The thing with taxonomies is that trying to make a category more precise tends to exclude things you want to include in it, and vice-versa. It is especially easy to find examples of this in nature, because nature has existed since long before humans had opinions about how things should be organized.
What is a cat? It's a small furry quadruped in family Felidae.
- Exception: cats may be quite large (lions, tigers).
- Exception: cats may have no fur (sphinx cats).
- Exception: cats may have fewer than four legs (e.g. due to injury).
Even questions that seem like they should be quite easy to settle, like "are these two gulls of the same or different species?", might be impossible to define formally due to things like <https://en.wikipedia.org/wiki/Ring_species>.
With the specific example of "no such thing as a tree", the category of plants that humans call "trees" isn't a genetically coherent group. Lots of different types of plants have woody stems and bark and leaves, and you can't group together all the things humans call trees without also including things that we definitely don't.
I definitely understand that the majority of taxonomies are problematic for the reasons you cited. When OP said "no such thing as a tree", I thought OP meant a taxonomic tree, not a literal plant tree, hence my example of binary numbers! Thanks for clarifying.
That said, taxonomic groupings can have both wide consensus and be useful, can't they? (Hand on chin... monotremes? hominids??)
The CS specific analogy might be, "Abstractions are leaky," or more broadly the, "map is not the territory."
Any complex-phenomena that is modeled with with a simplification will have places where that simplification fails. But models can still be highly useful, you just need to choose an appropriate level of abstraction, accept and manage any tradeoffs with exceptions, and move to better paradigm if one emerges.
Although if you want to get get technical, even evolutionary relationships are only trees if you throw out some of the information that doesn't fit the tree. It's truer to speak of phylogenetic networks that can take into account things such as horizontal transfer of genes and recombination.
I've pondered the "taxonomies as trees" as insufficient and broken. What I arrived at as "maybe this will work" is taxonomy as a high-dimensional sponge, where a thing may rest at a given point in high dimensional space (where the dimensions are characteristics of that thing) and may or may not be clustered with other things on certain axes.
Sort of like how word/semantic clustering works in LLMs.
This obviously isn't a fully formed idea, but it might make creating taxonomies easier? Taxonomic clusters? Something like that.
What is a cat? It's a small furry quadruped in family Felidae.
- Exception: cats may be quite large (lions, tigers).
- Exception: cats may have no fur (sphinx cats).
- Exception: cats may have fewer than four legs (e.g. due to injury).
Even questions that seem like they should be quite easy to settle, like "are these two gulls of the same or different species?", might be impossible to define formally due to things like <https://en.wikipedia.org/wiki/Ring_species>.
With the specific example of "no such thing as a tree", the category of plants that humans call "trees" isn't a genetically coherent group. Lots of different types of plants have woody stems and bark and leaves, and you can't group together all the things humans call trees without also including things that we definitely don't.