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Formal systems that cannot possibly be incomplete except for unknowns and unknowable

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  Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-04 21:23 -0500
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-05 12:50 +0300
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 10:39 -0500
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-06 13:02 +0300
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-05 10:47 +0000
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 16:03 -0500
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-06 08:30 +0000
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mikko <mikko.levanto@iki.fi> - 2025-05-06 13:04 +0300
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 07:04 -0400
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mr Flibble <flibble@red-dwarf.jmc.corp> - 2025-05-05 14:46 +0000
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Heathfield <rjh@cpax.org.uk> - 2025-05-05 16:51 +0100
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Mr Flibble <flibble@red-dwarf.jmc.corp> - 2025-05-05 16:10 +0000
            Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Heathfield <rjh@cpax.org.uk> - 2025-05-05 17:59 +0100
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 21:08 -0400
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 10:31 -0500
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-05 21:11 -0400
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 21:26 -0500
            Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-06 07:16 -0400
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-05-05 23:27 -0500
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Alan Mackenzie <acm@muc.de> - 2025-05-06 08:17 +0000
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Richard Damon <richard@damon-family.org> - 2025-05-06 07:20 -0400
            Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED olcott <polcott333@gmail.com> - 2025-05-06 12:46 -0500
              Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable ---ELABORATED Richard Damon <richard@damon-family.org> - 2025-05-06 22:07 -0400
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 16:24 +0000
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 10:55 -0600
        Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 17:30 +0000
          Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 11:43 -0600
    Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-15 16:49 +0000
      Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable olcott <polcott333@gmail.com> - 2025-11-15 11:19 -0600
    Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself olcott <polcott333@gmail.com> - 2025-11-16 09:29 -0600
      Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself HAL 9000 <hal@discovery.nasa> - 2025-11-16 16:46 +0000
        Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself olcott <polcott333@gmail.com> - 2025-11-16 11:07 -0600
        DD simulated by HHH cannot possibly terminate normally olcott <polcott333@gmail.com> - 2025-11-16 11:20 -0600
        Re: Kaz ---Keith said DDD simulated by HHH is equivalent to DDD calling itself "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-16 13:18 -0800

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#339812 — Formal systems that cannot possibly be incomplete except for unknowns and unknowable

When we define formal systems as a finite list of basic facts and allow 
semantic logical entailment as the only rule of inference we have 
systems that can express any truth that can be expressed in language.

Also with such systems Undecidability is impossible. The only 
incompleteness are things that are unknown or unknowable.

The language of such a formal system is an extended form of the Montague 
Grammar of natural language semantics. I came up with this mostly in the 
last two years. I have been working on it for 22 years.

The Montague Grammar Rudolf Carnap Meaning postulates are organized in a 
knowledge ontology inheritance hierarchy. 
https://en.wikipedia.org/wiki/Ontology_(information_science)
-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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#339813

On 2025-05-05 02:23:56 +0000, olcott said:

> When we define formal systems as a finite list of basic facts and allow 
> semantic logical entailment as the only rule of inference we have 
> systems that can express any truth that can be expressed in language.
> 
> Also with such systems Undecidability is impossible. The only 
> incompleteness are things that are unknown or unknowable.

A formal system has a formal language. Unless the language is too
restricted for most interesting purposes the negation of every
sentence is another sentence. In a consistent system some sentence
is unprovable. If the negation of that system is also unprovable
then the system is incomplete.

None of the features of specified above prevents an expressible unprovable
sentence that has an unprovable negation. While adding one of the pair
to the basic facts there is nothing to prevent an infinite set of such
pairs.

-- 
Mikko

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#339818

On 5/5/2025 4:50 AM, Mikko wrote:
> On 2025-05-05 02:23:56 +0000, olcott said:
> 
>> When we define formal systems as a finite list of basic facts and 
>> allow semantic logical entailment as the only rule of inference we 
>> have systems that can express any truth that can be expressed in 
>> language.
>>
>> Also with such systems Undecidability is impossible. The only 
>> incompleteness are things that are unknown or unknowable.
> 
> A formal system has a formal language. Unless the language is too
> restricted for most interesting purposes the negation of every
> sentence is another sentence. In a consistent system some sentence
> is unprovable. If the negation of that system is also unprovable
> then the system is incomplete.
> 

My system skips merely "provable" and goes directly to "provably true".
Expressions such as "This sentence is not true" and its negation
are not provably true, thus rejected as semantically unsound.

