XPost: sci.math, comp.theory
From: polcott333@gmail.com
On 11/25/2025 2:56 PM, Python wrote:
> Le 25/11/2025 à 21:20, olcott a écrit :
>> On 11/25/2025 2:05 PM, dart200 wrote:
>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote:
>>>> On 2025-11-25, olcott wrote:
>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote:
>>>>>> On 2025-11-06, olcott wrote:
>>>>>>> D simulated by H cannot possibly reach its own
>>>>>>> simulated final halt state.
>>>>>>
>>>>>> It has been shown /wth code/ that D simulated by H reaches its
>>>>>> return,
>>>>>
>>>>> Liar, Liar Pants on Fire !!!
>>>>
>>>> I made the code public; another person was able to build and get the
>>>> same results.
>>>>
>>>> Yes, it's a growing conspiracy against you, like the whole thing about
>>>> the world being round.
>>>
>>> it is kinda nuts how uniformly retarded people are about this
>>>
>>
>> I am working on building a foundation that can be
>> published in a peer reviewed journal. That is only
>> possible because of the excellent feedback that I
>> have received from LLM systems. Every conversation
>> that I have with an LLM system is brand new. This
>> allows me to present my view ever more succinctly.
>>
>> It turns out that my new formal foundation for
>> correct reasoning easily utterly eliminates
>> all undecidability and undefinability and it
>> does this by simply fully integrating semantics
>> syntactically in its formal language.
>>
>> Both Montague Grammar and the CycL language
>> of the Cyc project already do this.
>>
>> Semantic logical entailment is the only inference
>> step. My system basically extends the syllogism
>> to cover the entire body of all knowledge that
>> can be expressed in language.
>
> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical
> incompleteness.
> Below is the clear, technical explanation.
>
> 1. What Gödel’s incompleteness theorems actually say
>
> Gödel’s first incompleteness theorem applies to any formal system that is:
>
> Recursively axiomatizable (axioms and inference rules can be listed by a
> program),
>
> Consistent,
>
> Sufficiently expressive to encode basic arithmetic (Robinson arithmetic
> Q or stronger).
>
> Then:
>
> There exist true statements of arithmetic that the system cannot prove.
>
> No clever notation, ontology language, or knowledge-base trick can
> bypass this, because the theorem is about computability + representation
> of arithmetic, not about the syntax of the language.
>
> Gödel’s second incompleteness theorem says that such a system cannot
> prove its own consistency (again: subject to the above conditions).
>
> These results are fully stable under changes of language, ontology,
> semantic layers, etc.
>
> 2. Does CycL avoid incompleteness?
>
> No. CycL is an ontology language used by the Cyc project to encode
> commonsense knowledge using a vast collection of predicates, rules, and
> microtheories. But:
>
> CycL is not a complete formalization of arithmetic.
> Its microtheories intentionally avoid global consistency because
> knowledge is context-dependent.
>
> Cyc as a whole is not a single coherent formal system satisfying Gödel’s
> conditions.
> It is a heterogeneous, context-indexed collection of theories, some of
> which contradict others.
>
> Because it is not a single consistent recursively axiomatizable theory,
> Gödel’s theorems don’t even apply globally—but that does not mean Cyc
> “defeats incompleteness”; it just lives outside the scope of the theorem.
>
> Cyc’s strategy is not “beat incompleteness”; it is “use many partial
> microtheories and logical levels contextually”.
>
> This is like saying a library containing many inconsistent books
> “defeats incompleteness” — it does not; it simply is not a single
formal
> theory.
>
> Conclusion:
> CycL cannot be used to derive Peano arithmetic in a way that would make
> it complete, and Cyc does not claim otherwise.
>
> 3. Do Peter Olcott’s claims refute incompleteness?
>
> No. Peter Olcott is known online for repeatedly claiming to have
> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s
halting
> problem.
> His claims are universally rejected by logicians because they
> misunderstand the formal structure of the theorems.
>
> In all variants of his claims:
>
> He proposes procedures that assume access to semantic truth, something
> incompleteness forbids a formal system from capturing internally.
>
> Or he proposes recognition algorithms that fail on classic diagonal/
> self-reference constructions but does not notice the failure.
>
> Or he builds systems that are not recursively axiomatizable, and
> therefore Gödel’s theorem does not apply — but then he claims
“defeat”
> rather than “dodging the premises”.
>
> The pattern is always:
>
> Change the problem or the assumptions → claim the original theorem is
> wrong.
>
> This is equivalent to saying “I solved the halting problem… for programs
> that I forbid from diagonalizing.”
> That is not a refutation.
>
> 4. Why these approaches cannot refute incompleteness
>
> Gödel incompleteness is a meta-theorem.
> Any attempt to build a complete system for arithmetic must fail because:
>
> If the system is algorithmic, there’s a diagonal sentence G such that
>
> If the system is consistent: it cannot prove G.
>
That is true.
With my system there is one single all encompassing
formal system that contains every element of general
knowledge that can be expressed in language.
Because the formal language has all semantics fully
integrated into its syntax True(x) is exactly the
same thing as Provable(x). If you can't prove it
then it is not an element of the body of knowledge
that can be expressed in language.
--
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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