On 12/2/2025 3:56 AM, Mikko wrote:
>> olcott kirjoitti 1.12.2025 klo 14.19:
>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>> [ Followup-To: set ]
>>>>>
>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>
>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>
>>>>> [ .... ]
>>>>>
>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>
>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>         entailed by (1)
>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>       of the "theory of simple types"
>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>
>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>> is now a giant semantic tautology.
>>>>>
>>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>>> They're fundamental truths.
>>>>>
>>>>>> I just showed the detailed steps making both of
>>>>>> them impossible in the system that I just specified.
>>>>>> A counter-example is categorically impossible.
>>>>>
>>>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>>>> Theorem.
>>>>
>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>> requriements?
>>>
>>> Every element of the body of knowledge
>>> is not such a formal system.
>>
>> That's right, the body of knowledge is irrelevant here.
> 
> If we are not talking about elements of the body
> of knowledge that are missing or unknown truths
> then there is no notion of actual incompleteness
> that remains.

The body of knowledge includes that certain quesstions have answers
but doesn't include now what those answers are. For example, we
know that North Sentinel Island is population but we don't know
what language is spoken there. This and other examples show that
the body of knowledge is incomplete.

-- 
Mikko

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#641586

On 12/3/2025 5:17 AM, Mikko wrote:
> olcott kirjoitti 2.12.2025 klo 16.07:
>> On 12/2/2025 3:56 AM, Mikko wrote:
>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>> [ Followup-To: set ]
>>>>>>
>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>
>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>
>>>>>> [ .... ]
>>>>>>
>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>
>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>         entailed by (1)
>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>
>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>> is now a giant semantic tautology.
>>>>>>
>>>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>>>> They're fundamental truths.
>>>>>>
>>>>>>> I just showed the detailed steps making both of
>>>>>>> them impossible in the system that I just specified.
>>>>>>> A counter-example is categorically impossible.
>>>>>>
>>>>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>>>>> Theorem.
>>>>>
>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>> requriements?
>>>>
>>>> Every element of the body of knowledge
>>>> is not such a formal system.
>>>
>>> That's right, the body of knowledge is irrelevant here.
>>
>> If we are not talking about elements of the body
>> of knowledge that are missing or unknown truths
>> then there is no notion of actual incompleteness
>> that remains.
> 
> The body of knowledge includes that certain quesstions have answers
> but doesn't include now what those answers are. 

Unknowns are outside of the body of knowledge.

> For example, we
> know that North Sentinel Island is population but we don't know
> what language is spoken there. This and other examples show that
> the body of knowledge is incomplete.
> 

If anyone anywhere knows then it is in the body of general knowledge.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641604

olcott kirjoitti 3.12.2025 klo 18.13:
> On 12/3/2025 5:17 AM, Mikko wrote:
>> olcott kirjoitti 2.12.2025 klo 16.07:
>>> On 12/2/2025 3:56 AM, Mikko wrote:
>>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>>> [ Followup-To: set ]
>>>>>>>
>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>>
>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>>
>>>>>>> [ .... ]
>>>>>>>
>>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>>
>>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>>         entailed by (1)
>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>>       Where every semantic meaning is fully encoded syntactically
>>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>>
>>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>>> is now a giant semantic tautology.
>>>>>>>
>>>>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>>>>> They're fundamental truths.
>>>>>>>
>>>>>>>> I just showed the detailed steps making both of
>>>>>>>> them impossible in the system that I just specified.
>>>>>>>> A counter-example is categorically impossible.
>>>>>>>
>>>>>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>>>>>> Theorem.
>>>>>>
>>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>>> requriements?
>>>>>
>>>>> Every element of the body of knowledge
>>>>> is not such a formal system.
>>>>
>>>> That's right, the body of knowledge is irrelevant here.
>>>
>>> If we are not talking about elements of the body
>>> of knowledge that are missing or unknown truths
>>> then there is no notion of actual incompleteness
>>> that remains.
>>
>> The body of knowledge includes that certain quesstions have answers
>> but doesn't include now what those answers are. 
> 
> Unknowns are outside of the body of knowledge.
> 
>> For example, we
>> know that North Sentinel Island is population but we don't know
>> what language is spoken there. This and other examples show that
>> the body of knowledge is incomplete.
> 
> If anyone anywhere knows then it is in the body of general knowledge.

