As far as we (humanity) know, true randomness is still a thing. Quantum effects have no known predictors. From the article I linked: "Quantum mechanics predicts that certain physical phenomena, such as the nuclear decay of atoms, are fundamentally random and cannot, in principle, be predicted"

So Quantum science believes that true random does exist. Until someone demonstrates otherwise, or I start working on the problem, I'm good accepting that for now. The tests to demonstrate these ideas are fascinating: https://en.wikipedia.org/wiki/Bell_test_experiments

In the mean time, there's the very real concept of whether something is practically predictable, and a Geiger counter is currently not practically predictable. (And worth noting, it lands into the category of currently not theoretically predictable too.)

Personally, I feel like the definition "unpredictable" is quite good, especially for regular people. Going deeper than that requires all kinds of baggage and explanation. But the point the author made is very good -- people tend to start expecting things when "randomness" is involved, and that expectation is a problem, because randomness is unpredictable.

First of all, that statement doesn't really make much sense. By that definition, everything that you are unable to predict is random (to you), so, assuming that there are things that you are unable to predict, there are things that, from your perspective, are truly random, by that definition(!).

Unless, of course, by "truly random" you mean "random as per the definition that I prefer", in which case all you are really saying is that that definition differs from your preferred definition, which might be true, but isn't really much of an argument.

> I wonder if we can consider 'randomness' as an inherent quality of a system ...

No, that would be a useless concept. Randomness as an inherent quality of a system would be equivalent to the claim that we will never be able to predict the respective attribute of the system, i.e. it's a claim about the impossibility to ever know something. It's a perfectly valid concept, in that there might be things that we will never know, but it's utterly useless because we will never know that we won't ever know them, i.e., it's undecidable which elements are in the set and which are outside, unless we figure out how to predict them, in which case they don't fall under either definition anymore. The only thing we can say is that we don't know how to predict something right now.

The closest you can get to "objective randomness" is something like bell's inequality--but even that is falsifiable in principle.

Quantum theory specifies that this is impossible not just in practice but in principle. Radioactive decay on an individual-atom level is literally impossible to predict, and not just because we don't have sensitive enough measurements. "Arrangement and composition" don't have their standard meaning at atomic scale; particles are probability fields, not BBs.