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  • Proof Theoretic Semantics as a new Foundation for Mathematics, Logicand the Theory of Computation

    From olcott@polcott333@gmail.com to sci.logic,comp.theory,sci.math,sci.math.symbolic,comp.ai.philosophy on Thu Jun 25 09:47:34 2026
    From Newsgroup: comp.ai.philosophy

    https://philpapers.org/archive/OLCPTS-2.pdf
    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).

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  • From Mikko@mikko.levanto@iki.fi to sci.logic,comp.theory,sci.math,sci.math.symbolic,comp.ai.philosophy on Fri Jun 26 09:10:03 2026
    From Newsgroup: comp.ai.philosophy

    On 25/06/2026 17:47, olcott wrote:

    https://philpapers.org/archive/OLCPTS-2.pdf

    Essentially the article claims that Gödel's incompleteness resutls
    are correct and that the significancs of proof theoretic semantivs
    is mainly philosophical and not mathematical.

    The article also presents an attempt to solve the halting problem
    and a construction of an intput that the decider cannot decide
    correctly but fails to present any conclusion.
    --
    Mikko
    --- Synchronet 3.22a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to sci.logic,sci.math,comp.theory,comp.ai.philosophy on Fri Jun 26 07:56:32 2026
    From Newsgroup: comp.ai.philosophy

    On 6/26/2026 1:10 AM, Mikko wrote:
    On 25/06/2026 17:47, olcott wrote:

    https://philpapers.org/archive/OLCPTS-2.pdf

    Essentially the article claims that Gödel's incompleteness resutls
    are correct and that the significancs of proof theoretic semantivs
    is mainly philosophical and not mathematical.

    The article also presents an attempt to solve the halting problem
    and a construction of an intput that the decider cannot decide
    correctly but fails to present any conclusion.


    It is a verified matter of fact that within proof
    theoretic semantics undecidability derived from
    pathological self-reference (PSR) ceases to exist.
    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).
    --- Synchronet 3.22a-Linux NewsLink 1.2