> None of the features of specified above prevents an expressible unprovable
> sentence that has an unprovable negation. While adding one of the pair
> to the basic facts there is nothing to prevent an infinite set of such
> pairs.
> 

Basic facts are stipulated to be a finite set
of general knowledge of the world.


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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#339829

On 2025-05-05 15:39:56 +0000, olcott said:

> On 5/5/2025 4:50 AM, Mikko wrote:
>> On 2025-05-05 02:23:56 +0000, olcott said:
>> 
>>> When we define formal systems as a finite list of basic facts and allow 
>>> semantic logical entailment as the only rule of inference we have 
>>> systems that can express any truth that can be expressed in language.
>>> 
>>> Also with such systems Undecidability is impossible. The only 
>>> incompleteness are things that are unknown or unknowable.
>> 
>> A formal system has a formal language. Unless the language is too
>> restricted for most interesting purposes the negation of every
>> sentence is another sentence. In a consistent system some sentence
>> is unprovable. If the negation of that system is also unprovable
>> then the system is incomplete.
> 
> My system skips merely "provable" and goes directly to "provably true".
> Expressions such as "This sentence is not true" and its negation
> are not provably true, thus rejected as semantically unsound.

The references to truth and semantics make the system informal.

-- 
Mikko

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#339814

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> When we define formal systems as a finite list of basic facts and allow 
> semantic logical entailment as the only rule of inference we have 
> systems that can express any truth that can be expressed in language.

> Also with such systems Undecidability is impossible. The only 
> incompleteness are things that are unknown or unknowable.

Do you believe in the tooth fairy, too?

[ .... ]

> -- 
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

-- 
Alan Mackenzie (Nuremberg, Germany).

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#339822

On 5/5/2025 3:12 PM, Alan Mackenzie wrote:
> olcott <polcott333@gmail.com> wrote:
>> On 5/5/2025 2:34 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 5/5/2025 1:52 PM, Alan Mackenzie wrote:
>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>> On 5/5/2025 1:19 PM, Alan Mackenzie wrote:
>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 5/5/2025 11:05 AM, Alan Mackenzie wrote:
> 
>>>>> [ .... ]
> 
>>>>>>>>> Follow the details of the proof of Gödel's Incompleteness
>>>>>>>>> Theorem, and apply them to your "system".  That will give you
>>>>>>>>> your counter example.
> 
>>>>>>>> My system does not do "provable" instead it does "provably true".
> 
>>>>>>> I don't know anything about your "system" and I don't care.  If
>>>>>>> it's a formal system with anything above minimal capabilities,
>>>>>>> Gödel's Theorem applies to it, and the "system" will be incomplete
>>>>>>> (in Gödel's sense).
> 
>>>>>> I reformulate the entire notion of "formal system"
>>>>>> so that undecidability ceases to be possible.
> 
>>>>> Liar.  That is impossible.
> 
>>>>> [ Irrelevant nonsense snipped. ]
> 
>>>> When you start with truth and only apply truth preserving
>>>> operations then you necessarily end up with truth.
>>>> Is that too difficult for you?
> 
>>> Not at all.  One of the truths you inescapably end up with is Gödel's
>>> Theorem.  Either that, or the system is self-contradictory or too weak
>>> to do anything at all.
> 
>> Gödel's theorem cannot possibly be recreated when
>> True(x) is defined to apply truth preserving
>> operations to basic facts.
> 
> On the contrary, whether or not True(x) can be so defined, Gödel's
> theorem cannot be avoided.
> 
> [ .... ]
> 
>>> That would appear to be well beyond your level of understanding.  You
>>> ought to show some respect towards those who do understand these things.
> 
>> I have spent 22 years focusing on pathological self-reference.
>> My understanding really is deeper.
> 
> It might be a little deeper than it was, but that's not saying very much.
> The concept of proof by contradiction, for example, is way beyond you.
> Even the very idea of a mathematical proof, its status, its significance
> is beyond you.  You don't even understand what it is you're lacking.
> 
> Those 22 years have been suboptimally spent.
> 
> As I said, you ought to show a bit of respect to those who understand
> these mathematical things.
> 

So you don't understand that when True(x) is
defined to only apply truth preserving operations
to basic facts that are stipulated to be true
that every input including random gibberish
and self-contradiction IS DECIDABLE AS TRUE OR ~TRUE.

