I am ever so grateful to Bill Westmiller, whose comments are in bold:
All effects have an infinite number of material causes.
Causality doesn't stipulate the number of causes, only that there is *some* material cause for every effect. I understand that you want to make the case for infinity, but even an infinity does not mean that every effect is caused by *all* matter. For example, there's an argument to be made that no matter beyond our "light cone" can possibly affect anything in our proximity: it hasn't arrived yet. Yes, it will arrive some day, but until it does, it isn't a cause of any current effect.
... In science, as in life, we seek meaning by discovering the causes of effects.
Yes, but ... if all effects are a consequence of everything in the universe, we cannot discover ANY unique and proximate causative factor. Science attempts to *constrain* the possible causes for any experimental effect, relegating unknowable causes to "noise". That doesn't mean that all scientific experiments are inherently faulty or "wrong".
If causality is the proposition that all objects are influenced by the motions of other objects, then acausality is the absurd proposition that no objects are influenced by the motions of other objects.
You missed a word that you used earlier: "influenced by the motion of [ALL] other objects". In this case, you got it right, but the argument is still flawed. Spiritualists don't argue for acausality, but rather supernatural causality. You could argue the philosophical case that there can be no "thing" that has existence beyond nature, or merely that we couldn't possibly know anything about it, but you can't claim that they are opposed to the concept of causality.
The doctrine of absolute chance neatly avoided that.
I agree that "absolute chance" contradicts causation, but Aristotle was referring to unintended coincidences, which are perceived as a suitable effect of an unrelated act. Example: A statue of so-and-so fell onto the man who had murdered so-and-so. By chance that the murderer met his proper justice. Aristotle says that in its absolute sense (haplos) chance is the cause of NOTHING:
Of course, I totally agree with your disdain for Hans Reichenbach's acausality by chance. That error is perpetuated in many aspects of quantum mechanics, particularly Bell's Inequality.
I don't think any scientist can totally ignore the prevailing religious beliefs of their era. Some tried to make their theories "compatible" with spiritualism, just to gain social acceptance. Wrong, but forgivable.
By using an explicit assumption of infinity, Bohm demonstrated that the "cause" for an "effect" is never established with absolute certainty. We must always accept something less because both the cause and the effect, like the objects they describe, have infinite properties.
I don't think you can invoke Bohm to establish "infinite properties", only that some effects have unknown causes, which we reasonably assume to exist. He was talking about the expectation that the development of new sensing tools would discover previously unknown causes, not that they were infinite (and therefore incalculable). In seeking those unknown causes, we either find mitigated or unmitigated truths about reality.
The prediction, however, can never be perfectly accurate.
True, but logically irrelevant to human beings. The reality is that no human will ever be omniscient. For that matter, no God can be omniscient, since It would have no motive to ever act: It either knows the future state of all things or It acts to change them ... in which case, It doesn't know that It will act. One of the many contradiction of God's attributes.
Causality assumes that, because the universe is macroscopically and microscopically infinite, the number of these causes is in principle infinite.
Causality does not dictate infinity, since it is an "unmitigated truth" that no Thing can influence another Thing in the absence of motion ... which makes it proximate ... which requires time. Therefore, unless you want to postulate infinite velocity, you can't conclude infinite causation.
... the number of objects to be considered is infinite and each of them is in motion relative to each other and all other bodies in the universe.
In the context of your example, you seem to be suggesting that the velocity of gravity (or light) is infinite. If it is not, then remote objects do not affect proximate objects until some future time. They are not causes until they become causes for a proximate effect.
Nevertheless, we are able to compile partial, finite statements that we call causal laws and that we find relatively valid for specific instances.
The scientific method (experimentally) is to isolate effects, in order to determine a specific, proximate cause. I don't think anyone claims any "Black Box" is perfect, merely that it's sufficient to identify causes for specific effects. However, there are many causative events that have universal effect, such as gravity or the characteristics of light. They aren't just valid for "specific instances", but for all instances of a kind.
It seems to me sufficient to say that ALL evidence in human history establishes that every effect has *at least two* material causes (the actor and the acted upon). There is no contrary evidence. Therefore, causation is an "unmitigated truth".