It is not general knowledge as it is not known to anybody outside
North Sentinel Island.

I know the color of my bedroom wall. Is that general knowledge?

-- 
Mikko

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#641612

On 12/4/2025 3:29 AM, Mikko wrote:
> olcott kirjoitti 3.12.2025 klo 18.13:
>> On 12/3/2025 5:17 AM, Mikko wrote:
>>> olcott kirjoitti 2.12.2025 klo 16.07:
>>>> On 12/2/2025 3:56 AM, Mikko wrote:
>>>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>>>> [ Followup-To: set ]
>>>>>>>>
>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>>>
>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>>>
>>>>>>>> [ .... ]
>>>>>>>>
>>>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>>>
>>>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>>>         entailed by (1)
>>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>>>       Where every semantic meaning is fully encoded 
>>>>>>>>>>> syntactically
>>>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>>>
>>>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>>>> is now a giant semantic tautology.
>>>>>>>>
>>>>>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>>>>>> They're fundamental truths.
>>>>>>>>
>>>>>>>>> I just showed the detailed steps making both of
>>>>>>>>> them impossible in the system that I just specified.
>>>>>>>>> A counter-example is categorically impossible.
>>>>>>>>
>>>>>>>> Your construction is impossible, as proven by Gödel's 
>>>>>>>> Incompleteness
>>>>>>>> Theorem.
>>>>>>>
>>>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>>>> requriements?
>>>>>>
>>>>>> Every element of the body of knowledge
>>>>>> is not such a formal system.
>>>>>
>>>>> That's right, the body of knowledge is irrelevant here.
>>>>
>>>> If we are not talking about elements of the body
>>>> of knowledge that are missing or unknown truths
>>>> then there is no notion of actual incompleteness
>>>> that remains.
>>>
>>> The body of knowledge includes that certain quesstions have answers
>>> but doesn't include now what those answers are. 
>>
>> Unknowns are outside of the body of knowledge.
>>
>>> For example, we
>>> know that North Sentinel Island is population but we don't know
>>> what language is spoken there. This and other examples show that
>>> the body of knowledge is incomplete.
>>
>> If anyone anywhere knows then it is in the body of general knowledge.
> 
> It is not general knowledge as it is not known to anybody outside
> North Sentinel Island.
> 
> I know the color of my bedroom wall. Is that general knowledge?
> 

To simply things the body of general knowledge
can be everything written down in any published
book or published paper. Also anything that can
be deduced from these sources.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#641622

olcott kirjoitti 4.12.2025 klo 16.18:
> On 12/4/2025 3:29 AM, Mikko wrote:
>> olcott kirjoitti 3.12.2025 klo 18.13:
>>> On 12/3/2025 5:17 AM, Mikko wrote:
>>>> olcott kirjoitti 2.12.2025 klo 16.07:
>>>>> On 12/2/2025 3:56 AM, Mikko wrote:
>>>>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>>>>> [ Followup-To: set ]
>>>>>>>>>
>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>>>>
>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>>>>
>>>>>>>>> [ .... ]
>>>>>>>>>
>>>>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>>>>
>>>>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>>>>         entailed by (1)
>>>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>>>>       Where every semantic meaning is fully encoded 
>>>>>>>>>>>> syntactically
>>>>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>>>>
>>>>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>>>>> is now a giant semantic tautology.
>>>>>>>>>
>>>>>>>>>>> You can't "overcome" these theorems, since they're not 
>>>>>>>>>>> obstacles.
>>>>>>>>>>> They're fundamental truths.
>>>>>>>>>
>>>>>>>>>> I just showed the detailed steps making both of
>>>>>>>>>> them impossible in the system that I just specified.
>>>>>>>>>> A counter-example is categorically impossible.
>>>>>>>>>
>>>>>>>>> Your construction is impossible, as proven by Gödel's 
>>>>>>>>> Incompleteness
>>>>>>>>> Theorem.
>>>>>>>>
>>>>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>>>>> requriements?
>>>>>>>
>>>>>>> Every element of the body of knowledge
>>>>>>> is not such a formal system.
>>>>>>
>>>>>> That's right, the body of knowledge is irrelevant here.
>>>>>
>>>>> If we are not talking about elements of the body
>>>>> of knowledge that are missing or unknown truths
>>>>> then there is no notion of actual incompleteness
>>>>> that remains.
>>>>
>>>> The body of knowledge includes that certain quesstions have answers
>>>> but doesn't include now what those answers are. 
>>>
>>> Unknowns are outside of the body of knowledge.
>>>
>>>> For example, we
>>>> know that North Sentinel Island is population but we don't know
>>>> what language is spoken there. This and other examples show that
>>>> the body of knowledge is incomplete.
>>>
>>> If anyone anywhere knows then it is in the body of general knowledge.
>>
>> It is not general knowledge as it is not known to anybody outside
>> North Sentinel Island.
>>
>> I know the color of my bedroom wall. Is that general knowledge?

