Dear Heinrich,
thanks for your interesting comments! I'll have to have a look at your 'fundamental universe'. And you're right, I did read Gabriel's "Warum es die Welt nicht gibt" exactly because I also perceived some kinship in his ideas, but found it ultimately rather disappointing.
Regarding models and strong emergence, well, it depends what stance you take. The traditional view would be that models possess some immediate correspondence with the things they model, at least up to some suitable approximation, and that thus we should consider the entities they posit, and the explanations they provide, as giving us some insight into what really goes on in the world. Here, I think, strong emergence is troubling: in some sense, there would be certain things that violate Leibniz' principle of sufficient reason---facts about the world that would obtain without any answer to the question of why they should.
In some sense, though, this is also true in classical reductionist ideas---after all, if everything can be reduced to some set of base facts, then those facts themselves admit no further justification. From this point of view, strong emergence maybe doesn't seem that much worse---it merely adds additional 'fundamental' facts that obtain at some higher level of coarse-graining, for instance.
But in my view, all models are inaccurate to some degree---every model is incomplete by necessity, just as all axiomatic systems (of sufficient power) are. The world admits no more of a single model than mathematics admits of a single axiom system.
Are then facts that fail to fall under the purview of a given model strongly emergent? From the point of the view of the model, you might say so: after all, within that model, there is no way of reducing them to fundamental facts; they're true for no reason.
But this tells us something about the model, in my opinion, not something about the world. In other words, it's our problem, not that of the world---just as the fact that there is no single axiom system for all of mathematics ultimately may be considered a limitation of human mathematicians; if we weren't limited to finitely specifiable, effective systems, these problems wouldn't exist. So I think that if my thoughts entail strong emergence in some sense, then one also should think that mathematics contains strong emergence. But then it seems to me that's just fine, after all, mathematicians have still been able to make great strides in mathematical understanding post Gödel. (In that manner I, too, am optimistic about the progress of science---our understanding of the world will continually increase, but I don't think it will come to a true end point, although for all practical purposes, it eventually may.)
(By the way, have you seen Sabine Hossenfelder's take on strong emergence in this contest? I think it's a clever idea, although ultimately, I don't believe it really buys the necessary elbow room for things like free will.)
You're right also to point out the difference between consciousness, the sense of self, and so on. I wasn't intending to suggest an equivalence here, but I think there is a sort of progression---in order to be properly called 'conscious', you need to have a sense of self, and in order to have that, you need to be able to conceive of yourself as an entity distinct from the rest of the world, and in order to do so, you need to be able to model the world as sort of a container with you in it. Each lower rung is necessary, but not sufficient, for the next one. (As for literature on the subject of consciousness, I can't really claim to be an expert, but if you haven't read it, I still think that Jaegwon Kim's 'Philosophy of Mind' is one of the best overviews of the subject, and contains many references for further digging into the topics you find particularly interesting.)
There's also an issue regarding what constitutes a model that you highlight. In some sense, a brick is a model for our solar system---we could use it, say, in a model of the nearest couple of star systems. That empty beer bottle over there is Alpha Centauri, the football is Epsilon Eridani, and so on.
Undoubtedly, however, it would make for a very bad model of the solar system. That's because only its most elementary structure---the quantity, its being 'one thing'---is represented. So it's not clear in how far my talk about 'the world without models' is itself something of a model.
In particular, one also may talk about 'the round square cupola of Berkeley college', but does that necessitate a model of it? Can one model impossible objects? I think that one instead has models of its parts, or understands its properties individually, without really being able to put things together---so one knows (by model) what 'round' means, what 'square' means, what 'cupola' means and so on; but one can't really put these together, since that would be an impossible object. I think one understands 'the world without models' in a similar way.
Grüße zurück aus Köln,
Jochen