• New formal foundation for correct reasoning makes True(X) computable

    From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Tue Nov 25 14:20:48 2025
    From Newsgroup: comp.ai.philosophy

    On 11/25/2025 2:05 PM, dart200 wrote:
    On 11/25/25 10:46 AM, Kaz Kylheku wrote:
    On 2025-11-25, olcott <polcott333@gmail.com> wrote:
    On 11/25/2025 11:42 AM, Kaz Kylheku wrote:
    On 2025-11-06, olcott <polcott333@gmail.com> 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.
    --
    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.
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Python@python@cccp.invalid to comp.theory,sci.logic,sci.math,comp.ai.philosophy,sci.math on Tue Nov 25 20:56:05 2025
    From Newsgroup: comp.ai.philosophy

    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 <polcott333@gmail.com> wrote:
    On 11/25/2025 11:42 AM, Kaz Kylheku wrote:
    On 2025-11-06, olcott <polcott333@gmail.com> 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.

    If it proves G: it becomes inconsistent.

    If you try to use “semantics” or “truth”:
    Tarski’s theorem says arithmetical truth is not definable inside
    arithmetic itself.

    If you use a non-recursively-axiomatizable system:
    Gödel’s theorem no longer applies, but such a system cannot be
    implemented as a fully formal algorithmic reasoning machine.

    Cyc, Olcott, or any other system inevitably satisfies one of these escape conditions, but none actually produces a complete and consistent theory
    strong enough to capture arithmetic.

    5. The deep point:
    ➤ To refute incompleteness, one must produce a complete, consistent, computable theory of arithmetic.

    Nobody has ever achieved this, and it is mathematically impossible.

    Cyc is not a single consistent computable theory.

    Olcott’s systems are not both computable and consistent when applied to arithmetic.

    Changing the syntax does nothing: incompleteness is syntax-agnostic.

    6. Final conclusion

    The existence of CycL and the claims Peter Olcott makes do NOT refute
    logical incompleteness.

    CycL sidesteps the theorem by not being a single formal theory, not by defeating it.

    Olcott misunderstands the premises of incompleteness and his proposals
    either fall outside Gödel’s scope or break on diagonalization.

    Gödel remains intact.


    --- Synchronet 3.21a-Linux NewsLink 1.2