[darkmighty]

That definition of randomness is actually fine (randomness as ignorance), it's consistent, and the most often used definition actually. For example, take the Monty Hall problem: it doesn't matter what process Monty actually uses to choose doors, all that matter is you're ignorant of it (so you choose the uniform prior).

In fact I don't think many processes in nature are truly random (quantum phenomena have to have a large effect and you need to choose a no-hidden-variable theory), but it doesn't really matter. It's just a model.