Is this a car? When the choice is between a Toyota Corolla and a bicycle, the question is clear; but there are plenty of other things that lie on the borders, like a partially disassembled car, a Terrafugia Transition, an El Camino, a Trev, etc. Even the legal definitions that are promulgated by DMVs and state legislatures often fail as advances in technology create new things that the old definitions didn't account for (sometimes as an intentional attempt to sidestep legal limitations: many "smart cars" are three-wheelers for no other reason besides avoiding some of the safety requirements on cars in state laws).
In most cases, we would be better served by assuming definitions are of centers rather than borders. There's a center of the concept of a car that can be typified by something like, say, a Toyota Corolla; and the nearer something is to that, that is, the more like it that the thing is, the more we can call it a car. The point is there is no single, widely agreed upon demarcation at which things stop being cars. While we might still disagree about what is at the center, and where we stop using the word, the concept of dealing with definitions this way saves us from falling into the trap of imagining that there is, or even that there should be, agreement about these things. If your concept of "car" has its center on the Pontiac Mustang, that might differ from the person whose center is the Toyota Corolla, but not enough to cause the kind of intractable disagreements that tend to grow out of definition-based debates (like the abortion debate).
There's a temptation, which one of the posters flirts with, to abandon the value of taxonomy entirely, but this is mostly based on the standard problem of definitions being centers but treated as borders. You can't ever make a border-based definition of what constitutes "classic rock" or "boogie woogie" that is immune to the problem of people disagreeing about whether this band or that song fits into it, because the whole approach, of defining based on borders, is flawed. However, you can certainly make a list of ten songs such that almost anyone would agree that all ten are definitely classic rock, and definitely sit near the center of what classic rock means, and thus convey accurately and usefully a definition of classic rock that isn't plagued by controversy since it doesn't focus its attention on the areas of contention.
That's not incidental, though. That's the whole point. There's a definite style that you could identify which can be best defined by its similarity to "Boogie Woogie Bugle Boy" but which may or may not have a widely accepted name. The fact that it has a definitive center, a Platonic ideal, demonstrates that it does exist conceptually as a category. More importantly, the value of categorization itself is not limited by the fuzziness of the borders -- you just have to stop focusing on the borders.
(The question of whether naming, or as it's usually called pejoratively, "labelling," things, is inherently a destructive or limiting act, is a whole other philosophical subject about which I have written and will no doubt write again.)
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