(2) Suppose we were to find some process in nature that were truly random. What effect would this have on how we think of causality?

It depends on what you mean by “truly random”.

Suppose we have an electron, a, with a spin of Sz=+½. Before measurement of Sx, it's indeterminate whether a will be either Sx=+½ or Sx=–½. I'm, however, still able to predict that on measurement it will be either Sx=+½ or Sx=–½. So, there is still some order in a's behaviour. I think this is probably compatible with traditional views of causality[1].[2]

But now suppose that instead, one moment, a is around the nucleus of a hydrogen atom in an Earth laboratory; the next, it's suddenly a proton of carbon headed towards the Sun; then, gold headed to Mars. It seems to me it would be in principle impossible to predict what would happen on measuring a. And I think that this kind of completely orderless behaviour may be incompatible with traditional views on causality.

(1) Does randomness actually exist?

Whether randomness in the first sense actually exists is an empirical question, best left to scientists. I'm not, however, sure about randomness in the second sense. (I'm open to any empirical evidence for randomness in the second sense, but suspect it impossible.)


[1]I would, I think, say that a has a disjunctive disposition for Sx to be either Sx=+½ or Sx=–½ upon measurement.
[2]Very open to physicists correcting me on the details here.

iwpoe wrote:

It would be interesting to me to know whether when something is declared a stochastic system in science if this is generally done without attempt at metaphysical import. Is it merely a matter of the model having predictive power or does one say *no, this really is done in a way that's in principle without reason*?

The former. Philosophically speaking, every physicist I've talked to is a strict determinist with a Parmenides theory of time, both of which are incompatible with true randomness existing.

iwpoe wrote:

Has there ever been a case of a previous stochastic system being switched to a deterministic model?

Yes. Population growth was long thought to be a shochastic system, but after the advent of Chaos theory, it was shown that population growth is actually a deterministic system with extreme sensitivity to initial conditions.
 

Also related to this:

https://www.quantamagazine.org/20160802-unified_theory_of_randomness/