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

On 07/01/2026 07:59 AM, olcott wrote:
> On 7/1/2026 7:13 AM, Ross Finlayson wrote:
>> 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
>
> Correct reasoning is not correctly evaluated on the
> basis of who came up with the ideas. These ideas either
> has a sound basis or not.
>
> It just the same thing that I have been saying fir years.
> True on the basis of meaning expressed in language must
> have a direct semantic connection to those things in the
> directly in the formal system of this language that make it
> true.
>
> (a) Cats are animals
> (b) Animals are living things
> (c) ∴ Cats are living things
>
> No jumping outside of the language to a separate model.
>
>> 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.
>>
>
> That is what I just showed.
>
>> 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, ....
>>
>
> The only way to obtain a correct foundation of these
> things is to reverse-engineer them from first principles.
>
> If one does not do that then the extraneous baggage
> of the differing human perspectives prevent a fully
> coherent view.
>
>

That's just syllogism, and makes for constructivism
since any sort stipulation, like an axiom, is unfounded.

The "axiomless natural deduction" to arrive at "axiomless
geometry" and "axiomless arithmetic" is a usual notion that
mathematical platonists have, though these days sometimes
they call themselves structural realists to not concern
dear old Bertrand, then though logicist positivists take
that label without fulfilling its definition.


Syllogism is subject ordering, and Aristotle reads every
syllogism its statements in every order, for example to
detect cycles and disambiguate them, which otherwise a
linear reader will fail to detect.


The "principle of _thorough_ reason" is more than the
"principle of 'sufficient' reason", then that in a
wider account of a wider, fuller dialectic, what's
sound, thorough, fulfilling, and fair.


Mentioning something like Prawitz' "inversion principle"
and about both the restriction _and_ the recovery, and
more than Russell's mere "isolation in significance and
significance in isolation", means that restricting (ignoring)
the resolution of any and all paradoxes leaves the door ajar
just like quasi-modal logic and principle of explosion.


So, maybe readers and researchers in foundations should start
with outlining the requirements and desiderata of a theory
that's constant, consistent, complete, and concrete,
and see how axiomless natural deduction fulfills that
with a comprehensive yet paradox-free account, and
that's the usual account since antiquity and even since
before recorded times, then it's called "mathematical platonism",
since issues of the human condition itself are subjective,
and whether Thoth or Hermes Trismagistus has an ankh for reason
or spiral for infinity, in at least one account there's both.

Thoth -> thought
Logos -> logic
Ma'at -> math


Aristotle won't be made a fool, and more than merely
half-Aristotleans have always both prior and posterior accounts.