[kp1197]

I don't buy the argument that merely because solutions exist, they can spontaneously be "chosen" by the system, even if such choosing doesn't break rules. We are talking about an idealized setup using disproven physics, so it's weird to talk about correctness. But I think the author is invoking a variety of Murphys law: Anything that can happen, might happen spontaneously. If that's true in idealized Newtonian physics world, maybe we should "fix" that? Or maybe the question of what to do about weird multiple solution sotuations is simply not in the scope of Newtons theory.

[sebzim4500]

This is just what determinism means: that for a given intial condition there is only a single solution obeying the rules.

The article demonstrates that newtonian mechanics is not deterministic, which is surprising at least to me.

[mvaliente2001]

I think parent comment (by @sebzim4500) is the clearest most concise summary of the argument stated in the article.