>> -- 
>> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
>> hits a target no one else can see." Arthur Schopenhauer
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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#339828

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> On 5/5/2025 3:12 PM, Alan Mackenzie wrote:
>> olcott <polcott333@gmail.com> wrote:
>>> On 5/5/2025 2:34 PM, Alan Mackenzie wrote:
>>>> olcott <polcott333@gmail.com> wrote:
>>>>> On 5/5/2025 1:52 PM, Alan Mackenzie wrote:
>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>> On 5/5/2025 1:19 PM, Alan Mackenzie wrote:
>>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>>> On 5/5/2025 11:05 AM, Alan Mackenzie wrote:

>>>>>> [ .... ]

>>>>>>>>>> Follow the details of the proof of Gödel's Incompleteness
>>>>>>>>>> Theorem, and apply them to your "system".  That will give you
>>>>>>>>>> your counter example.

>>>>>>>>> My system does not do "provable" instead it does "provably true".

>>>>>>>> I don't know anything about your "system" and I don't care.  If
>>>>>>>> it's a formal system with anything above minimal capabilities,
>>>>>>>> Gödel's Theorem applies to it, and the "system" will be incomplete
>>>>>>>> (in Gödel's sense).

>>>>>>> I reformulate the entire notion of "formal system"
>>>>>>> so that undecidability ceases to be possible.

>>>>>> Liar.  That is impossible.

>>>>>> [ Irrelevant nonsense snipped. ]

>>>>> When you start with truth and only apply truth preserving
>>>>> operations then you necessarily end up with truth.
>>>>> Is that too difficult for you?

>>>> Not at all.  One of the truths you inescapably end up with is Gödel's
>>>> Theorem.  Either that, or the system is self-contradictory or too weak
>>>> to do anything at all.

>>> Gödel's theorem cannot possibly be recreated when
>>> True(x) is defined to apply truth preserving
>>> operations to basic facts.

>> On the contrary, whether or not True(x) can be so defined, Gödel's
>> theorem cannot be avoided.

>> [ .... ]

>>>> That would appear to be well beyond your level of understanding.  You
>>>> ought to show some respect towards those who do understand these things.

>>> I have spent 22 years focusing on pathological self-reference.
>>> My understanding really is deeper.

>> It might be a little deeper than it was, but that's not saying very much.
>> The concept of proof by contradiction, for example, is way beyond you.
>> Even the very idea of a mathematical proof, its status, its significance
>> is beyond you.  You don't even understand what it is you're lacking.

>> Those 22 years have been suboptimally spent.

>> As I said, you ought to show a bit of respect to those who understand
>> these mathematical things.

> So you don't understand that when True(x) is
> defined to only apply truth preserving operations
> to basic facts that are stipulated to be true
> that every input including random gibberish
> and self-contradiction IS DECIDABLE AS TRUE OR ~TRUE.

That's like being challenged by a young child to understand some detail
of his newest fantasy.  Except you're not a child, and ought to have an
adult's sense of proportion and reality, and a sense of your own
limitations.  You're lacking these.

> -- 
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

-- 
Alan Mackenzie (Nuremberg, Germany).

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#339830

On 2025-05-06 08:30:28 +0000, Alan Mackenzie said:

> [ Followup-To: set ]
> 
> In comp.theory olcott <polcott333@gmail.com> wrote:
>> On 5/5/2025 3:12 PM, Alan Mackenzie wrote:
>>> olcott <polcott333@gmail.com> wrote:
>>>> On 5/5/2025 2:34 PM, Alan Mackenzie wrote:
>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>> On 5/5/2025 1:52 PM, Alan Mackenzie wrote:
>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 5/5/2025 1:19 PM, Alan Mackenzie wrote:
>>>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>>>> On 5/5/2025 11:05 AM, Alan Mackenzie wrote:
> 
>>>>>>> [ .... ]
> 
>>>>>>>>>>> Follow the details of the proof of Gödel's Incompleteness
>>>>>>>>>>> Theorem, and apply them to your "system".  That will give you
>>>>>>>>>>> your counter example.
> 
>>>>>>>>>> My system does not do "provable" instead it does "provably true".
> 
>>>>>>>>> I don't know anything about your "system" and I don't care.  If
>>>>>>>>> it's a formal system with anything above minimal capabilities,
>>>>>>>>> Gödel's Theorem applies to it, and the "system" will be incomplete
>>>>>>>>> (in Gödel's sense).
> 
>>>>>>>> I reformulate the entire notion of "formal system"
>>>>>>>> so that undecidability ceases to be possible.
> 
>>>>>>> Liar.  That is impossible.
> 
>>>>>>> [ Irrelevant nonsense snipped. ]
> 
>>>>>> When you start with truth and only apply truth preserving
>>>>>> operations then you necessarily end up with truth.
>>>>>> Is that too difficult for you?
> 
>>>>> Not at all.  One of the truths you inescapably end up with is Gödel's
>>>>> Theorem.  Either that, or the system is self-contradictory or too weak
>>>>> to do anything at all.
> 
>>>> Gödel's theorem cannot possibly be recreated when
>>>> True(x) is defined to apply truth preserving
>>>> operations to basic facts.
> 
>>> On the contrary, whether or not True(x) can be so defined, Gödel's
>>> theorem cannot be avoided.
> 
>>> [ .... ]
> 
>>>>> That would appear to be well beyond your level of understanding.  You
>>>>> ought to show some respect towards those who do understand these things.
> 
>>>> I have spent 22 years focusing on pathological self-reference.
>>>> My understanding really is deeper.
> 
>>> It might be a little deeper than it was, but that's not saying very much.
>>> The concept of proof by contradiction, for example, is way beyond you.
>>> Even the very idea of a mathematical proof, its status, its significance
>>> is beyond you.  You don't even understand what it is you're lacking.
> 
>>> Those 22 years have been suboptimally spent.
> 
>>> As I said, you ought to show a bit of respect to those who understand
>>> these mathematical things.
> 
>> So you don't understand that when True(x) is
>> defined to only apply truth preserving operations
>> to basic facts that are stipulated to be true
>> that every input including random gibberish
>> and self-contradiction IS DECIDABLE AS TRUE OR ~TRUE.
> 
> That's like being challenged by a young child to understand some detail
> of his newest fantasy.  Except you're not a child, and ought to have an
> adult's sense of proportion and reality, and a sense of your own
> limitations.  You're lacking these.

Senility can be like infantility expept that senility is permanent.

-- 
Mikko

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#339815

On 5/4/25 10:23 PM, olcott wrote:
> When we define formal systems as a finite list of basic facts and allow 
> semantic logical entailment as the only rule of inference we have 
> systems that can express any truth that can be expressed in language.
> 
> Also with such systems Undecidability is impossible. The only 
> incompleteness are things that are unknown or unknowable.

Can such a system include the mathematics of the natural numbers?

If so, your claim is false, as that is enough to create that undeciability.

> 
> The language of such a formal system is an extended form of the Montague 
> Grammar of natural language semantics. I came up with this mostly in the 
> last two years. I have been working on it for 22 years.
> 
> The Montague Grammar Rudolf Carnap Meaning postulates are organized in a 
> knowledge ontology inheritance hierarchy. https://en.wikipedia.org/wiki/ 
> Ontology_(information_science)

And the problem is that either your claim is wrong, or your logic system 
is just shown to be too small to be useful for many of the things we 
want to be able to do because it can't support the mathematics of 
Natural Numbers.

You don't seem to understand that all the properties you don't like 
about Logic Systems are all conditioned on the ability for the system to 
have a certain level of power in their ability to do logic. "Tpy" 
systems that have been limited below that level will not experiance the 
problems, but also are too weak to do the problems we typically want to 
do with logic.

This ultimate shows your fundamental misunderstanding of what you are 
talking about, especially your inability to handle abstractions, and 
things that can create "infinities".

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#339816

On Mon, 05 May 2025 07:04:15 -0400, Richard Damon wrote:

> On 5/4/25 10:23 PM, olcott wrote:
>> When we define formal systems as a finite list of basic facts and allow
>> semantic logical entailment as the only rule of inference we have
>> systems that can express any truth that can be expressed in language.
>> 
>> Also with such systems Undecidability is impossible. The only
>> incompleteness are things that are unknown or unknowable.
> 
> Can such a system include the mathematics of the natural numbers?
> 
> If so, your claim is false, as that is enough to create that
> undeciability.
> 
> 
>> The language of such a formal system is an extended form of the
>> Montague Grammar of natural language semantics. I came up with this
>> mostly in the last two years. I have been working on it for 22 years.
>> 
>> The Montague Grammar Rudolf Carnap Meaning postulates are organized in
>> a knowledge ontology inheritance hierarchy.
>> https://en.wikipedia.org/wiki/
>> Ontology_(information_science)
> 
> And the problem is that either your claim is wrong, or your logic system
> is just shown to be too small to be useful for many of the things we
> want to be able to do because it can't support the mathematics of
> Natural Numbers.
> 
> You don't seem to understand that all the properties you don't like
> about Logic Systems are all conditioned on the ability for the system to
> have a certain level of power in their ability to do logic. "Tpy"
> systems that have been limited below that level will not experiance the
> problems, but also are too weak to do the problems we typically want to
> do with logic.
> 
> This ultimate shows your fundamental misunderstanding of what you are
> talking about, especially your inability to handle abstractions, and
> things that can create "infinities".