> To simply things the body of general knowledge
> can be everything written down in any published
> book or published paper. Also anything that can
> be deduced from these sources.

General knowledge also includes that there are claims that might be
deducible from published knowledge or might be not, and it is not
yet known whether or how. Examples of such claims can be found in
published sources.

-- 
Mikko

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#641639

On 12/5/2025 3:03 AM, Mikko wrote:
> olcott kirjoitti 4.12.2025 klo 16.18:
>> On 12/4/2025 3:29 AM, Mikko wrote:
>>> olcott kirjoitti 3.12.2025 klo 18.13:
>>>> On 12/3/2025 5:17 AM, Mikko wrote:
>>>>> olcott kirjoitti 2.12.2025 klo 16.07:
>>>>>> On 12/2/2025 3:56 AM, Mikko wrote:
>>>>>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>>>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>>>>>> [ Followup-To: set ]
>>>>>>>>>>
>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>>>>>
>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>>>>>
>>>>>>>>>> [ .... ]
>>>>>>>>>>
>>>>>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>>>>>
>>>>>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>>>>>         entailed by (1)
>>>>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>>>>>       Where every semantic meaning is fully encoded 
>>>>>>>>>>>>> syntactically
>>>>>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>>>>>
>>>>>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>>>>>> is now a giant semantic tautology.
>>>>>>>>>>
>>>>>>>>>>>> You can't "overcome" these theorems, since they're not 
>>>>>>>>>>>> obstacles.
>>>>>>>>>>>> They're fundamental truths.
>>>>>>>>>>
>>>>>>>>>>> I just showed the detailed steps making both of
>>>>>>>>>>> them impossible in the system that I just specified.
>>>>>>>>>>> A counter-example is categorically impossible.
>>>>>>>>>>
>>>>>>>>>> Your construction is impossible, as proven by Gödel's 
>>>>>>>>>> Incompleteness
>>>>>>>>>> Theorem.
>>>>>>>>>
>>>>>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>>>>>> requriements?
>>>>>>>>
>>>>>>>> Every element of the body of knowledge
>>>>>>>> is not such a formal system.
>>>>>>>
>>>>>>> That's right, the body of knowledge is irrelevant here.
>>>>>>
>>>>>> If we are not talking about elements of the body
>>>>>> of knowledge that are missing or unknown truths
>>>>>> then there is no notion of actual incompleteness
>>>>>> that remains.
>>>>>
>>>>> The body of knowledge includes that certain quesstions have answers
>>>>> but doesn't include now what those answers are. 
>>>>
>>>> Unknowns are outside of the body of knowledge.
>>>>
>>>>> For example, we
>>>>> know that North Sentinel Island is population but we don't know
>>>>> what language is spoken there. This and other examples show that
>>>>> the body of knowledge is incomplete.
>>>>
>>>> If anyone anywhere knows then it is in the body of general knowledge.
>>>
>>> It is not general knowledge as it is not known to anybody outside
>>> North Sentinel Island.
>>>
>>> I know the color of my bedroom wall. Is that general knowledge?
> 
>> To simply things the body of general knowledge
>> can be everything written down in any published
>> book or published paper. Also anything that can
>> be deduced from these sources.
> 
> General knowledge also includes that there are claims that might be
> deducible from published knowledge or might be not, and it is not
> yet known whether or how. Examples of such claims can be found in
> published sources.
> 

