XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   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   
   >>>>>>> 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   
   >>>>>>>   
      
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