XPost: sci.math, comp.theory
From: polcott333@gmail.com
On 11/25/2025 5:25 PM, Python wrote:
> Le 26/11/2025 à 00:21, olcott a écrit :
>> On 11/25/2025 5:14 PM, Python wrote:
>>> Le 25/11/2025 à 22:27, olcott a écrit :
>>>> On 11/25/2025 3:12 PM, Python wrote:
>>>>> Le 25/11/2025 à 22:09, olcott a écrit :
>>>>>> On 11/25/2025 3:03 PM, Python wrote:
>>>>>>> Le 25/11/2025 à 22:01, olcott a écrit :
>>>>>>>> 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
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