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

On 06/30/2026 08:01 PM, olcott wrote:
> 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.
>>
>
>

That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of
sufficient reason" about what an inference is. The Tractatus
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.

A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.

Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".


Old schlock wrapped as new, ....