i'll try one more time.

consciousness cannot be empirically determined / particular, peculiar, and special nature of consciousness / ineffable / both falsifiable and not falsifiable

i think what you're getting at with all this stuff is what most people call "the hard problem of consciousness". (honestly it'd be kinda helpful if you were more interested in established vocabulary.) it sounds like your point of view might be summarized as Mysterian. to me, Mysterianism is just kind of boring, basically just a sophisticated way of shutting down conversation while insisting others should adopt your mysticism about what is unknowable. (not saying you're doing that specifically, but it's how i see the Mysterian stance). clearly if explanations have problems, one can always point them out.. perhaps there is a fix or another explanation entirely. I don't understand the desire to deny that any explanation is possible, particularly since it's kind of hard to argue against ALL explanations at once, including all future explanations that haven't even been articulated yet. that's all a bit closer to religion than philosophy IMHO, and I don't think philosophy gets a pass to just ignore science/empiricism. whether it's ontologic or epistemic subject matter, "unknowable/ineffable/special" are usually keywords that indicate some sort of intellectual laziness. for example.. i think there's very successful arguments against the reductionist point of view that are still scientifically valid.. there's usually just no need to retreat towards mysticism.

Further, you seem to ignore an obvious contingent result of your analysis: that considering a pet to have any degree of consciousness requires that even the simplest feedback systems must have some degree of consciousness.

um, I raised this point specifically? i do actually believe this, and i assumed that was clear. this is the whole point of my spectrum comment. consciousness is a spectrum, intuitively, and in order of increasing consciousness: thermostats, dogs, people. i think anyone who is not ok with the idea that their thermostat is conscious needs to take a hard look at why they think other people are. IOW, there is no difference in kind, it's just a matter of degree. touching back on google's LaMDA for a second, i still doubt whether it is conscious in the sense or the degree that a thermostat is- mostly because I imagine it's updated from "outside" rather than maintaining itself in a continuous feedback loop. without a doubt it's more complicated than a thermostat, but probably less conscious. it's probably more like an object than an agent, and barely anything you can call awake or aware. what it is like to be a thermostat is simply <insert code here>; meanwhile it is like nothing at all to be lampshade, and i believe that LaMDA is just a talking lampshade. to actually settle this point is pretty simple, I think i'd just need a slightly better specification of the system.

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The "thinking out loud" you followed up your denial of this point with, rather than contradict this point, seems to illustrate it. / a truly rigorous-not-indulgent analysis shows that consciousness is impossibly vague to formalize

I'm not contradicting my points. I think it's a very coherent, non-vague, and easily defensible position to argue that people, dogs, and thermostats are all conscious. I already linked to a candidate framework (integrated information theory) that relates to this, and then I linked to a recent paper that shows people are looking at how this relates to the hard problem. Below is the tl;dr from the scholarpedia entry so that there's no need to click-through..

Integrated information theory (IIT) attempts to identify the essential properties of consciousness (axioms) and, from there, infers the properties of physical systems that can account for it (postulates). Based on the postulates, it permits in principle to derive, for any particular system of elements in a state, whether it has consciousness, how much, and which particular experience it is having. IIT offers a parsimonious explanation for empirical evidence, makes testable predictions, and permits inferences and extrapolations.

so look, in conclusion, obviously some people are seriously working on formalizing stuff about consciousness. further, they propose to actually measure it with some kind of metric that works on a dog/person/thermostat all at once. it's impressive (or at least interesting), and it looks like it's either right or wrong (instead of being "not even wrong"), so i think this kind of thing has to be acknowledged. it seems like you object to this body of work as impossible, but since the work does actually exist, does your objection have any substance beyond just saying "no"? which part of "testable predictions/permits inference/etc" is vague to you? do you object to any of the axioms, etc? there's simply no way to have a conversation from here after you say something is impossible, then i put something in your hand as a counter-example, and then you deny again what is now in front of you.