Re: Theatheory (not Re: Olcott's system (not Hobbes))

On 07/16/2026 02:00 PM, Ross Finlayson wrote:
> On 07/16/2026 08:25 AM, Ross Finlayson wrote:
>> On 07/16/2026 08:08 AM, Ross Finlayson wrote:
>>> On 07/16/2026 12:42 AM, Mikko wrote:
>>>
>>>> Foundations are simple:
>>>>  From nothing you can construct the empty set, which is the prototype
>>>> of the natural number zero. For every other natural number you can
>>>> construct the prototype from the prototype of the prvious one as the
>>>> union of the prefious prototype and the singlet set containing the
>>>> previous set. There are well known (and other) ways to construct the
>>>> integers from then natual numbers, the rational numbers from the
>>>> integers, and the real numbers from rationals. From reals one can
>>>> construct the unverse and all its contents and their behaviours.
>>>>
>>>
>>>
>>> "Nothing" and "the empty set" aren't necessarily the same,
>>> while it may be agreeable that "the fundamental question of
>>> meta-physics" is "why is there something rather than nothing".
>>>
>>>
>>> The usual notions of "empty set" and "inductive set" are
>>> given as introducing constants into the language of ZF set theory,
>>> yet, besides that expansion-of-comprehension, then ZF's are also
>>> restriction-of-comprehension, "ordinary empty set" and "ordinary
>>> inductive set", when for example the empty set and the inductive
>>> set aren't unique, and there are "extra-ordinary" empty and
>>> inductive sets, that quantification over elements finds.
>>>
>>>
>>> Then, the "Void" and "Universe" are "complementary duals",
>>> reflecting on philosophy's usual account of "Nothing" and
>>> "Being" as the considerations of those.
>>>
>>>
>>> Foundations _are_ simple: in fact so simple that then how
>>> they arrive and making for the approfondissement of the
>>> objects of logic and mathematics, involves super-classical
>>> reasoning quite directly then making for paradox-free reason
>>> of the completeness in repleteness of infinity and continuity.
>>>
>>>
>>> "A-Theory" it's called here, "theatheory", a "Null Axiom Theory".
>>>
>>>
>>
>> "Being" and "Nothing", or "Sein" and "Nichtes",
>> these are the usual premier concepts in philosophy,
>> since the ancient Greeks with "Being: no Nothing",
>> then Hegel with "Nothing and Being", that then the
>> 20'th century arrived at "existentialism and nihilism",
>> when they are flip sides of a coin each other themselves.
>>
>>
>> It's called canon, we already have one.
>>
>>
>
> Researchers in Foundations since forever usually at least
> once arrive at Mathematical Platonism that the universe of
> mathematical objects with infinity and continuity exists
> and that this brings along logic also, thus resulting for
> a sort of "axiomless geometry" and "axiomless arithmetic"
> to subsume and be sublime to "Archimedean arithmetic"
> and "Euclidean geometry", then for algebra and DesCartes,
> the arithmetic and geometry and algebra and analysis.
>
>
> This is among reasons why "old wrapped as new" gets old.
>
> This is the plain old plain old,
> "Hilbert's Infinite, Living, Working Museum of Mathematics",
> now with "the Great Atlas of Mathematical Independence"
> in "paradox-free reason".
>
>
>
> This sort of holistic dual monism is considered a more thorough
> and mature account opposed to the fragmented synthetic pluralism
> of the nominalist fictionalist variety for a mathematics replete
> with infinity and continuity.
>
>
> For example, bringing Pythagoreanism and Cantorianism back
> together again, the Atlas makes bridges (ponts, analytical
> bridges) for this.
>
> Otherwise those competing claims of opposing views only see
> each other as "Giant Monsters of Mathematical Independence".
>
>
> That there's a universe at all implies that they're wrong,
> or, generously, "incomplete".
>
>
>
>

In theatheory there are a number of claims made.

It's its own meta-theory, it's true, it's complete,
it's consistent, it's constant consistent complete
and concrete, it's got de res de racio de natura de re,
it makes axiomless logic, mathematics, and perhaps physics,
it's real, it's dually-self-infraconsistent while paradox-free
and extra-ordinary, it's common-sensical, these kinds of things.

It interprets proof and model theory, with logic and mathematics,
these kinds of things.


It's canonical, ....