From Newsgroup: comp.theory
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).
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