From Newsgroup: comp.theory
On 9/12/2026 4:56 PM, dart200 wrote:
On 9/12/26 2:40 PM, olcott wrote:
Nick:
Now that you have had a long time to discuss this
much of that paper is fairly novel, especially including the refutation
to the church-turing thesis. i have not discussed that in particular
with anyone thus far, and only realized in the last month
what is the simplest essence of your whole claim?
https://zenodo.org/records/22715824
there are a variety of understandings and claims conveyed in that paper
and they build on each other in manner i cannot just reduce to a single sentence
which part would you like to discuss?
I had NotebookLM sum it up for me. It seems to be
the best at analyzing papers because it forces
grounding in the paper overruling its own training.
This paper by Nicholas K. Swenson argues that undecidability in
computing is not a series of distinct problems, but a single
self-referential set-classification paradox rooted in the Turing machine
model itself. The author critiques contemporary claims by Hamkins and
Nenu, asserting that TuringrCOs original circle-free problem is
fundamentally identical to the halting problem because both involve
machines that contradict their own classifications. By introducing a
terminal machine that incorporates an idealized human agent, Swenson
suggests that deterministic logic can resolve these paradoxes through
semantic analysis and reduction. This interaction demonstrates that
certain sequences, like the total anti-diagonal, can be computed by an
agent even if they remain addressable impossibilities for standard
machines. Ultimately, the source seeks to refute the Church-Turing
thesis by proposing that human-led mechanical processes possess a computational power that transcends the inherent limitations of the
Turing model.
--
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 general 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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