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

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".