To elaborate on this a bit: One may argue that "a state" is a simpler concept than "a superposition of all state". Even in pure mathematics [1], I don't think

To elaborate on this a bit: One may argue that "a state" is a simpler concept than "a superposition of all state". Even in pure mathematics [1], I don't think that (say) real numbers are less fundamental than natural (unlike Kronecker in "Natural numbers were created by God, everything else is the work of men"). What's true for the set theory route, does not need to be true for any possible mathematics, including those created by other species. For me, it is perfectly conceivable that some aliens use Hilbert space, and for them natural numbers are a particular concept (finitely dimensional vector -> n=1 -> zeros of sin(𝜋z) = 0 & Γ(z+1) is finite, or something in that line). In this sense, if you understand quantization as a map between a set (e.g. {0, 1}) and a vector space over a set (e.g. |psi> = a |0> + b |1>), then it is harder within this conceptualization. For aliens, "a basis state" (i.e. |0> or |1>) might be not an object worth studying on its own. When it comes to the path from classical to quantum physics - yes, it is full of question marks. The only hints I know come from "Quantum principle of relativity" by Dragan & Ekert (previously on arXiv with a more inflammatory title, "Why devil plays dice?"). Yes, there is a contrast with cases, in physics, in which a more advanced theory could be deduced purely with the elimination of inconsistencies, or strive for mathematical beauty, e.g.: E/M -(symmetry)-> Maxwell equations -(Minkowski transformation)-> Special Relativity or non-relativistic quantum -(SR)-> Dirac equation -(Klein paradox)-> QFT At the same time, I think it is a wild hypothesis that "any physics theory point to a more advanced theory only with its own ugliness and inconsistencies". Furthermore, like almost anyone, I used to believe that it is always possible to reduce a "more advanced" theory to a "less advanced" one. Sure, for SR you take v/c << 1 and you are done. For anything dealing with emergent phenomena, well - it is (IMHO) not as straightforward as it may seem at the first glance. Decoherence is one of these cases. For even simpler ones - how to turn molecules of water into their macroscopic properties (temperature, pressure, viscosity). Yes, we can do it (well, with T and p, but still - not viscosity); but if we haven't seen any field in our life, we would not ask such questions in the first place. Even the concept of temperature would be some arbitrary, made-up quantity. Anecdote on a students' conference there were two talks after each other - one on bubbles in beer, and the other - C-star-algebras. The latter claimed that it is the more fundamental, ergo better, way of dealing with physics. Iwo Bialynicki-Birula (theoretical physics) smiled and asked the second speaker: "And how would you derive the beer bubble from C-star-algebras?") [1] Disclaimer: I believe that mathematics is created by humans, not something existing on its own. An abstraction of our language, and our sensory experiences. If we were a slime mold, maybe we wouldn't come with the idea of integers at all. Evolutionary speaking, integers are an abstraction over counting own offsprings, and perhaps - estimating strengths of groups when hunting or protecting. As a side note, it was really fun to have a longer conversation with Penrose, having very different views (also: I am Everettian, and have a naturalistic view towards consciousness, in the spirit of Dennett). After that, I got a clear idea that "the root of all misconceptions" is the assumption that mathematics exists beyond a human concept.