Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > sci.logic > #341881

individuals = Ur-Elements, usually not part of ZFC (Was: Use ChatGPT for digging around in the wikidata [Pragmatic KG realism ])

Cross-posted to 3 groups.

Show all headers | View raw

Hi,

I was not pointing at class / set distinction.
Lets lump sum class and set into pne thing,
distinct from the inviduals, which usual don't

exist in ZFC. To have individuals lets say
we have ur-elements. So its ZFCU. So what
does the ABox talk about? What does the TBox

talk about. And how do they talk?

Bye

P.S.: One definition is that the ABox talks
about "concrete entities".

Ross Finlayson schrieb:
> On 11/08/2025 09:42 AM, Ross Finlayson wrote:
>>> Mild Shock schrieb:
>>
>>>> Its mainly a probem of what quantifiers are allowed.
>>>> Do you only allow quantifying over individuals, or
>>>> also over classes?
>>>>
>>
>> Class/set distinction is a usual thing, like for example
>> in Russell's Principia Mathematica or in Metamath, and
>> often it's readily demonstrable inconsistencies thusly,
>> then whether those are simply examples or blind edicts,
>> has that classes and sets can't really be different
>> when one is just "elt" and the other "members",
>> in a theory of one relation that's a set theory.
>>
>> It's a usual idea to start with an object that's
>> both bottom and top, and fill in the middle,
>> instead of presuming to add the top.
>>
>>
>> Then there are ideas like deconstructive accounts of
>> arithmetic, so that increment and ... and division and ...
>> are two separate options, sort of _not_ Presburger arithmetic
>> after Peano arithmetic, making for a sort of "long subtraction",
>> say, it's a usual sort of account since the Middle Egyptians
>> built arithmetic about division (thirds usually) while the
>> Greeks had their "magnitudes", yet the tools the constructions
>> make for both doubling and halving as primary.
>>
>>
>> It's a usual idea to suggest that the nested intervals
>> argument for uncountability doesn't apply to the rationals
>> since they don't have the least-upper-bound property and
>> though they're infinitely divisible that though the
>> antidiagonal argument can make for a rational antidiagonal
>> that they're countable.
>>
>> Then, it's sort of at issue that one might look into
>> the "quasicontinuous" or other ideas about Dana Scott and
>> Jimmie Lawson more about box and circle modalities
>> that timidly sort of Bishop and Cheng and partially-ordered-ring
>> with rather-restricted-transfer-principle yet Jordan measure
>> and here "sweep", or, like "rationals are HUGE" off the
>> old "FOM" list, this kind of thing, about the three continuous
>> domains the line-reals field-reals signal-reals bit.
>>
>> Then, where class/set distinction is a usual thing and like
>> Russell says "it's much easier to write set-theoretic results
>> in terms of classes instead of sets" then that these days the
>> things like the Lean have "auto" and this kind of thing,
>> makes for readily demonstrable inconsistencies. Then Russell's
>> "isolation" and "significance" that are sort of his bane since
>> he's basically axiomatized himself right, so comes off as a
>> very-much hypocritical flake, while at least a formalist a
>> few days a week, anyways set-theory is just a theory-of-one-relation,
>> in set theory's case "elt", there are others, like part theory
>> and particularly ordering theory, since ordinals and cardinals
>> aren't the same thing.
>>
>> They're each things - just not the same thing, numbering and counting.
>>
>>
> 
> It's like defining "Falting purity",
> Scholze defines it "Scholze is clean" while
> Falting defines it "Scholze is dirty".
> 
> (And Friedman's like "the rationals are still HUGE".)
> 
> Before getting into the rigamarole of Large Cardinals,
> which are neither sets nor cardinals in set theory,
> one needs address Russell's retro-thesis or the great
> idea of a ruliality of course, a regularity or Well-Foundedness,
> that at least Zermelo and Fraenkel also have Well-Ordering,
> then when Voevodsky for the illative/univalent/Martin's Axiom
> have a Well-Dispersion, Russell for being right is at least
> twice wrong. "ZFC plus two Large Cardinal Axioms, one
> for the illative and the other saying it's all not wrong."
> 
> Since, looking at von Neumann ordinals as containing their
> lessers yet not themselves, the set of those would be
> the Russell paradox, that Russell made fiat into existence
> while having sub-marined Frege's otherwise what it is, then
> that Russell basically cadged Frege and also Peirce, while
> Whitehead is just a plain fictionalist, has that Zorn or Ono
> and also Martin each their axioms as they may be bring all
> their distinctness results now instead of uniqueness results.
> 
> 
> If you look at my video essays like "paradox-free reason"
> and "rulial foundations" after "Foundations briefly" it
> may help understand why inductive ignorance isn't so
> invincible after all.
> 
> "Not ultimately untrue", say. Making for a bit of quantifier
> disambiguation or what Feferman said, or box and circle like
> Scott, the Berkeley-school tease about that Tarski's quite broken,
> with Goedel starting "model-relativist monotonic entailment
> sure ain't complete".
> 
> 
> It's a continuum mechanics, ....
> 
> 

Back to sci.logic | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

Re: Use ChatGPT for digging around in the wikidata [Pragmatic KG realism ] (Re: From Biota to Bluewhale: No TBox and ABox Discipline?) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-08 09:42 -0800
  Re: Use ChatGPT for digging around in the wikidata [Pragmatic KG realism ] (Re: From Biota to Bluewhale: No TBox and ABox Discipline?) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-08 10:01 -0800
    individuals = Ur-Elements, usually not part of ZFC (Was: Use ChatGPT for digging around in the wikidata [Pragmatic KG realism ]) Mild Shock <janburse@fastmail.fm> - 2025-11-08 20:13 +0100
      Re: individuals = Ur-Elements, usually not part of ZFC (Was: Use ChatGPT for digging around in the wikidata [Pragmatic KG realism ]) Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-11-08 12:00 -0800
        i = Individuals , o = Proposition, see Alonzo Church (Was: individuals = Ur-Elements, usually not part of ZFC) Mild Shock <janburse@fastmail.fm> - 2025-11-08 21:23 +0100

csiph-web