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

On 6/30/2026 9:47 PM, Ross Finlayson wrote:
> On 06/30/2026 10:36 AM, Ross Finlayson wrote:
>> On 06/30/2026 07:53 AM, olcott wrote:
>>> 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".
>>>>
>>>>
>>>
>>>
>>>
>>>
>>
>> "Curry's poor substitute" at least rejects material implication.
>>
>> Matters of meaning or the epistemological is a field called "semiotics".
>> Semantics after syntax is properly logical, that's all.
>>
>>
>>
>>
>>
>>
>> Cycle-detection is a usual routine involving memory and time, the
>> resources.
>>
>>
>>
>>
>> The Liar Paradox is just a template of what would be a fallacy:
>> two wrongs don't make a right.
>>
>> unify_with_occurs_check(and(false(LP), true(LP)))
>>
>> Two wrongs don't make a right.
>>
>>
>>
>> Russell's retro-thesis is hypocrisy veiled as authority.
>>
>>
>> Where's the GUID for "dictionary", or "vocabulary", and what's in it.
>> "Cat" is a word.
>>
> 
> It's fair to say "the Liar Paradox is false",
> then that the negation translates through the copula "is"
> to result "this sentence is true", a meaningless, empty tautology
> (except as quoted a meaningless, empty, tautology).
> 
> It doesn't work on other "paradoxes", though.
> 

Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system

Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.

> 
> Finlayson's paradox: there are none.
> 


-- 
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).