I know that it is certainly possible for the universe to be stochastic at one level, but deterministic at a higher level. For example, I have read that while quantum mechanics is a stochastic theory, at the scale of molecules and higher, the stochasticity "washes out", and the phenomenon becomes deterministic. But what about the reverse? That is, is it possible for the universe to be deterministic at one level, but not deterministic at higher levels? For example, while the scale of molecules might be deterministic, the scale of human behavior might be stochastic. Personally, I believe that "once deterministic at one level, always deterministic at all higher levels". But have any philosophers argued that a deterministic base level can give rise to a stochastic higher level?
Only ever, approximately deterministic.
Even randomness 'contained' to very small sizes can have large scale impacts, like say in the case of three-body interactions of blackholes where the tiniest variations we think physics can allow will matter. Article on here: The three-body problem shows us why we can’t accurately calculate the past. These cases might be rare though. And indeed, it took very careful observations to show the universe is not classical and deterministic, but quantum and indeterministic. The consequences are usually limited to small scales though, and that is the sense in which classical mechanics are a pretty good approximation, in most situations.
The converse, is that emergent behaviours in a deterministic universe, can lead to gigantically more efficient calculations, such that we regard the deterministic 'layer' as only meaningful in principle. A good example is predicting other humans based on their character, rather than the quantum states of their electrons - the latter would require such a complex calculation that it would be a full simulation of a human, and still be extremely sensitive to initial conditions, whereas the character model should likely provide useful insights for a wide set of circumstances.
It is not possible for the Universe being deterministic at any level. Only theories can be deterministic, practical reality is never.
Quantum level is clearly probabilistic, but probabilistic randomness does not "wash out" completely at any scale. In large solid objects the probabilistic variation is smaller than the accuracy of any measurement device. Fluids behave stochastically at all levels.
But the measurement error itself says loud and clear that reality is not deterministic. In a deterministic system there are no errors, everything proceeds with absolute precision. Reality is full of all kinds of noises and turbulences, errors and misinterpretations.
Ill-formed question. It is just a speculation sustained on multiple forms of SUBJECTIVITIES, so, no answer, until solving all of them:
- Outside of our minds, there are no rainbows, cookies, engineers, rocks or noses; everything is just atoms or fields (or something else, more pure and factual which we cannot know due to or limitations). Every subject can split the same system in different types and numbers of parts (e.g. for A, a house is bricks, wood, sand, etc., for B, it is spaces, walls, etc.). Ergo, systems are SUBJECTIVE assessments about the environment. When you speak about "levels" you are speaking about systems and parts, which are SUBJECTIVE.
- Atomic behavior was deterministic in classical sciences, and later it became stochastic. Ergo, deterministic and stochastic are SUBJECTIVE appreciations. You are assuming stochastic/deterministic behaviors are absolute and they are not: they are SUBJECTIVE.
- You can describe with a huge precision what will happen to an isolated cloud (e.g. thermodynamics can do so). But thermodynamic systems are ideals, not realities (starting from the fact that there are no closed systems in nature; thermodynamic systems ARE closed). A cloud, inside the natural environment (e.g. floating in the sky) becomes unpredictable in the long term. Worst even, when we consider that there are no 100% probabilities in nature. Ergo: any type of "determinism", for whatever "level" is SUBJECTIVE. A ball which is predictable with a
Probability < 100%is essentially unpredictable. Determinism becomes then PROBABILISTICALLY SUBJECTIVE. All your "washing-out" notion represents only metaphysical ideals (like thermodynamic systems).
In terms of reducability, it is possible, depending on specifics, to have a deterministic system reduce to a non-deterministic one. But this is not generally possible.
As an image: if we push a toy boat in a bathtub in one direction, it will move pretty straight no matter tiny waves. But if the waves are big enough, it can move anywhere, chaotically, and it is not possible to make the boat move straight.
We could call a universe with such very tiny waves quasi-deterministic. In a quasi-deterministic system or universe, there still remains a tiny margin of error, but all practical results would be undistinguishable from an actual deterministic system.
Note that due to chaos theory, even tiniest errors can have large consequences (so the boat imagine can be misleading), but for practical purposes like engineering, the same problem exists with certain deterministic systems due to errors in measurement and observation. Measuring with tiny unpredictable errors in a deterministic system would generate quasi-non-determinism. This would be "as good as real random" for most practical purposes.
In a quasi-deterministic universe, it can be possible to tap into the underlying non-deterministic processes to generate non-deterministic large processes, but for most purposes it could be cheaper at similar quality to just use quasi-non-determinism on top of quasi-determinism.
In an actually deterministic system or universe, no truly non-deterministic system can be built if we assume reducability.
However reducability itself is an assumption, and mind-body dualist and spiritual people reject such reductionism for our universe.
Even in a truly deterministic universe with full reducability, for agents inside that universe, it may be impossible to tell whether process are non-deterministic or just quasi-non-deterministic.
In the bathtub image: when nobody is able to exactly measure the tiny waves, it does not matter for practical purposes if they are actually deterministic or not.
In that sense, even if our universe was deterministic (on some scale), due to limitations in observability we might only ever be able to make stochastic models about certain processes, and very weak ones if chaos theory is involved.
One area of reading that can help are text about counter-measures casinos are taking against cheaters using cameras and computers to predict where a ball in a roulette table will settle. That might help understand quasi-determinism and quasi-non-determinism.