Yes this is correct.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

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#641664

olcott kirjoitti 5.12.2025 klo 19.31:
> On 12/5/2025 3:03 AM, Mikko wrote:
>> olcott kirjoitti 4.12.2025 klo 16.18:
>>> On 12/4/2025 3:29 AM, Mikko wrote:
>>>> olcott kirjoitti 3.12.2025 klo 18.13:
>>>>> On 12/3/2025 5:17 AM, Mikko wrote:
>>>>>> olcott kirjoitti 2.12.2025 klo 16.07:
>>>>>>> On 12/2/2025 3:56 AM, Mikko wrote:
>>>>>>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>>>>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>>>>>>> [ Followup-To: set ]
>>>>>>>>>>>
>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>>>>>>
>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>>>>>>
>>>>>>>>>>> [ .... ]
>>>>>>>>>>>
>>>>>>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>>>>>>
>>>>>>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>>>>>>         entailed by (1)
>>>>>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>>>>>>       Where every semantic meaning is fully encoded 
>>>>>>>>>>>>>> syntactically
>>>>>>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>>>>>>
>>>>>>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>>>>>>> is now a giant semantic tautology.
>>>>>>>>>>>
>>>>>>>>>>>>> You can't "overcome" these theorems, since they're not 
>>>>>>>>>>>>> obstacles.
>>>>>>>>>>>>> They're fundamental truths.
>>>>>>>>>>>
>>>>>>>>>>>> I just showed the detailed steps making both of
>>>>>>>>>>>> them impossible in the system that I just specified.
>>>>>>>>>>>> A counter-example is categorically impossible.
>>>>>>>>>>>
>>>>>>>>>>> Your construction is impossible, as proven by Gödel's 
>>>>>>>>>>> Incompleteness
>>>>>>>>>>> Theorem.
>>>>>>>>>>
>>>>>>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>>>>>>> requriements?
>>>>>>>>>
>>>>>>>>> Every element of the body of knowledge
>>>>>>>>> is not such a formal system.
>>>>>>>>
>>>>>>>> That's right, the body of knowledge is irrelevant here.
>>>>>>>
>>>>>>> If we are not talking about elements of the body
>>>>>>> of knowledge that are missing or unknown truths
>>>>>>> then there is no notion of actual incompleteness
>>>>>>> that remains.
>>>>>>
>>>>>> The body of knowledge includes that certain quesstions have answers
>>>>>> but doesn't include now what those answers are. 
>>>>>
>>>>> Unknowns are outside of the body of knowledge.
>>>>>
>>>>>> For example, we
>>>>>> know that North Sentinel Island is population but we don't know
>>>>>> what language is spoken there. This and other examples show that
>>>>>> the body of knowledge is incomplete.
>>>>>
>>>>> If anyone anywhere knows then it is in the body of general knowledge.
>>>>
>>>> It is not general knowledge as it is not known to anybody outside
>>>> North Sentinel Island.
>>>>
>>>> I know the color of my bedroom wall. Is that general knowledge?
>>
>>> To simply things the body of general knowledge
>>> can be everything written down in any published
>>> book or published paper. Also anything that can
>>> be deduced from these sources.
>>
>> General knowledge also includes that there are claims that might be
>> deducible from published knowledge or might be not, and it is not
>> yet known whether or how. Examples of such claims can be found in
>> published sources.

> Yes this is correct.

Therefore it is not correct to say that all claims decucible from
general knowledge are in general knoledge. The claims that are
deducible from general knoledge but neither known to be deducible from
the common knowledge nor ottherwise knwon are not in general knowledge.
This is an incompleteness in general knowledge.

