We present various arguments for an open-ended nature of the Universe, especially in the light of quantum foundations, including quantum gravity, and the questions of computability and undecidability. We also comment on the role of the choice of the number field in our descriptions of the regularity of natural phenomena and we argue for the emergent nature of the laws of nature at different scales of the Universe. Finally, in this context we make some remarks regarding the Universe-Multiverse debate.
Tatsu Takeuchi