Re: DAG of all general knowledge that can be expressed in Language

On 7/1/2026 12:31 PM, Ross Finlayson wrote:
> On 07/01/2026 10:57 AM, olcott wrote:
>> On 7/1/2026 12:00 PM, Ross Finlayson wrote:
>>> 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,
>>
>> The entire body of knowledge expressed in language
>> (a) Encodes all of the empirical "atomic facts" as axioms
>> this merges the analytic/synthetic distinction into one
>> analytic system. https://plato.stanford.edu/entries/analytic-synthetic/
>>
>> (b) Provide a finite list of the possible semantic relations
>> between/among the elements of (a) and these are specified
>> syntactically using a system similar to CycL.
>> https://en.wikipedia.org/wiki/CycL
>>
>> (c) This whole thing is stored in a knowledge ontology
>> https://en.wikipedia.org/wiki/Ontology_(information_science)
>> Hierarchy of simple type theory.
>> https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
>>
>> Now we have the entire body of general knowledge that
>> can be expressed in language as a set of stipulated
>> semantic relations between finite strings.
>>
>>> 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.
>>>
>>>
>>>
>>
>>
> 
> That's not "a priori truth".
> 
> That's just a "convenient" lie to make some system of inference
> considered itself compelled complete yet make it slavish while
> really it's merely a model of a partial half-account of reason,
> that fragmented synthetic pluralism and inconstancy in definition.
> 
> 
> Adding an element to another element is synthetic
> (where did it come from?), partitioning an element
> into two is analytic (how was it already there?).
> 
> 
> The usual account of mathematical platonism is analytic,
> the usual account of logicist positivism is synthetic,
> they are two different things.
> 
> 
> Usual accounts of incompleteness like the Hilbert-Bernays paradox
> confirm and certify that "logicist positivist nominalist theories"
> are at best "merely and completely science".
> 
> Then, the account that it's not a science, is wrong.
> 
> Anybody can have a quite thorough body of knowledge -
> if it doesn't change it's considered they stopped learning,
> not that there isn't anything left to learn.
> 
> Quit trying to tell people they can't learn, it's insulting.
> 
> 

Well, we have to remember that Olcott has claimed to be god.