-- 
Mikko

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#641675

On 12/6/2025 3:39 AM, Mikko wrote:
> olcott kirjoitti 5.12.2025 klo 19.31:
>> On 12/5/2025 3:03 AM, Mikko wrote:
>>> olcott kirjoitti 4.12.2025 klo 16.18:
>>>> On 12/4/2025 3:29 AM, Mikko wrote:
>>>>> olcott kirjoitti 3.12.2025 klo 18.13:
>>>>>> On 12/3/2025 5:17 AM, Mikko wrote:
>>>>>>> olcott kirjoitti 2.12.2025 klo 16.07:
>>>>>>>> On 12/2/2025 3:56 AM, Mikko wrote:
>>>>>>>>> olcott kirjoitti 1.12.2025 klo 14.19:
>>>>>>>>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>>>>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>>>>>>>>> [ Followup-To: set ]
>>>>>>>>>>>>
>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>>>>>>>>> dart200 <user7160@newsgrouper.org.invalid> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> [ .... ]
>>>>>>>>>>>>
>>>>>>>>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>>>>>>>>
>>>>>>>>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>>>>>>>>>       be expressed in language is entirely composed of
>>>>>>>>>>>>>>>     (1) A finite set of atomic facts
>>>>>>>>>>>>>>>     (2) Every expression of language that is semantically
>>>>>>>>>>>>>>>         entailed by (1)
>>>>>>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>>>>>>>>>       Postulates combined with The Kurt Gödel definition
>>>>>>>>>>>>>>>       of the "theory of simple types"
>>>>>>>>>>>>>>>       https://en.wikipedia.org/wiki/ 
>>>>>>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>>>>>>>>>       Where every semantic meaning is fully encoded 
>>>>>>>>>>>>>>> syntactically
>>>>>>>>>>>>>>>       as one fully integrated whole not needing model theory
>>>>>>>>>>>>
>>>>>>>>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>>>>>>>>> is now a giant semantic tautology.
>>>>>>>>>>>>
>>>>>>>>>>>>>> You can't "overcome" these theorems, since they're not 
>>>>>>>>>>>>>> obstacles.
>>>>>>>>>>>>>> They're fundamental truths.
>>>>>>>>>>>>
>>>>>>>>>>>>> I just showed the detailed steps making both of
>>>>>>>>>>>>> them impossible in the system that I just specified.
>>>>>>>>>>>>> A counter-example is categorically impossible.
>>>>>>>>>>>>
>>>>>>>>>>>> Your construction is impossible, as proven by Gödel's 
>>>>>>>>>>>> Incompleteness
>>>>>>>>>>>> Theorem.
>>>>>>>>>>>
>>>>>>>>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>>>>>>>>> requriements?
>>>>>>>>>>
>>>>>>>>>> Every element of the body of knowledge
>>>>>>>>>> is not such a formal system.
>>>>>>>>>
>>>>>>>>> That's right, the body of knowledge is irrelevant here.
>>>>>>>>
>>>>>>>> If we are not talking about elements of the body
>>>>>>>> of knowledge that are missing or unknown truths
>>>>>>>> then there is no notion of actual incompleteness
>>>>>>>> that remains.
>>>>>>>
>>>>>>> The body of knowledge includes that certain quesstions have answers
>>>>>>> but doesn't include now what those answers are. 
>>>>>>
>>>>>> Unknowns are outside of the body of knowledge.
>>>>>>
>>>>>>> For example, we
>>>>>>> know that North Sentinel Island is population but we don't know
>>>>>>> what language is spoken there. This and other examples show that
>>>>>>> the body of knowledge is incomplete.
>>>>>>
>>>>>> If anyone anywhere knows then it is in the body of general knowledge.
>>>>>
>>>>> It is not general knowledge as it is not known to anybody outside
>>>>> North Sentinel Island.
>>>>>
>>>>> I know the color of my bedroom wall. Is that general knowledge?
>>>
>>>> To simply things the body of general knowledge
>>>> can be everything written down in any published
>>>> book or published paper. Also anything that can
>>>> be deduced from these sources.
>>>
>>> General knowledge also includes that there are claims that might be
>>> deducible from published knowledge or might be not, and it is not
>>> yet known whether or how. Examples of such claims can be found in
>>> published sources.
> 
>> Yes this is correct.
> 
> Therefore it is not correct to say that all claims decucible from
> general knowledge

I never said that they were.

>  are in general knoledge. The claims that are
> deducible from general knoledge but neither known to be deducible from
> the common knowledge nor ottherwise knwon are not in general knowledge.
> This is an incompleteness in general knowledge.
> 

Claims that can be deduced from published knowledge
can be construed to be the body of general knowledge.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

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