Irreducibility sounds different to my ears, it means that emergent properties are more due to biological-level structures rather than pure physics. Of course it's all physics underneath but that doesn't say a lot.
But what if the irreducible cell is made up of normal matter, but it has strongly emergent properties that can't be explained simply in terms of structure and function of it's physical properties? That's what would make it irreducible, if such things do exist.
I suppose there's a scale at which the "gap" becomes too large to call it "physics," but the larger the scale, the stranger it would be to find something irreducible across so many levels.
I don't want to argue about this or any word, but I think what was meant - and what I too would say - is that some things are emergent properties of interacting things. Yes, they consist of "physics stuff" following "physics rules", but also, together they create something new, on a higher level. If you take it apart it's gone, of course, and you go back to the physics. To give an example, something deliberately slightly extreme or ridiculous (depending on your POV): Try to examine the game of chess by looking at the atoms involved in a physical game.
Or, when I zoom in too far the forest disappears and I end up with first trees, then branches, then cells, then "physics". But someone who gets a degree in forest management does not benefit from learning particle physics, aside from the intellectual exercise of course. Some things stop existing if you zoom in too far, there is no "forest" or "love" or "chess" any more all the way "down there".
I think there is a misunderstanding, people talking past one another. Some people (here, but in general) think what is meant is something "meta-physical", esoteric. At least for me that's not true at all. There isn't anything magic, there is physics. But it took me decades to get to the POV that I tried to present here, which is just a different angle - and "POV" (literally, just shifting position, still looking at the same physical scientifically explorable universe). I think this is like what I remember from many higher math education revelations - you fail to see what the teacher is trying to say, and when you finally see it it' sooooo simple, just a different point of view, not actually different from what you know. What I'm trying to say is, if you don't understand what someone might mean like in this case, talking about "emergent properties" and the like, please don't assume they leave known science behind to go on an esoteric trip. It's got something to do with us not being "god", seeing the entire universe at once, but only being able to shine an extremely tiny extremely focused beam at one extremely tiny detail. So even if we had a few formulas for _everything_ (all energy, all matter, incl. what now is the dark stuff), it would not help us when we try to shine our tiny light at a higher level, so we need a different model even though the components everything is made of are more "fundamental". When you have surgery, you don't want a particle physicist wielding the knife, and you probably don't care if the surgeon would fail every elementary quantum physics question. It is just not useful if you want to do something on a much higher level.
It may not be so to a "god", but to our small minds all those basic tiny "physics things" working together create something new on top of them, and it gets lost if you start looking at the parts. Of course those components, atoms and below, are still explainable using nothing but physics. Just not a huge amount all of them together, interacting in ways for which we have created models far above physics, unless you look at mass/force/etc. Each time you zoom in you see the physics (or if you drop tree and measure the force of its impact, but even the part of physics you use there is far above the low level stuff).
Last example: Imagine all models gone, in all fields. Only the most low level physics exists. Try to explain the chess rules :)
Anyway, that's just my interpretation.
Whether emergence can explain everything is another matter though, and I think that's where "irreducibility" might come into play.
So why do we have these threads right here, that prompted me to write this?
> Whether emergence can explain everything
Nothing can explain "everything". What does that even mean? I refer back to my comment. You use the right tool for the job, and that is a different one depending on context and "zoom level". See my comment? As I already wrote, even if you had a "perfect" low(est) level model, of what use is it to you on a much higher level? You cannot deal with an unmanageable amount of "low level" model (the "but in theory" argument is not even a good one in theory - reminds me of "but I can in theory imagine things happening at the exact same time light years away" before relativity became way too established for anyone to dare make that kind of statement to not be laughed at). You can't use the same model for everything. Even if you had the perfect knowledge of the lowest level you'd have "emergent models" on higher levels. You can't work with quantum theory to explain chess (which, in addition, is disconnected from the actual physical chess pieces used, it could even just be electrons in a computer instead of wooden or metal or plastic chess pieces).
PS:
Using the opportunity of the follow up comment to add to my original one:
Another POV is - just another mental model, not "the ultimate explanation for everything", one model among many - is that the low(est) level just is the hardware, the silicon. When you write software you don't care about the (exchangeable, extremely variable) hardware underneath. Without it there would not be "chess" - there would be many "chesses" because the game in software would be something completely different from the game using wooden pieces. We would not see any of those high level concepts because we would drown in detail.
I'm not saying I argue for the opposite, but that is very definitive statement in need of a very strong argument to be taken seriously.
> What does that even mean?
Things that we don't even know how to talk about yet, like consciousness.
Even if consciousness is just an emergent phenomenon, this still doesn't explain the subjective experience of consciousness. Subjective experience might be irreducible, but it might not. We don't know yet.
From what I understand, you're claiming that we can't explain higher levels of emergence in terms of lower levels. But that's not true, and your example of hardware/software is the prime example of that. We can explain or model every level of abstraction perfectly in terms of the preceding, lower level of abstraction, until we get to the quantum mechanical properties of the substrate your software is running on.
Whether it's practical to talk about the rules of chess in terms of QM is another matter - it's not - but I'd maybe argue that's because we're not intelligent enough to hold enough information at once in our brains, not because of some inherent impossibility of doing so.
Profound.