Then provide a counter example that shows indeterminism without resorting to "true randomness", which is something that you can likewise not prove.
? Randomness is simply that an event that has a outcome that is not predetermined. Say a button that pressed had a 50% chance of shooting you with lighting and a 50% chance of making doves appear. If there is NOT randomness then you have determinism. Indererminsim means there is randomness. You're basically asking me to show A and assume not A. If I was omnipotent and could rewrite reality as I choose I could not do this. It obviously is impossible, but again this is simply assuming the conclusion.
using the word "never" is very very dangerous in this context. it's like using the word "impossible".
Under current scientific theory it is impossible to exceed the speed of light with information. Perhaps the scientific theory is wrong. That doesn't mean it is possible under current scientific theory.
Which is introducing a new assumption: the assumption that some (random) things don't have a cause, or the assumption that everything has a cause? According to a proper application of Occam's Razor, "true randomness" is the less simple explanation, given that all other physical events require a cause to have an effect. To set a precedent to disprove this, name one non-random event whereby an effect is not preceded by a cause.
If something isn't random its obviously caused by something even if the cause is simply a law of physics. You might as well be asking me to show why a square could have three sides. (If this isn't the case please come up with some imagined "non-random" event that is not preceded by a cause.) To overturn a past assumption one does not need to show a logical impossibility. The bar of overturning past theory is not logical impossibility.
And it isn't introducing a new assumption. Its saying there is nothing. That there are no hidden numbers. Assuming that say... "there are no imps behind Ebola" is not an assumption its a lack of one. Your the one assuming hidden numbers. Assuming a lack is not an assumption at all. Scientists when they found out about disease transfer did not assume that imps followed diseases around. They assume the diseases damaged people.
Model 1: When you have an unstable atom it has a chance of decaying every unit of time.
Model 2: When you have an unstable atom there are hidden variables that determine how long it will take for this atom to decay, and somehow these hidden variables just happen to match the would be decay pattern for a random decay pattern with no hidden variables.
This does not answer the question.
Determinism says that this is still only the appearance of true randomness, since the observer becomes part of the observed system, and therefore taints the results. It does generate what looks like, from inside the system, a random number, but an ideal external observer with, as you say, perfect knowledge and computation would likely find the result all too predictable. Yes, I'm aware that the practicality of finding the ideal external observer might be a tad difficult, but we're not talking about what is practical, we're arguing on the Internet! And doing thought experiments, I guess that's important to add.
Determenism can say whatever it wants (can philosophical positions have wants?). But that doesn't make it true.
Yes it is! The position of indeterminism says that their are events that can't be predicted no matter the amount of knowledge or computational capability. That doesn't make it true either!
So what you're saying is that scientific experimentation, unable to find a causal explanation for apparent randomness, accepts randomness as a given, despite the fact that absence of evidence is completely unverifiable, and thus not reproducible? That is the complete antithesis of the scientific method.
Assuming truly hidden variables is the anti-thesis of science. Since they are hidden they can't be tested. Science must be falsifiable.