I contend that this is a metaphysical (i.e. non-material) question. It is unfalsifiable and, by definition, open to speculation. It would take the isolation of only one 'nonsense event' (an event without cause) to prove the possibility of a true random number. But this is the trouble that quantum physicists are up against. Observation demands a context. But context is defined by observation of one more more events relative to a backdrop of another, coinciding set of events.
For example (that is to say: to oversimplify for the sake of understanding):
Imagine a hugely complex, non-linear array of dominos all set up to fall into each other so that, given that one of them falls (see oversimplification - what made the initial domino fall?) and ignore the cause of this initial fall for the sake of argument, then the subsequent chain of falling dominos would be a good illustration of determinism - the fall of one domino becomes the cause of the fall of its neighbor (the effect) which, in turn, becomes the cause of the fall of its neighbor, etc. As long as there are dominos in sufficient proximity to others the chain of falling will continue.
In this model, if a domino stood back up - or fell in advance of being struck by a falling neighbor - and it was inpossible to show there was any cause of this aberant behavior, the scientist would immediately beging to hypothesize an undetected cause. Perhaps the domino righted itself because it bounced off an elastic spot in the floor. Perhaps the domino fell out of sequence because of a flaw in its manufacture that made it unstable and more 'sensitive' to the vibration of the floor caused by the distant falling dominos.
You can see how part of the context we observe our experiments in is an expectation that things happen for a reason - almost by definition. Therefore, even if we were to observe something happening for no reason, we would immediately begin to try and determine the reason.
Having said all that (and you can see in my blog as well) I agree that a random event - or even the possibility of a random event - would allow for a truly free choice. However, the burden of proof is on the proof of random - not on the disproof of determinism. And since proofs are based on a method that assumes determinism ... you see the problem.
I am skeptical that any event is random in the sense of being uncaused. But even if there are uncaused events, it does not follow that a decision based on one is free; it would simply be caused by a random event. Even if a particular human decision was uncaused, that would not make it free; it would simply be a random decision. Randomness ≠ freedom.
I've been bothered by a usage here and a couple of other discussions. The following equivalence seems to be accepted without question: random = uncaused
I just went to the first 10 or so sites returned by a Google search for "random definition". Not a single one reflects the above equivalence. Most of them seem to have something like "without definite aim, direction, rule, or method" as the core meaning with variations about it. In my 50+ years of awareness, I've never run across the supposed equivalence either--maybe I've just led a sheltered life.
It seems to be that folks around here are so indoctrinated with arguments about First Cause, etc., having to do with god(s) that they don't want to say anything that could be heard as even remotely similar so they deny that uncaused events exist. And they then label those uncaused events as "random" as a shorthand for dismissing them.
I think it is pretty clear that random things exist. Take, for example, the decimal expansion of the number pi. From every analysis I've ever seen or heard of, that sequence of digits fulfills the definition of random as it is used by mathematicians, scientists, and technologists. Cause has nothing to do with that sequence.
One need only make a decision based on the outcome of a random event. If I say that I will make a decision on whether the outcome of soccer game "coin toss" will be based upon the 43,745 digit of the decimal (base 10) expansion of pi, have I made a random event occur? I didn't create the digit--it 'exists' as part of the definition of the number pi but which did I "choose" that number? Cannot that be the random event?
What if I said, "A digit from the decimal expansion of the number pi based upon the number of radioactive particles emitted from this piece of uranium in the next 13 seconds being used to determine the number of decimal digits to skip past the decimal point."
I find the whole strategy of random=uncaused to be an interesting but not very accurate maneuver to beg the question in order to deny free will and force a "choice" of strict determinism.
I think that this equating is grounded in causes being determinable. Apparently, if you can't determine a cause, then a cause doesn't exist--that being for why a result was 1 instead of 0.
If random = uncaused, then caused = determinable, as the latter equivalence yields the former, and naturally yeilds, in general random = uncaused = undeterminable and nonrandom = caused = determinable.
Whether this is valid or not I'm no longer sure, but it's what's going on in people's minds, I'm sure.
I was wondering where that came from. I didn't mean to imply it, thought I would agree that "uncaused" is inherently random; the reverse isn't necessarily true.
If there is an uncaused event, by virtue of it having no predetermination it is necessarily random. But that has little to do with the question I am proposing regarding free will.
What I am saying is that "if" there is a such thing as random (a real life event), then a decision can be made that is not "subject to" all the prior events that went towards making that decision. It thereby becomes decoupled from every other cause that went into making that decision leaving a truly autonomous choice independent of prior influences.
As an aside: you are right about how mathematicians use pi as random because they don't know the pattern, yet; or if there is one, so it suffices. Note that pi is not a thing but an algorithm that outputs a symbolic relationship (as string of numbers).
The output (string) may be considered random, but note, whoever performs the algorithm gets the same string. The string, albeit random, is caused -- by the algorithm.
Set two people or two computers to use the same algorithm and get a DIFFERENT string, with no actual difference in computation and that's what I call "uncaused" and thereby necessarily random!
Sorry, that was a quick throw down remark. I guess I need to say what free is. In the above, by free I mean chosen, in the sense of by free will. If what we say or do or think is something random, then even we, the perpetrators, don't know in advance what it will be. Thus we could only know what the thought or action or speech is after the fact, and have no attachment to the way in which it arose.
In the sense I mean it, if something is random it is totally unpredictable - there is no means by which it is possible to say, in advance, what the outcome will be.
I am not venturing here into whether or not randomness is possible, or whether or not it must be uncaused, or whether it may be possibly caused, simply that if it exists, then IF a human thought or action or speech is arrived at, at random, it cannot have been chosen, (ie. not free). To choose, we must consider options, and select prior to undertaking whatever it is.
If free and not random, we could say: 'I will have eggs for breakfast'. If random we would be obliged to say: 'I wonder what I will have for breakfast.'
None of this supports freewill, because we can choose eggs for breakfast, even if we do not have what is called freewill. We just can't choose them if, (the root cause of), the choice is random.