Thanks, everyone, for your clarifications of my somewhat muddled comments. There are two definitions of determinism that we can consider:
Determinism-1: We (humans) are able, at least in principle, to predict with certainty the future (or, if you like, the outcome of a certain experiment.
Determinism-2: The future is determined by the past (regardless of whether we can predict it).
I was basically referring to Determinism-1 in my comments: no, our best theories do not let us predict things with certainty. I think this is the conclusion no matter what interpretation you put on QM.
I think I am agnostic on Determinism-2. I am sort of an operationalist on this: anything that cannot be measured there is no point in arguing about. Since QM doesn’t allow us, even in principle, to predict the future with certainty, I have no way of knowing whether the future is determined by the past or not. On other words, is the randomness of QM predictions due to our lack of knowledge, or due to some sort of underlying “true randomness”? I can’t measure the difference, so I can’t answer the question.
In my view, though, the situation is actually a lot worse than this. We can’t predict the future of, say, the Universe, because we can’t determine the current quantum state of the Universe. A quantum state requires a state preparation procedure, a repeatable process that produces definite probabilities for measurable quantities. How can I, even in principle, do this for the Universe? Or even, say, the Earth?