Hi Gardarene. Thanks for your patience regarding my reply. Now that I'm at work...
See the very last line of this response for a nice primer of what's written between this and that.
I sometimes like to think of our......confusion with QM as akin to "mesoscopic bias" (hereafter "mesoscopic" is basically shorthand for "everyday/classical length scales"). There isn't anything inherently special about the scales we live at, it's just what we're used to, but given our tendency to making everything revolve around us, we are prone to treat certain length scales as "normal", whereas I don't really think there's any such thing. Certainly not within physics, it simply just does its thing. Chomsky is certainly right in that this probably is a consequence of our evolution - and his idea seems to me to be applicable to sentient species. That's not to say QM would play no role in natural selection at all - pretty sure I've seen various papers looking at quantum effects in the substructure of cellular life. Obviously though, this would not be something that they are aware of as they have no awareness to speak of.
Per the first part, see my response to Eudaimonist:
And perhaps we can say that understanding how or that something works doesn't mean one understands why it works. Even more specifically, being able to model a phenomenon or set of phenomena means we have a grasp on what these things do; it doesn't mean we know the reason for why this phenomena came to be and how it works in relation to sets of phenomena outside it. I may know that two plus two equals four, but that doesn't mean I understand whether mathematics are objective or limited solely to our heads. [Emphasis mine]
I would also argue that our scales are by definition anthropocentric, so I question speaking about scales as opposed to things that revolve around us. Perhaps a trivial point.
Regarding QM and its application to biology, that's interesting, but it's an ontological consideration, when I'm talking epistemology. To speak sanely, QM arguably does apply very much to the very cells we have, but I'm talking about our understanding and its relation to QM.
My response here was largely directed at your use of the word "infinite". While you seem to moved away from that, I'm still not entirely clear on what you intended to say in its stead. Your claim that QM is more fundamental and that that undermines classical mechanics strikes me as the same kind of bias as mesoscopic bias, except with a more explicit focus on QM. I don't really see why it should "undermine" it. Why can't physics simply be regarded as a spectrum of regimes, e.g. QM-probabilistic -> classical -> relativistic, with some blurring at the boundaries? (And for that matter, classical mechanics is a subset of relativistic mechanics too, but why is QM being labelled as fundamental and not SR/GR? I realise that that's as much to do with our current physics being incomplete as much as anything else, but it does seem to confound the construction of your argument somewhat.)
"Infinite" is rhetoric for, for our purposes, "incommensurate with our understanding," i.e., infinitely beyond our comprehension -- which might be (literally) a wrong way of speaking (incommensurability might not be in the same epistemic ballpark as infinity). I do think "infinite" was reasonably rhetorical, but I apologize if that wasn't clear. Good God, listen to my jibberjabber.
As for QM undermining classical mechanics, I think that's both true (as you seem to claim) but more deeply false. We can still speak of causality as with a mechanistic epistemology, so long as we're not literal with this causality; if you really want to get down to it, Hume proved (arguably) during the Enlightenment that we have absolutely no observation of causality, but only infer it because of what he called "custom", or our tendency to associate two things and thereby assume causality. In this sense, QM is beside the point. But I still think it applies: QM has given us the idea that mechanism, speaking objectively with its application to the subatomic world (and I'm happy, by the way, to say that my understanding of QM is "moderate" at best compared to others like yourself), is indeed false, given that things just don't work in this cut-and-dry causal fashion on the most fundamental level.
How is classical mechanics "undermined" when the effect of QM at mesoscopic length is so small as to be trivial? Some basic case of quantum weirdness like Heisenbergian uncertainty is bounded by Planck's constant, which is an incredibly small number if you cast it in SI units, which are basically mesoscopic dimensional scales. I personally don't really see why some miniscule fraction of uncertainty should "undermine" classical physics on the mesoscopic level. No, it doesn't apply to every physical scenario, granted, but I don't think that totally trashes it either. It simply means that different length scales have different physics.
And because we know these scales are there doesn't mean we properly understand the scales in terms of their relation to other phenomena (which, to me, is the right direction toward defining "understanding"). See above. Keep in mind (and it's hard to say "keep in mind" without sounding condescending, which is the last thing on my mind) that I'm using the "weirdness" (in the sense of incomprehensibility, which goes beyond being able to scale it) of QM as an epistemic springboard to allowing "weird" metaphysical claims (such as God) to have more applicability with such a "weird" or "screwy" universe than one in the 19th century, where the overriding scientific epistemology was very, very much understandable -- what's more understandable than straight cause and effect?
I think there's also a unspoken assumption in operation here that we should be able to measure and determine reality with absolute certainty. Maybe the issue here is that humans are simply mistaken to expect such a thing.
That's the idea I'm kind of working against, and which I agree with Chomsky in rejecting. But isn't quite the heart of my (I now see not-too-clear, sorry) OP.
Er.....that isn't really helping me, sorry.
Why not?
I've never really gotten why there are so many issues with probabilistic mechanics. No, you can't predict individual events, but you can recover a probability distribution for identical scenarios. The quantum double slit experiment's photon distribution is perfectly predictable, even though the trajectories of individual photons are not. Again, I can understand this being a bit of a shock if you were previously under the impression that you could track photon trajectories, but I think it's simply a case of reappraising your expectations. Again, the screwiness has limits, and it disappears once you start looking at events on the level of distributions rather than individual events. And I think this is why I'm still having issues with "screwy" - it seems to treat mesoscopic bias as some kind of extant thing or property of reality to be concerned about, rather than simply treating it as a bias.
My point is that predictability is *not* tantamount to comprehension. You can measure pretty much anything, but that sure as heck (to me at least) doesn't mean you understand how it works. You might call it the difference between "how" and "why". I can predict how my wife will act when I do something that will make her angry, but I'm still not quite sure why that is (but I'm working on it; we're both shrinks, so please atheistically pray for our children).
If you want it put pithily (or perhaps pedantically....or simply just "poorly"

), I think one can be mechanistic with regard to probabilistic mechanics.
I like that!
My point was simply that I think you could have constructed a syllogism of similar form pre-QM, but with "screwy" replaced with "orderly", given the state of physics at that time. It would also have been incorrect. Now to some degree, that's down to the level of physics understanding, but that's not to say that mesoscopic bias wasn't in play either, shaping our arguments for the worse. Maybe now it's just trying to take advantage of "screwiness" rather than "orderliness"
I think QM is fundamentally "screwy" -- not, take note, in relation to itself, i.e., by assuming that because we can model or scale that or how QM works, we therefore know why it does. I imagine I could find plenty of physicists who would distinguish the why from the how, but that would take work.
So maybe much of our differences can be narrowed down to "why" and "how" questions?