The World Is Built on Probability (1988)
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Both. The latter is obviously true, and quantum physics tell us that the former is also true.
And the author knows (this in the book):
"Elements of quantum mechanics are also involved, and this allows the author to demonstrate how probabilistic laws are basic to microscopic phenomena."
True is a dangerous word to use in science, since our understanding can always change. What QM tells us is that our best understanding of the world at the micro physical is based on probability. Whether this is actually true of the world is open to interpretation.
I have my own "take" on math. Of course we enjoy math as an end unto itself. But when we use it for practical purposes, we choose math tools that we expect to work for the problems that we're trying to solve. In the case of probability and statistics, those tools are useful for situations where we know something about a set, but not everything. There are other situations where we use calculus, algebra, and so forth.
Incomplete knowledge corresponds to a lot of problems and situations in our world, and so prob & stats are useful for modeling those situations. But it doesn't require the world to be fundamentally probabilistic.
Quantum mechanics is the best thing we have to an exactly correct physical theory, and it is tied completely up with probability. So probability in the form of "genuinely random" is very fundamental.
As you go up from that level, our knowledge is limited at every turn, so it's hard to separate the one from the other ("genuinely random" vs. limited knowledge).
For example, you may have a large-scale physical system governed by differential equations, but the boundary conditions are not exactly known or knowable, or the governing equations are not closed (i.e., they depend on other things outside the system).
The only thing they agree on is the equations. Once you ask the question of "and what situation are we facing in the real world" consensus starts to break down.
Interestingly, the core of probability - the "Random Variable" is almost completely unobservable in the world of science. Everything in classical mechanics turned out to be deterministic. The parts that were grappled with statistics were probably not random effects, but unpredictable deterministic effects. For example, the measurement errors could be treated as random variables, but ultimately were not expected to be random in cause.
Compare this to geometry and algebra, where I would argue it is easier to find a 'real' example right from the get go. Opinions, obviously, vary.
Though non-local hidden variable theories need to be reconciled with special relativity lest it be possible to transmit information faster than light.
See the non-local, higher-ordering properties of true holograms and eg. this mixed fluid experiment: https://www.youtube.com/watch?v=UpJ-kGII074
More on all this in Michael Talbot's amazing book "Holographic Universe": https://wikischool.org/book/holographic_universe
Then we would be back in a universe where we have an extremely useful concept in the humble random variable, and no examples of anything that is fundamentally random. If I start with a random variable, I couldn't reasonably approximate it with a real phenomenon, because the phenomenon would be deterministic.
Compare that to a line - I can define a line between the center of mass of my two hands. We can quibble all day about whether that is a well defined definition (I suppose it isn't), but if I wanted to approximate a real line with two points in space I could.
I contend this is an interesting an important difference between subjects like geometry and subjects like statistics. The underpinnings of statistic are _extremely_ philosophical.
For example, a coin flip is physically deterministic but you can't take advantage of that in a normal coin flip situation. But if you have a chunk of radioactive material and two particle detectors held nearby, I don't know of any way even theoretically to determine which will trigger first -- that would be physically nondeterministic (unless I'm wrong, but other situation could be i.e. famously quantum experiments).
Then, most of the situation that are physically nondeterministic are things that we experience is a way that is aggregated over a large number of events: i.e. you aren't seeing individual particle emissions, you are just eventually getting radiation poisoning. It takes special equipment to experience the probabilistic nature of nuclear radiation, brownian motion, etc.
So there are really lots of natural processess that are probabilistic but you only experience them in aggregate which conceals it, but then you have incomplete knowledge about the world which re-introduces the uncertainty.
All are statistical in nature. Nature is built on probability.
The book itself is amazing but I’ve been sitting with this idea for awhile now and am becoming increasingly convinced that what we call consciousness might require entropy for us to recognize it as such ... in a way — if we believe that consciousness requires probability, then might we subsequently lose the ability to believe in any state of existence where probability played no role ...?