Do you agree?
And even on the quantum level, it's not like anyone is able to falsify determinism; due to uncertainty and a lack of understanding, all we have are pdfs, right?
The world is full of unpredictable noise, ultimately because of quantum mechanics. This noise inevitably gets amplified to the point where it affects the behavior of complex macroscopic systems.
> And even on the quantum level, it's not like anyone is able to falsify determinism
Since physics is an empirical science it's never possible to be certain of anything. However the evidence against quantum mechanics being deterministic is quite strong. In particular Bell's inequality shows that such a deterministic theory if it is compatible with known experimental results would have to violate the principle of locality.