Είναι αποδείξιμη η ανυπαρξία της πανοντοαξιωματικότητας; / Is the inexistence of omniontoaxiomatics provable?

## Is it provable that there is no omniontoaxiomatics?

David Deutsch’s constructor theory is an ontoaxiomatic theory mechanism (probably infinite ontoaxiomatics exist not included in David Deutsch’s approach).

But it is probably wrong to claim that "we cannot prove that omniontoaxiomatics" is impossible.
(It's hard [it might be impossible] to have final ontoaxiomatic theories, but we can have applied mathematical proof-like interpretations; which are rigorous enough even though not purely rigorous.)

First of all we have to prove that at least two axiomatic systems are different/nonidentical (here not ontological axiomatic systems) (that isn't immediately relevant, but it is useful as mathematical techniques).

Then we have to at least define two ontoaxiomatic systems. Quantum mechanics is an ontological axiomatics (due to causopermeability [causal permeability] the future ideal quantum mechanics is identical to its axiomatics/axiomatic algorithm). There is no future ideal quantum mechanics according to the incompleteness of axiomatics, only better versions of it; but we can understand the basic mechanism of our local universe.

Proving (at least via applied mathematics) that the omniontoaxiomatics doesn't exist doesn't require infinite proofs.
We'll have to have two ontoaxiomatic theories which are incompatible; non describable under the same substantiality without extras. If we create a list of ontoaxiomatic systems we may claim that these systems are a coherent whole "with some extra mathematical operations not included in their main ontoaxiomatics". But that part: "extra mathematical operations" would cause weakness in the self-causality criterion of their substantiality. Any substantial world [ontological Turing machine] would have to be its own software and hardware, and adding "extras" to an ontoaxiomatics would decrease or cancel its self-causality potential. We cannot speak in general. Each specific claim has to be calculated separately.

Proving that some mathematical objects are mutually incompatible isn't an impossible neither an unsurmountable task. Also not all the reasons of mutual exclusion have to be proven. One will suffice; but because modern approaches are based on applied mathematics whose axiomatic foundations are hazy [due to allomathematical approaches = mathematics with different axiomatics; the stronger axiom wins the argument; this sounds like filthy mathematics/nonrigorous mathematics, but some extremely difficult problems can only be approached via applied mathematics, at least at the first stage] (see: 2021 Quanta Magazine summary on mathematics; specifically: 2021's Biggest Breakthroughs in Math and Computer Science - Quanta Magazine - YouTube). If we use semi-rigorous approaches (in some cases we can only approach a problem with many different techniques, but it's extremely hard [but not impossible] to causally connect them) then a single proof of mutual exclusion won't cut it/won't suffice; we might need 30 proofs to boost our case (if all support the same claim its a victory; if some opposing proofs occur, the axiomatically fundamental prevails [that sound bad, but it's not rare in applied mathematics]). This sounds non-ideal, but we can do something on proving that the omniontoaxiomatics doesn't exist; we can makes steps towards the proof.

According to my view, it is provable (in a rigorous manner) that the omniontoaxiomatics (= the common foundational theory of all the mathematically possible universe-like worlds) doesn't exist (most possible worlds are mutually exclusive/of incompatible substantialities/non-parallelizable universes).

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If your goal is to prove that there is no omniontoaxiomatics, you will compare two universe-like ontophysics that give you the hint they are mutually exclusive in the first place. You wouldn't waste huge resources on comparing two mathematically kindred universes which probably belong in the same multiverse and can be interpreted as components of a common wider substantiality.

## comment 1:

single final theory = omniontoaxiomatics = means identical/tautological And you are correct. Your points are correct. I don't reject your general points (I am a different person thus I express things differently). Mathematically it is incalculable to discover the infinite possible different final theories (which is NOT one single theory) of alternative physics.

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My longer texts might be boring, but I expose some of these issues. Humanity has to evolve these ideas. There is a view that there is no pure causal stratification, but causopermeability (Leonard Susskind correctly claims that we humans stratify the phenomena, but nature is a causal connectome). According to the infinite causal layering (Russian doll wavefunctional hypernymization) hypothesis, we aren't able to causally interact outside our Hubble volume (subluminally expanding sphere of causality; outside it the universe expands superluminally), but Hubble volumes are overlapping ad infinitum, but introduce Everettian alternatives (because outside our Hubble volume we cannot ever lock the exact same outcomes in an exact same substantiality, and more Everettian alternatives emerge, the more Hubble volumes a compared region is afar from Earth. Due to the overlapping nature of Hubble volumes, the overall universe (which is an erroneous term, because infinity is a process; not a narrow spatiotemporal unity) is a range of interlinked substantialities, but not a single substantiality. There cannot be a single final theory of the single substantiality if nonparallelisable universes exist (that is the case according to my view).

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If we ask the wrong questions we'll be trapped. It is more important to evolve one's questions, than to evolve one's answers, because humanity has many thinkers, and when one fails to perform, others complete the task. If you ask a biased question which imprisons you, you will never find the answer. final rigorous axiomatic theory = the erroneous claim that: 1. the infinite nature of substantiality is not infinite but finite in its ontological description (according to some views we might have an infinite universe with finite foundations, but according to the causopermeability view, the ontology of the universe is identical to its quantum foundations and identical to the ever expanding ingredients of the universe, which like the number π, cannot be written down in a finite data medium. The number π can be mathematical described in a finite way. We don't know if "the final theory of our specific universe" which isn't identical to the Everything, is like π which is describable in some forms in a finite way. That remains an open question.), 2. that mutually exclusive universes coexist in an erroneous omnimetaverse.

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Physicists confuse "the final theory of our local universe" with "the final theory of any possible universe including the mutually exclusive ones". We can reword the "final theory hypothesis" into the question: "Does our local universe has a finite ontoaxiomatics or does the ontoaxiomatics of our local universe is open to deviate in order it deals with the problems of axiomaticity [incompleteness and/or inconsistency]?" Claiming that the Earth is the center of the Solar System; that the Milky Way is the whole Universe and that there is a single common foundation to all possible universe-like worlds is wrong (absolute empiricism can never reveal the full range of the quantum foundations of our local universe; modern science accepts empiricism and rigorous and coherent mathematical proofs). \_\_\_\_\_\_\_\_ We shouldn't use the term Final Theory because it's wrong, biased and vague. We should bifurcate it into: 1. the claim that quantum mechanics has a finite description which doesn't Everettianly multifurcate ad infinitum creating an infinite theory (some infinite theories can be described in a finite way; others not; we don't know yet; if the deviation is structurally fundamental, we will not be able to express the infinite quantum foundations in a finite manner) 2. the false claim that mutually exclusive universes belong in the same hypernymic substantiality, because we are wrong

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If a theory requires infinite symbols to be described and if it cannot be expressed in a general descriptive manner, it will never get finalized (except if the deviations are trivial... but if substantiality is hypernymizable (= able to be observed in a thought experiment as a wider grouping) then ontological deviations are of hypernymized significance (universe-strain variants near our local universe will initially have trivial deviations, but as we move further the ontoaxiomatic deviations gradually become significant [we don't know that, but it's a possibility]). A non-finalizable theory can only be described with partial mathematical descriptions and partial oratorical descriptions, but still we'll miss infinite significant elements of it.