XPost: comp.theory, sci.math, sci.lang
From: polcott333@gmail.com
On 11/29/2025 5:55 AM, Alan Mackenzie wrote:
> [ Followup-To: set ]
>
> In comp.theory olcott wrote:
>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>
>>> In comp.theory olcott wrote:
>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>> dart200 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.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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