You are fucking clueless about mathematics it seems: it is not possible to 
create infinites using the mathematics of natural numbers (clue: division 
by zero is undefined and infinity is not a number).

/Flibble

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#339819

On 05/05/2025 15:46, Mr Flibble wrote:
> On Mon, 05 May 2025 07:04:15 -0400, Richard Damon wrote:

<snip>

>>
>> This ultimate shows your fundamental misunderstanding of what you are
>> talking about, especially your inability to handle abstractions, and
>> things that can create "infinities".
> 
> You are fucking clueless about mathematics it seems: it is not possible to
> create infinites using the mathematics of natural numbers (clue: division
> by zero is undefined and infinity is not a number).

How many integers are there?

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

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#339820

On Mon, 05 May 2025 16:51:18 +0100, Richard Heathfield wrote:

> On 05/05/2025 15:46, Mr Flibble wrote:
>> On Mon, 05 May 2025 07:04:15 -0400, Richard Damon wrote:
> 
> <snip>
> 
> 
>>> This ultimate shows your fundamental misunderstanding of what you are
>>> talking about, especially your inability to handle abstractions, and
>>> things that can create "infinities".
>> 
>> You are fucking clueless about mathematics it seems: it is not possible
>> to create infinites using the mathematics of natural numbers (clue:
>> division by zero is undefined and infinity is not a number).
> 
> How many integers are there?

Irrelevent: set theory is a different category.

/Flibble

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#339821

On 05/05/2025 17:10, Mr Flibble wrote:
> On Mon, 05 May 2025 16:51:18 +0100, Richard Heathfield wrote:
> 
>> On 05/05/2025 15:46, Mr Flibble wrote:
>>> On Mon, 05 May 2025 07:04:15 -0400, Richard Damon wrote:
>>
>> <snip>
>>
>>
>>>> This ultimate shows your fundamental misunderstanding of what you are
>>>> talking about, especially your inability to handle abstractions, and
>>>> things that can create "infinities".
>>>
>>> You are fucking clueless about mathematics it seems: it is not possible
>>> to create infinites using the mathematics of natural numbers (clue:
>>> division by zero is undefined and infinity is not a number).
>>
>> How many integers are there?
> 
> Irrelevent

That's not how you spell 'infinitely many'.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

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#339823

On 5/5/25 10:46 AM, Mr Flibble wrote:
> On Mon, 05 May 2025 07:04:15 -0400, Richard Damon wrote:
> 
>> On 5/4/25 10:23 PM, olcott wrote:
>>> When we define formal systems as a finite list of basic facts and allow
>>> semantic logical entailment as the only rule of inference we have
>>> systems that can express any truth that can be expressed in language.
>>>
>>> Also with such systems Undecidability is impossible. The only
>>> incompleteness are things that are unknown or unknowable.
>>
>> Can such a system include the mathematics of the natural numbers?
>>
>> If so, your claim is false, as that is enough to create that
>> undeciability.
>>
>>
>>> The language of such a formal system is an extended form of the
>>> Montague Grammar of natural language semantics. I came up with this
>>> mostly in the last two years. I have been working on it for 22 years.
>>>
>>> The Montague Grammar Rudolf Carnap Meaning postulates are organized in
>>> a knowledge ontology inheritance hierarchy.
>>> https://en.wikipedia.org/wiki/
>>> Ontology_(information_science)
>>
>> And the problem is that either your claim is wrong, or your logic system
>> is just shown to be too small to be useful for many of the things we
>> want to be able to do because it can't support the mathematics of
>> Natural Numbers.
>>
>> You don't seem to understand that all the properties you don't like
>> about Logic Systems are all conditioned on the ability for the system to
>> have a certain level of power in their ability to do logic. "Tpy"
>> systems that have been limited below that level will not experiance the
>> problems, but also are too weak to do the problems we typically want to
>> do with logic.
>>
>> This ultimate shows your fundamental misunderstanding of what you are
>> talking about, especially your inability to handle abstractions, and
>> things that can create "infinities".
> 
> You are fucking clueless about mathematics it seems: it is not possible to
> create infinites using the mathematics of natural numbers (clue: division
> by zero is undefined and infinity is not a number).
> 
> /Flibble

Then what is the size of the set of Natural Numbers?

what is the sum of all the Natural Numbers?

