XPost: sci.math, comp.theory
From: user7160@newsgrouper.org.invalid
On 11/25/25 1:03 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
>>> 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.
>
> The idea of a single, all-encompassing formal system in which every
> meaningful statement is expressible and in which True(x) ≡ Provable(x)
> is internally inconsistent, because as soon as the language is
> expressive enough to contain elementary arithmetic—inevitably required
> if it is to “contain every element of general knowledge expressible in
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