Categories are only useful for comparisons.
We can’t evaluate categories by how well they describe their contents, because categories never provide absolutely accurate descriptions of the things they contain. If they did, each thing would be a category of its own.
Differences are nebulous
Why do categories describe relative differences? Because things are neither completely abstract nor completely distinct. All things are different from each other, but only in shades of relative difference.
As David Chapman of Meaningness puts it, differences are nebulous—cloud-like.
“From a distance, clouds can look solid; close-up they are mere fog, which can even be so thin it becomes invisible when you enter it.
Clouds often have vague boundaries and no particular shape.
It can be impossible to say where one cloud ends and another begins; whether two bits of cloud are connected or not; or to count the number of clouds in a section of the sky.
If you watch a cloud for a few minutes, it may change shape and size, or evaporate into nothing. But it is impossible to find an exact moment at which it ceases to exist.
It can be impossible to say even whether there is a cloud in a particular place, or not.”
At some level of completely abstract generalization, all is one; but at another level of purely concrete description, each thing is discrete.
So any useful method of abstraction must retain some concreteness. Without concreteness, there would just be one name for everything. All is one.
Likewise, any useful method of concrete description must retain some abstraction. Without abstraction (aka generalizability), our thinking power would be constrained by the need to describe everything precisely.
For instance, you couldn’t say “Would you please move that chair?” and assume the listener knew what to move. You’d have to say something like “Would you please move that device for sitting upon, consisting of four legs and a seat, made of polished mahogany?” Even that might not be specific enough—let alone all the specificities you’d need to describe “would” and “you” and “move.”
Intelligence means making accurate generalizations
To think intelligently—to come up with thoughts that are accurate and useful—you must combine the concrete with the abstract.
In other words, you must combine the narrowly descriptive with the broadly generalizable—in a way that describes reality accurately (because it describes the truth of things), but not so accurately as to be unwieldy (which would be useless).
Note: All descriptions are generalizations. That’s because all descriptions involve words, and all words are abstractions (to paraphrase Wittgenstein). The question is whether the generalizations are useful. We want accuracy and generalizability.
Categories make it easier to think intelligently
The way to go about categorization is to recognize that things are neither completely the same nor completely distinct. To think intelligently, you must choose the level of abstraction (categorization) that suits your task.
To quote David Chapman again:
“Boundaries are always nebulous: vague, changeable, and purpose-dependent. […] Where we draw [the boundary] varies according to what we are doing—and rightly so.”
 This is a revised version of an older post, Categories – v1 (draft). I’m leaving the old version up in case anyone wants to see it (as I wish more writers would, because I love seeing early drafts).
 I know that’s vague, but I read it in Amusing Ourselves to Death (by Neil Postman) and liked it.
 I got this from a Kurzgesagt video, “What Is Intelligence? Where Does it Begin?” (youtube.com/watch?v=ck4RGeoHFko). Specifically, this quote at 0:19: “In a nutshell, intelligence is a mechanism to solve problems.”
Paul Graham talks about the accurate + generalizable combo in “General and Surprising.” (Except he takes accuracy as a given for good ideas, and focuses on the quality of novelty/surprisingness instead.)
Scott Aaronson gives an excellent overview of the boundary-nebulosity problem—including examples like whether whales should be called fish, Pluto should be a planet, and “a tiny exclave of Turkish territory [should exist] in the middle of a Syrian village”—in “The categories were made for man, not man for the categories.”