The properties of the Natural Numbers deal with the infinite.

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#339817

On 5/5/2025 6:04 AM, Richard Damon wrote:
> On 5/4/25 10:23 PM, olcott wrote:
>> When we define formal systems as a finite list of basic facts and 
>> allow semantic logical entailment as the only rule of inference we 
>> have systems that can express any truth that can be expressed in 
>> language.
>>
>> Also with such systems Undecidability is impossible. The only 
>> incompleteness are things that are unknown or unknowable.
> 
> Can such a system include the mathematics of the natural numbers?
> 
> If so, your claim is false, as that is enough to create that undeciability.
> 

It seems to me that the inferences steps that could
otherwise create undecidability cannot exist in the
system that I propose.

For example: "This sentence is not true" cannot be
derived by applying semantic logical entailment to
basic facts. It is rejected as semantically unsound
on this basis.

Try to show any complete concrete example using
a system of basic facts and applying semantic logical
entailment where undecidability can be derived.

>>
>> The language of such a formal system is an extended form of the 
>> Montague Grammar of natural language semantics. I came up with this 
>> mostly in the last two years. I have been working on it for 22 years.
>>
>> The Montague Grammar Rudolf Carnap Meaning postulates are organized in 
>> a knowledge ontology inheritance hierarchy. https://en.wikipedia.org/ 
>> wiki/ Ontology_(information_science)
> 
> And the problem is that either your claim is wrong, or your logic system 
> is just shown to be too small to be useful for many of the things we 
> want to be able to do because it can't support the mathematics of 
> Natural Numbers.
> 

It can say anything that can be said. It is the complete set
of all general knowledge that can be expressed in language.

> You don't seem to understand that all the properties you don't like 
> about Logic Systems are all conditioned on the ability for the system to 
> have a certain level of power in their ability to do logic. 

Semantic logical entailment is rich enough to say anything
that can be said.

> "Tpy" 
> systems that have been limited below that level will not experiance the 
> problems, but also are too weak to do the problems we typically want to 
> do with logic.
> 
> This ultimate shows your fundamental misunderstanding of what you are 
> talking about, especially your inability to handle abstractions, and 
> things that can create "infinities".


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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#339824

On 5/5/25 11:31 AM, olcott wrote:
> On 5/5/2025 6:04 AM, Richard Damon wrote:
>> On 5/4/25 10:23 PM, olcott wrote:
>>> When we define formal systems as a finite list of basic facts and 
>>> allow semantic logical entailment as the only rule of inference we 
>>> have systems that can express any truth that can be expressed in 
>>> language.
>>>
>>> Also with such systems Undecidability is impossible. The only 
>>> incompleteness are things that are unknown or unknowable.
>>
>> Can such a system include the mathematics of the natural numbers?
>>
>> If so, your claim is false, as that is enough to create that 
>> undeciability.
>>
> 
> It seems to me that the inferences steps that could
> otherwise create undecidability cannot exist in the
> system that I propose.'

Only because it seems to create a trivially small system.

> 
> For example: "This sentence is not true" cannot be
> derived by applying semantic logical entailment to
> basic facts. It is rejected as semantically unsound
> on this basis.

So?

> 
> Try to show any complete concrete example using
> a system of basic facts and applying semantic logical
> entailment where undecidability can be derived.

That isn't what I said. I said that you system, to be decidable, 
couldn't include the mathematics of the Natural Numbers.

Show me how you generate those, and do not also allow for the Godel 
proof of incompleteness or undeciability.

> 
>>>
>>> The language of such a formal system is an extended form of the 
>>> Montague Grammar of natural language semantics. I came up with this 
>>> mostly in the last two years. I have been working on it for 22 years.
>>>
>>> The Montague Grammar Rudolf Carnap Meaning postulates are organized 
>>> in a knowledge ontology inheritance hierarchy. https:// 
>>> en.wikipedia.org/ wiki/ Ontology_(information_science)
>>
>> And the problem is that either your claim is wrong, or your logic 
>> system is just shown to be too small to be useful for many of the 
>> things we want to be able to do because it can't support the 
>> mathematics of Natural Numbers.
>>
> 
> It can say anything that can be said. It is the complete set
> of all general knowledge that can be expressed in language.

So, it include the statement "This statement is not true"?


