I found a paper that talked about paraconsistent logic systems (https://en.wikipedia.org/wiki/Paraconsistent_logic) and trivialist systems (https://en.wikipedia.org/wiki/Trivialism) and the possibility of integrating them into a computable program, since their definition is computable (that is, although they would involve uncomputable or even logically impossible things, defining these systems is a computable action)

But the problem is that in a simulation of a universe, a trivialist universe/system, for example, would be defined as existing within a box inside that universe. To the beings inside that simulation it would be stated that this universe would exist inside that box. But because of the fact that such trivialist system would contain impossible/uncomputable things, it would not actually exist and inside the box there would be actually nothing (since it could not be actually computed).

But since Schmidhuber's theory would not strictly be a literal computer, (it states that informational processes similar to those occurring in a computer would create our universe) could it work in a different way? I mean, could we have a computable statement/definition/condition/system/program about a trivialist or paraconsistent universe/system that would actually create them? So just the computable program/definition of such systems would be enough and these uncomputable universes/systems would (actually) appear spontaneously (without the need of computing them, which would be impossible)? So if we had a program which would define trivialist/paraconsistent systems in a computable way (as their definition s computable), would they actually be realised in his theory? (Sort of like in Tegmark's hypothesis where the definition of a mathematical structure would be enough for it to exist.)

If Schmidhuber's hypothesis could not do this and couldn't "indirectly" produce uncomputable things and a trivialist system could not exist within this theory, could this be done by Wheeler's it from bit? Or Weizsäcker's ur-theory?

PS: Please I need answers more based in computational science and physics. I ask this question here because it is involved with philosophical systems.


Trivialism: https://en.wikipedia.org/wiki/Trivialism

Paraconsistent systems: https://en.wikipedia.org/wiki/Paraconsistent_logic

Schmidhuber's hypothesis (in pancomputationalism part): https://en.wikipedia.org/wiki/Digital_physics

Tegmark's hypothesis: https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

Wheeler's it from bit: https://plus.maths.org/content/it-bit

Weizsäcker ur-alternatives theory: https://arxiv.org/pdf/quant-ph/9611048.pdf

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