Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs

On 6/30/2026 8:23 AM, Ross Finlayson wrote:
> So, if you want to know more about my theory, which is an account
> of reason, and for Foundations, then I'd suggest first making for
> yourself a "universal education", then finding resolutions to the
> "paradoxes" of mathematical logic, 

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔               01 02
01 G
02 ¬               03
03 Prov_PA         04
04 Gödel_Number_of 01  // cycle indicates no well-founded justification 
tree exists.

ZFC already handled Russell's Paradox converting set
theory into Naive set theory.

It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.

Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

> then revealing the "super-classical"
> results of classical mathematics, then for the "extra-ordinary" the
> "great atlas of mathematical independence", then for "higher
> mathematics", and quite about "continuity" and "infinity",
> then there's also "the physics" after "the logic" and "the mathematics".
> 
> 




-- 
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).