Most concepts break down on borderline cases, within and without biology. Those motivated will abuse this to argue that those concepts don't meaningfully exist at all.
Take our color perception as an obvious example: We clearly see different types of color, despite us being unsure at the thresholds in between, and the actual electromagnetic radiation of visible light being a continuous wavelength range.
That is just a fundamental limit of our reasoning. We mentally make models of the world to make sense of it. These models have to be of less complexity than reality, ergo they have to cluster perceptions, ergo we have to categorize.
And even when the attributes are discrete, phenomena tend to be highly combinatorial.
Leaving lots of room for new combinations to be discovered that will upset our taxonomies.
The definition of steel is pretty hard-edged. A polymer of C, H, and O isn't steel.
The definition of a quasar is similar. There are "maybe quasars", but that's from lack of data, not lack of definition clarity.
A circle is pretty exactingly defined. Mathematicians aren't fuzzy on that.
Just like geology doesn't have a great definition for their subject of study (the earth). They have a definition that works really well, but because they only have one example, the definition ain't stress tested.
Slightly less silly: it took the discovery of lots more bodies inside and outside the solar system (dwarf planets here, exoplanets elsewhere) for astronomers to really nail down the definition of planet.
The definition is fuzzy because the concept is fuzzy! Even something that we in every day life see as settled such as a species is not always clear-cut. Cat or dog? That's usually easy. Member of a species yes or no? Not so easy, and in some cases subject to considerable debate and even then unresolved.
For instance:
https://en.wikipedia.org/wiki/Species_complex
And:
https://en.wikipedia.org/wiki/Ring_species
Boundaries are hard, just like naming things.
It is misconception that hair and nails continue to grow. What happens is the that kind and soft tissues dehydrate and shrink and the hairs and whiskers stick out more. Growth stops soon after oxygen and nutrients stop being delivered.
Autopoiesis and Cognition: The Realization of the Living (1980)
https://en.wikipedia.org/wiki/Autopoiesis_and_Cognition:_The...
Unfortunately out of print.
The result is a landscape of fuzzy definitions mostly centered around that last one.
> This seems to be how our minds model at least some concepts as well [...]
Since we have existed for 100's of thousands of years, and formal thinking only a couple hundred as a widespread practice, only habitually by a modern minority, and then for a tiny minority of daily concepts -- that is very nearly the only way we encode concepts.
In fact, we no doubt actually encode formal concepts using clustered characteristic thinking. We have just intentionally narrowed characteristics down to the point that the result is formal thinking.
Yes a two step.
Spoken words forced/helped us divide up completely fuzzy concepts into discretized hierarchies of less and less fuzzy concepts over time.
And then written symbols, enabled a trend of identifying more and more simple I.e “primitive” abstract concepts (culminating in true, false, 1, 2, 0, infinity, node, edge, …) that let us reformulate and better understand complex fuzzy concepts as compositions of primitive concepts.
Language and then pen/paper.
Instead of the concepts being like a box where something is definitely in the box or not in the box like in mathematics or maybe physics, the concepts are more like a clustering of characteristics in a high-dimensional space or landscape of variation, where things are classified according to their similarity to a central paradigm case. (This seems to be how our minds model at least some concepts as well, as evidenced by our being faster at categorising cases that are closer to some paradigm case)
One notorious example is the concepts of male and female: yes, there are borderland examples of individuals who can't be classified as either, but almost everyone clusters sufficiently closely to the distinct paradigmatic cases that the concept has an obvious utility.
But the same thing happens everywhere in biological classification: whether something is a mammal or not becomes fuzzy as we go back in evolutionary time, and whether something is alive or not is similar.