Any foundational theory has ontoaxiomatic consequences

## Any foundational theory has ontoaxiomatic consequences (even if you are Sabine Hossenfelder)

Any foundational theory has ontoaxiomatic consequences (even if you are Sabine Hossenfelder)

Any foundational theory (not a simplification, for example Newtonism) has unseen consequences (impact) on the foundations of its particular substantiality (for example the physical world is a substantial system).

the foundations of a particular substantiality = an ontological substantiality (ontological vs scientific; science tries to reach the ontological truth)

A particular foundational substantiality is the foundations of quantum mechanics (see also: topological quantum field theory).

If you don't care about ontoaxiomatics = the axiomatic foundations of substantial systems, like the universe; like the foundations of quantum mechanics; that doesn't mean that ontoaxiomatics doesn't exist.

ANY, I repeat, ANY foundational theory has an impact on the axiomatic system it belongs, even if the theorist who postulates it doesn't understand the criteria of ontological axiomatics.

All axiomatic systems face limitations (problems of axiomaticity/the foundational problems of axiomatic systems): incalculability, incompleteness, inconsistency.

The common mathematics doesn't have an axiomatics originated from the same rigorous causality (some axioms do, but not all). Different mathematics = allomathematics are mathematics originated from a different list or algorithm of axioms. Common mathematics were initially created to be useful for calculations, but allomathematics can be created for other purposes or just for fun (but they should be rigorous, otherwise the resulting axiomatic system is neither mathematical nor allomathematical).

The physical world is based on some particular allomathematics (infinite allomathematics are possible). The physical world doesn't have to be easy, hard or so-and-so difficult for us to understand.
The physical world has to meet the criteria of substantiality (substantiality is hypernymic to physics; here we focus on ontophysics because science tries to reach ontophysics = scientophysics tries to reach ontophysics [to be more detailed, correct, better describe the natural world and have more coherent foundations]).

Why the universe is allomathematical and not based on common mathematics?

Allomathematics IS mathematical. It is logically rigorous. It's simply based on different axioms or axiomatic algorithm.

The universe is allomathematical because the common mathematics don't have an axiomatics that meets the criteria of substantiality: self-causation, totally common origin, ontological Turing machine [subcategory of the Turing machine] which is its own axiomatics, software and hardware all made of the same nature/program; but causal closure is wrong, because causal closure [if we analytically describe the phenomena and we don't simplify them as when we present supposedly ideal closed systems] is impossible in nature (it doesn't meet the prerequisites for substantiality = ontoaxiomatics), because an open-connectome of proceduralities (see: David Tong on Quanta Magazine, see: quantum field theory [the deeper we look, the more there is; quantum field theory is very close to the ontoaxiomatics of our universe]). An Everettian constructor (combination of many-worlds interpretation and constructor theory) is required even in the ontoaxiomatics of our universe = the foundations of quantum mechanics (otherwise we don't understand what foundational theory is, and we don't understand what the axiomatical prerequisites are, and what ontoaxiomatics is [all these are the same for our universe; ontoaxiomatics can be used hypernymously for different substantialities other than our universe]).

(Even the common mathematics is an allomathematics. Different civilizations might have slightly different axioms, or metaaxioms = axioms created by thinkers because previous axioms expose a lack of axioms.)

Why having the exact allomathematics matters?
When you have the exact allomathematics of the universe, you can describe its foundations as a whole (but David Deutsch and others have a different view; maybe there isn't a sole common physical foundations, but the physical foundations might be a puzzle of constructors with causopermeability = causal permeability amongst them. But at least, that causopermeability gives a common ground, and the overall fundamentally open foundations of quantum mechanics can be better presented. Fundamentally open foundations = Everettian constructor or Everettian causopermeable constructors, means that the true physics = ontophysics (not simply modern science = scientophysics) is truly open, but physicists shouldn't be sad, because axiomatically afar = fundamentally deeper constructors affect lesser and lesser the standard model of particle physics. Thus physics is infinite, but manageable with perturbation theory and other techniques; and there are many close foundations of quantum mechanics we'll be able to describe.

The exact allomathematics of our universe theoretically can describe it as an open whole = open infinite connectome, and our common mathematics (MIT and many other universities experiment with mathematics based on different axiomatics = allomathematics) but we don't have infinite paper to write all its foundations; but we can describe its closest foundations (some thinkers disagree and claim that the universe isn't based on a single allomathematics; but on many different Deutschian constructors; but the different allomathematics are compatible even in that case within the same universe due to direct causality and causopermeability between different physical processes/procedures/proceduralities).

With our common mathematics we still can describe the universe (we don't have infinite data storage, ontophysics is fundamentally open due to the prerequisites for substantiality, but physics can always improve) but in a more fragmented manner. The exact allomathematics would give a more coherent physics; our common mathematics still can give a very good physics but NOT all axiomatic systems are mutually compatible, and some are partially compatible. Thus because common mathematics is logically rigorous, still we can describe every part of the foundations of physics, but not necessarily in an efficient way; which is maximally important, because if the common mathematics requires enormous formulas and the allomathematics slightly smaller formulas to describe the exact same phenomena, then probabilistically it is less likely we'll be able to improve physics at a fast pace (finding the exact allomathematics might be impossible, because the allomathematics of the ontophysics of our universe is one and the same [we don't fully know that axiomatic system; and it's fundamentally open but accessible]; but at least we should try different allomathematics to describe physics and then transcribe allomathematics into common mathematics (even new symbols and operations should be created for some extreme allomathematics; of course at the end we'll transcribe any useful formulas into common mathematics; allomathematics is by no means useless because different axiomatics [axiomatic lists or axiomatic algorithms not based on lists and mixed axiomatics] are faster (and slower) on solving different problems (this is maximally important in computer science; different allomathematics are faster on calculating different problems).

Imagine you want to keep science nice and clean, and you simply describe the phenomena in the most succinct manner rejecting hidden universes, hidden variables, hidden physical metaaxiomatics (foundational laws resulting from foundational laws). You cannot. ANY, I repeat, ANY foundational theory (of some substantiality = a universe-like axiomatic system = ontophysics = the ideal physics and not the scientophysics of modern science) has an impact on the axiomatic system it belongs, even if the theorist who postulates it doesn't understand the criteria of ontological axiomatics (common mathematics initially was created for practical calculations and not for meeting the criteria of substantiality: self-causation, axiomatic workarounds like the uncertainty principle and the ontological enlargement of the universe which is a form of ontological entropy, ontological Turing machine, etc.).