I agree with the idea, but the examples in the post seem kinda bad to me. Unfortunately, I cannot think of my own at the moment - my usual go to example of discovering and formalizing a concept is the definition of the boundary/interior/exterior in topology, and this post makes me realize that that example fails to illustrate some central parts of concept discovery!
Ideally there's an example that I, personally, mostly discovered, so that I know what it feels like.
[I was aiming for legibility to a limited extent only. This post got extracted from a bigger post I've been writing and is meant mostly as a reference, and thus it may make more sense in context than in isolation.]
(Spiritually related: Yes, It's Subjective, But Why All The Crabs?[1])
(Alternative title: Yes, It's A Spectrum, But Why All The Structure?)
Many important concepts are only partially grasped. For some of those, it seems fruitful to identify certain postulated key/primary characteristics that quantitatively distinguish examples from non-examples, putting the former on one "end" of the multidimensional spectrum and the latter on the other "end".
It might seem that this approach has a significant peril because by constructing a continuous multidimensional spectrum to discuss properties of such phenomena, we also cause them to dissipate into insignificance, as they allow for examples of the phenomena satisfying those properties to a minimal extent to fit into the frame. We tried to clarify the concept — find its "True Name", a "natural" boundary separating it from everything else — but our effort turned against us: we dissolved the boundary.
This, however, is not true. We can intuitively recognize certain "clear"/"unambiguous"/"paradigmatic" examples of the phenomena. It does not necessarily give us that much information about where exactly the boundary is between the paradigmatic examples of the category and other phenomena. It is often probable that the boundary — insofar as it makes sense to conceive of it at all — is actually rather vague.
Nevertheless, certain regions of the phenomena are characterized by scoring high on the primary characteristics in terms of which the space exhibits interesting characteristics as a result of having a certain combination of the primary characteristics.
It is all a spectrum. But look! This region is emptiness, devoid of life. Most that is not void is inert dust. But that little corner over there — even if the coordinates I know are only approximate — is where interesting stuff happens.
I am going to give between two and four (depending on the way of counting) examples to illustrate what I mean by this and why this might be a good way to think about this.
Godfrey-Smith Cubes
In Darwinian Populations and Natural Selection, Peter Godfrey-Smith (PGS) introduces several characteristics of populations of biological organisms that are crucial from the perspective of enabling evolutionary dynamics. Among others, he singles out fidelity of heredity, dependence of evolutionary fitness on intrinsic properties (i.e., those of the organism, rather than contingent facts about the environment), and smoothness of the fitness landscape. "Paradigmatically Darwinian populations", those evolving populations in which significant novelty can emerge and can give rise to complex and adapted structures (to use Godfrey-Smith's terminology), score high on all three, with "less-paradigmatic" populations taking in-between-ish levels.[2]
Image source: https://petergodfreysmith.com/Dpops_Figure_3-1.jpg
Two chapters later, PGS defines collective reproducers as entities capable of self-sufficient reproduction that are composed of entities that themselves are self-sufficient reproducers.[3] Here again, he introduces three organizing features of collective reproducers: bottleneckishness (B) (the narrowing down of scope/size/number of lower-level units transmitted between generations), germ line sequestration (G) (the degree of reproductive specialization of parts), and integration (I) (division of labor/mutual dependence/loss of autonomy of parts, the maintenance of a boundary between a collective and its outside).
The relevance of those three is that the higher B, G, and I, the clearer the distinction between reproduction and other reproduction-like phenomena, such as growth. This is relevant if we want to talk about the possibility and coherence of phenomena such as group selection or "cultural evolution"[4]
Image source: https://petergodfreysmith.com/Figure_5-1_Dpops.jpg
Sometimes we can define/delineate/[point at] a certain phenomenon in terms of several features (that we take as primary/generator-like/defining/particularly informative), such that, even though this description admits uninteresting, degenerate examples, there is some vague region in this space in which interesting things start to happen, because the combination of high degrees on the relevant characteristics causes an interesting, unique dynamic to emerge.
In From Bacteria to Bach and Back, Daniel Dennett took inspiration from PGS's cubes and created a few of his own to illustrate similar multidimensional spectra. For example, here is one illustrating the spectrum from Darwinian phenomena at (0,0,0) to intelligent design at (1,1,1), which thus warrants gluing it to the (1,1,1) corner of PGS's first cube.
Image source: https://youtu.be/AZX6awZq5Z0?si=JpbvmnmdiFHVXtkP&t=2326
And here is Rosa Cao's from her talk "Agency and giving a damn":
Lyfe
In Defining Lyfe in the Universe, Bartlett and Wong want to … define life, except without anchoring too much on the contingent features of Terran life.
They propose "four pillars" of lyfe: dissipation, autocatalysis, homeostasis, and learning. All of them are strictly necessary for lyfe, but incomplete combinations also yield interesting categories of phenomena.
Image source: https://pmc.ncbi.nlm.nih.gov/articles/PMC7235751/
The regions labeled as 6, 7, and 8 correspond to "almost lyfe", phenomena missing exactly one of: autocatalysis, homeostasis, or learning.
Closing remarks
But see here for a contra to this specific example
PGS introduced more characteristics, but, alas, drawing more-than-3-dimensional cubes is kinda wonky.
See also: Scaffolded Reproducers, Scaffolded Agents.
Both of which the author has opinions on, but I'll let you read the book.
Pronounced "loyf".