> 
>> You don't seem to understand that all the properties you don't like 
>> about Logic Systems are all conditioned on the ability for the system 
>> to have a certain level of power in their ability to do logic. 
> 
> Semantic logical entailment is rich enough to say anything
> that can be said.

Really, so how do you derive mathematics from it?

> 
>> "Tpy" systems that have been limited below that level will not 
>> experiance the problems, but also are too weak to do the problems we 
>> typically want to do with logic.
>>
>> This ultimate shows your fundamental misunderstanding of what you are 
>> talking about, especially your inability to handle abstractions, and 
>> things that can create "infinities".
> 
> 

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#339825

On 5/5/2025 8:11 PM, Richard Damon wrote:
> On 5/5/25 11:31 AM, olcott wrote:
>> On 5/5/2025 6:04 AM, Richard Damon wrote:
>>> On 5/4/25 10:23 PM, olcott wrote:
>>>> When we define formal systems as a finite list of basic facts and 
>>>> allow semantic logical entailment as the only rule of inference we 
>>>> have systems that can express any truth that can be expressed in 
>>>> language.
>>>>
>>>> Also with such systems Undecidability is impossible. The only 
>>>> incompleteness are things that are unknown or unknowable.
>>>
>>> Can such a system include the mathematics of the natural numbers?
>>>
>>> If so, your claim is false, as that is enough to create that 
>>> undeciability.
>>>
>>
>> It seems to me that the inferences steps that could
>> otherwise create undecidability cannot exist in the
>> system that I propose.'
> 
> Only because it seems to create a trivially small system.
> 

When I told you that the system comprises the entire
set of all general knowledge that can be expressed in
language many many times, you must have a mental defect
to to think that this system is very small.

>>
>> For example: "This sentence is not true" cannot be
>> derived by applying semantic logical entailment to
>> basic facts. It is rejected as semantically unsound
>> on this basis.
> 
> So?
> 
>>
>> Try to show any complete concrete example using
>> a system of basic facts and applying semantic logical
>> entailment where undecidability can be derived.
> 
> That isn't what I said. I said that you system, to be decidable, 
> couldn't include the mathematics of the Natural Numbers.
> 

It does includes the mathematics of natural numbers
expressed as basic facts and truth preserving
operations applied to these basic facts.

When you start with truth and only apply truth
preserving operations you necessarily only end
up with truth. This means that you NEVER end
up with any undecidability.

The Liar Paradox: "this sentence is not true"
is rejected as untrue because it cannot be derived
by applying only truth preserving operations to
basic facts.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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#339831

On 5/5/25 10:26 PM, olcott wrote:
> On 5/5/2025 8:11 PM, Richard Damon wrote:
>> On 5/5/25 11:31 AM, olcott wrote:
>>> On 5/5/2025 6:04 AM, Richard Damon wrote:
>>>> On 5/4/25 10:23 PM, olcott wrote:
>>>>> When we define formal systems as a finite list of basic facts and 
>>>>> allow semantic logical entailment as the only rule of inference we 
>>>>> have systems that can express any truth that can be expressed in 
>>>>> language.
>>>>>
>>>>> Also with such systems Undecidability is impossible. The only 
>>>>> incompleteness are things that are unknown or unknowable.
>>>>
>>>> Can such a system include the mathematics of the natural numbers?
>>>>
>>>> If so, your claim is false, as that is enough to create that 
>>>> undeciability.
>>>>
>>>
>>> It seems to me that the inferences steps that could
>>> otherwise create undecidability cannot exist in the
>>> system that I propose.'
>>
>> Only because it seems to create a trivially small system.
>>
> 
> When I told you that the system comprises the entire
> set of all general knowledge that can be expressed in
> language many many times, you must have a mental defect
> to to think that this system is very small.

No, the problem is that you are imagining doing something you can not 
do. The problem is your logic is self-inconsistant, as you then limit it 
by only what it provable by semantic logical entailment (per your 
understanding of it) but much of knowledge is about systems that are not 
so restricted, so that knowledge can not be finitely represented in such 
a system.

How does your system have mathematics? Do you list the ENTIRE addition 
table, all Aleph0 x Aleph0 entries of it?

> 
>>>
>>> For example: "This sentence is not true" cannot be
>>> derived by applying semantic logical entailment to
>>> basic facts. It is rejected as semantically unsound
>>> on this basis.
>>
>> So?
>>
>>>
>>> Try to show any complete concrete example using
>>> a system of basic facts and applying semantic logical
>>> entailment where undecidability can be derived.
>>
>> That isn't what I said. I said that you system, to be decidable, 
>> couldn't include the mathematics of the Natural Numbers.
>>
> 
> It does includes the mathematics of natural numbers
> expressed as basic facts and truth preserving
> operations applied to these basic facts.

