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This uncertainty principle cuts down Laplace’s determinism at the roots.

It most certainly does! The author of Mécanique Céleste — Celestial Mechanics — presupposes a universe that is deterministic, material, and essentially mechanical in its operations. It is what it is, independent of any observer.

Yet Laplace's worldview is an a priori assumption projected onto reality. The worldview itself is not the outcome of scientific investigation. It is a metaphysical, subjective commitment that exists prior to any science being done at all.

There are three very common scientific "attitudes" or a priori commitments/worldviews that people still seem to want to cling to, even though they have been thoroughly discredited by modern quantum physics:

Determinism — the central metaphor here is the idea of the "clockwork universe." Determinism holds that all processes in the universe are entirely determined, such that if we could but know "the exact location and velocity of all the particles in the universe at a given moment, then it would be theoretically possible to have complete knowledge of the universe for all times antecedent or subsequent to this." This is pretty much Laplace's claim — which cannot but strain our credulity IMHO, for what person can know "the exact location and velocity of all the particles of the universe at any particular instant?" Such a person would have to be God himself — but God is pretty much what Laplace is trying to obviate in his exercise. The "God of the gaps" is gotten rid of; and the "new god" — the mechanistic scientist — takes his place.

But then, there's nothing particularly "scientific" in any of this.
Materialism — holds that "the universe is ultimately composed of stable, individual parts that interact with other parts, all of which are fully external to one another." It assumes — a priori — "that a material body remains fully itself regardless of the passage of time," that a material entity "is the same no matter how long or short the span of time involved." Whitehead called this assumption an instance of the fallacy of simple location, which holds that any bit of matter "is where it is, in a definite finite region of space, and throughout a definite finite duration of time, apart from any essential reference to other regions of space and to other durations of time." Such a presupposition has been thoroughly exploded by modern quantum physics, which envisions "matter" not as a "solid," but as an energetic, vibratory phenomenon, subject to non-local causes. (Mechanistic materialism absolutely insists that all causation is local.)
Reductionism — holds that all the phenomena of any level of reality can be accounted for in terms of a more basic or simple explanation arising at a lower level. "The most immediate examples are the belief that consciousness may be reduced to the level of biological activity, or that the workings of biology may be reduced to the level of chemistry, chemistry to physics, and so on."

Again, these three world views are not the products of scientific investigation; they are not findings of any kind of scientific research. Rather, they exist prior to any research being done at all. Yet they do condition (even pre-qualify or pre-determine) the types of results that will be deemed "scientifically acceptable."

...It is a banality to point out that the mechanistic-materialistic stance elucidated by Newton [and Laplace] in the seventeenth century remains the axis of our tacit metaphysics even today, simply because it mirrors the way the solid bodies of reality interact with our locally evolved sense.... So long as scientific theories "work" in a narrower, technical sense, most physicists are content to live in a pre-Einsteinian, "common sense" universe, ignoring the unavoidable metaphysical implications of quantum and relativity theories. But, because science has failed to draw out these implications, it "increasingly finds itself enmeshed in a cosmic tapestry of the impossible":

The subatomic physicist must incessantly account for what he cannot intellectually believe: an electron changes from one orbit to another without ever having traveled through space; an electron fired at a screen with two holes in it goes through both apertures at once; a positron ... can only be explained as moving backward in time; a neutrino, which has no mass, no charge, and no magnetic field — and which hence cannot be truly said to exist — passes through our bodies and through the crust of the earth as if those 'objects' did not exist for it — in fact, quite like a ghost."

Your friend, Merv, asked: "Shouldn’t this 'hiddenness' be just as applicable to a Laplacian ‘billiard ball’ universe as the QM ‘mischief behind locked doors’ universe?" It seems to me what is "hidden" are those aspects of the world that are undetectable by means of direct sense perception. But Laplace's expectation seems to have been that sense perception is truly our best, "objective" guide to reality. He evidently had immense confidence in sense perception, so much so that it appears the only things in the universe that truly exist for him are those objects which can be validated by sense. In essence, the universe is "reduced" to that which is visible to the eye, and manipulable by hands. Everything else is a "fiction," by (a priori) definition.

This is just another way man has of making himself "the measure" of reality....

Merv observed to George, "This uncertainty principle cuts down Laplace’s determinism at the roots.” It would certainly appear to do so! That's because Laplace's theory assumes/demands that we know the positions and velocities of all parts of the universe in the instant, and this we can never know. Had Niels Bohr gotten his preferred name accepted for what is now known as the uncertainty principle, perhaps this necessary "ignorance" would be better understood.

IIRC, Bohr wanted to call Heisenberg's discovery the indeterminacy principle. That's because "uncertainty" denotes something we could know, but simply do not at the present time; while "indeterminacy" denotes something we cannot know in principle. If one determines the velocity of a particle, one cannot simultaneously determine its position, and vice versa. One cannot have both at once; where one has one of these measurements, one cannot have the other — at the same time; i.e., in a single experimental set-up.

I certainly agree with George here: "Quantum mechanics does not say that there is no external reality at all, but that that reality is not strictly separated from our consciousness.”

Which is so ironic: Ever since Francis Bacon, science has been committed to "objectivity" — that is, the eradication of all "subjective" elements, most notably including such "metaphysical entities" as mind and consciousness — from its methods. And then along comes quantum mechanics, which mandates the observer — mind, consciousness — as an indispensable component of any experimental situation.

What is strange in this situation is that there seems really to be no arbitrary boundary between mind and matter. As Dr. Godwin suggests, "the assumption of an objective world completely independent of consciousness, leaves everything on 'our' side of the line unexplained and unexplainable, in theory, in fact, and even in principle."

Why is Merv looking to chaos theory to explain anything about the world? The theory presupposes, not an ordered universe, but a fundamentally disordered one. Plus clearly Merv sees the problem: "...error amplification makes sensitivity to initial conditions virtually infinite, and we can’t be infinitely precise in describing an initial state...." Indeed. How do we know we have captured all the relevant initial conditions?

In closing, I'd just like to excerpt from my dearest sister in Christ Alamo-Girl's outstanding observations, from a recent post:

Unknowables are part of the human condition — we are not able to remove ourselves from "all that there is" to observe it "all at once." The human observer is part of his observation. We cannot physically sense how fast we moving, relativistic time, cosmos to quantum proportions. Jeepers we cannot see inside a closed box much less know what the other guy is thinking. We cannot even physically sense the present since time elapses between sense and cognition..... Science appropriates a great deal from mathematics and often more than it can chew. Infinity, for instance, does not translate well because space/time is finite. And the mathematical term "random" is not correctly applied when the system is unknown or unknowable — and the total number and types of dimensions much less fields are unknowable on principle. "Unpredictable" would be accurate. Ditto for "information" and so on. This leaves the consumer believing science knows more than it could possibly know.... Merv should not be concerned about the gaps but take comfort in the big why, i.e. why this instead of nothing at all?

I so agree. Merv is trying to work these problems "bottom up," while I think he'd get farther if he worked them "top-down" — starting with "the big why"....

Or whys: Why is the universe the way it is, and not some other way? And Why is there anything at all, why not nothing?

Just some thoughts, FWIW. Thank you ever so much, dear Matchett-PI, for this outstanding, thought-provocative essay/post! And many thanks to Merv, as well.