Consensus should determine what's taught in science classes. Why?

No, anything can be arranged in a nested hierarchy. You just have to pick arbitrary divisions. I could for example arrange minerals into silicates and non-silicates, then divide the non-silicates into -ides and -ates, the former into oxides, sulfides, and “other”, and so on. Note that I could use the same criterion twice or more at different parts of the tree, that the order in which I pick the characters is important in determining the hierarchy, and other indices of arbitrariness. Now it’s true that some things lend themselves to a hierarchy better than others, as Linnaeus discovered. But you can still do it. What you are perhaps talking about is a natural or true or discoverable nested hierarchy, and few things fit that well. Life and languages are all that come to mind at the moment.

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Languages at borders between countries do not fit a discoverable nested hierarchy.

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I don’t know what you meant by that.

They tend to be hybrids.

This hybridization is not limited to border regions, though; in Bangalore, the Kannada spoken is 15-25% English. English and Hindi are far more closely related to each other than either is to any of the four major South Indian Dravidian languages (Kannada is one of these).

That makes for a lot of anamastoses in any tree, which violate nested hierarchy.

Ah. loan words. Generally these are considered not to obscure the tree pattern. English is a fine example: a Germanic language chock full of French and Latin loan words.

I’m all but certain that these dialects are borrowing more than words.

What else? Borrowing of grammar is exceedingly rare.

I think that the weird English-French thing that happened starting in 1066 is about the closest thing in linguistics to endosymbiosis. Even now it’s odd how often there’s a fancy way to say something with French-rooted words and a plain way to say it with Anglo-Saxon rooted words. I’ve always wanted to learn enough Old English to read Beowulf in the original, but, oh, the time required! Hwaet!

What about Pidgins, Creoles, Spanglish, Camfranglais, etc?

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thus making it not really nested, as you can’t say that everything with x is within everything with y.

While considering counterexamples I realised that astronomical bodies can be nested by what they orbit (everything that orbits Jupiter orbits the sun), and rivers by what they flow into (Everything that flows into the Thames flows into the North Sea).

What about them?

Now we are descending into semantic hell. What does “really nested” mean? What does “cannot” mean? We make use of many artificial nested hierarchies. The geological time scale, for example, is one such. The Cretaceous is really nested within the Mesozoic, and the Campanian is really nested within the Cretaceous. But it’s still an artificial hierarchy, because they’re all arbitrary divisions.

Similarly, in your hypothetical above, “x” and “y” are not even groups defined within the system; they appear to be character states. If we say x = “is blue” and y = “has four wheels”, we could indeed produce a nested hierararchy in which the group of blue four-wheeled things is nested within the group of four-wheeled things, even though some blue things were not included. But that two would be arbitrary, since there would be no objective reason not to classify blue things as a group in which there where some blue four-wheeled things, with non-blue four-wheeled things outside the group. Still a nested hierarchy, though.

They would appear to be the result of languages intermingling beyond mere loan words.

That there are no violations of the nesting. That if you divide vehicles into “blue / non-blue” and then into “four-wheeled / non-four-wheeled” you will find that either all the “four-wheeled” vehicles are “blue” or all the “four-wheeled” vehicles are “non-blue”.

The Campanian is not partly in the Cretaceous and partly in the Devonian. “Four-wheeled vehicles” would be partly in the “blue” category and partly in the “non-blue” category. Not really nested.

I wouldn’t say so.

That just isn’t true. You will find that some of the four-wheeled vehicles are flue and some of them are not blue. You are confusing character states with defined groups. In your scenario, “blue” does define a group, but “four-wheeled” defines two separate groups, one within the blue vehicles and one within the four-wheeled vehicles. That’s perfectly acceptable for an artificial nested hierarchy.

You again confuse the criteria used to define groups with the groups themselves. In your scenario, “four-wheeled vehicles” are not a group, but “blue vehicles” are, and “four-wheeled blue vehicles” are. Similarly, the army is a nested hierarchy, but every division has artillery battalions, infantry battalions, tank battalions, etc. An individual infantry battalion is a group within the nested hierarchy, but the characteristic of infantry-ness or “infantry battalions” is not a group.

Obviously. It was an example of something that isn’t really nested. I think your “artificial” vs “natural” distinction is the same as the distinction I’m making, just with different terminology.

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Back to what “really nested” means. Or I suppose that all depends on what you think “is” is. Semantic hell.

Well you started it: “a natural or true or discoverable nested hierarchy”. Same thing.

I’d much rather discuss nested hierarchies of rivers or astronomical bodies.

Yet “here only” and “there only,” expressions we simply don’t use in US/UK/NZ/Oz English (not certain about the last two), correspond to single adverbs in Kannada. The same is true for some common adjectives and pronouns.