Then it isn't finite, as the operations of Set Theory that produce the 
Natural Numbers are not expressable by your logic system, thus you set 
of basic facts needs to be infinite in size.

> 
> When you start with truth and only apply truth
> preserving operations you necessarily only end
> up with truth. This means that you NEVER end
> up with any undecidability.

Sure you do. What non-truth perserving operation did Godel or Turing use?

> 
> The Liar Paradox: "this sentence is not true"
> is rejected as untrue because it cannot be derived
> by applying only truth preserving operations to
> basic facts.
> 

So?

Computation Theory is based on Truth Perserving operations, and there is 
no Turing Machine that can compute the Halting Property for all possible 
programs (given via a representation) does not exist, and thus the 
problem is uncomputable, and it is possible for any Formal System that 
supports the properties of the Natural Numbers to produce a Primiative 
Recursive Relationship G, such that the statement that "there does not 
exist a natural number g, such that g satisfies G", which will be true, 
but can not be proven in that system.

Your problem is you are just too ignorant of what you talk about, and 
assume (stupidly) that anything you don't understand can't be true.

Sorry, you are just proving your stupidity and ignornace, and made 
yourself into a pathological liar by not caring about the truth.

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#339826

On 5/5/2025 10:31 AM, olcott wrote:
> On 5/5/2025 6:04 AM, Richard Damon wrote:
>> On 5/4/25 10:23 PM, olcott wrote:
>>> When we define formal systems as a finite list of basic facts and 
>>> allow semantic logical entailment as the only rule of inference we 
>>> have systems that can express any truth that can be expressed in 
>>> language.
>>>
>>> Also with such systems Undecidability is impossible. The only 
>>> incompleteness are things that are unknown or unknowable.
>>
>> Can such a system include the mathematics of the natural numbers?
>>
>> If so, your claim is false, as that is enough to create that 
>> undeciability.
>>
> 
> It seems to me that the inferences steps that could
> otherwise create undecidability cannot exist in the
> system that I propose.
> 

The mathematics of natural numbers (as I have already explained)
begins with basic facts about natural numbers and only applies
truth preserving operations to these basic facts.

When we begin with truth and only apply truth preserving
operations then WE NECESSARILY MUST END UP WITH TRUTH.

When we ALWAYS end up with TRUTH then we NEVER end up with UNDECIDABILITY.

Its not that hard, iff you pay enough attention.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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#339827

[ Followup-To: set ]

In comp.theory olcott <polcott333@gmail.com> wrote:
> On 5/5/2025 10:31 AM, olcott wrote:
>> On 5/5/2025 6:04 AM, Richard Damon wrote:
>>> On 5/4/25 10:23 PM, olcott wrote:
>>>> When we define formal systems as a finite list of basic facts and 
>>>> allow semantic logical entailment as the only rule of inference we 
>>>> have systems that can express any truth that can be expressed in 
>>>> language.

Including the existence of undecidable statements.  That is a truth in
_any_ logical system bar the simplest or inconsistent ones.

>>>> Also with such systems Undecidability is impossible. The only 
>>>> incompleteness are things that are unknown or unknowable.

>>> Can such a system include the mathematics of the natural numbers?

>>> If so, your claim is false, as that is enough to create that 
>>> undeciability.

>> It seems to me that the inferences steps that could
>> otherwise create undecidability cannot exist in the
>> system that I propose.

> The mathematics of natural numbers (as I have already explained)
> begins with basic facts about natural numbers and only applies
> truth preserving operations to these basic facts.

> When we begin with truth and only apply truth preserving
> operations then WE NECESSARILY MUST END UP WITH TRUTH.

You will necessarily end up with only a subset of truth, no matter how
shouty you are in writing it.  You'll also end up with undecidability, no
matter how hard you try to pretend it isn't there.

> When we ALWAYS end up with TRUTH then we NEVER end up with UNDECIDABILITY.

Shut your eyes, and you won't see it.

> Its not that hard, iff you pay enough attention.

It's too hard for you.  As I've already suggested in another post, you'd
do better to show some respect to those who understand the matters you're
dabbling in.  Accept that your level of understanding is not particularly
high, and _learn_ from these other people.

> -- 
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

-- 
Alan Mackenzie (Nuremberg, Germany).

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