XPost: sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 11/25/2025 6:29 PM, dart200 wrote:   
   > 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   
      
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