Categorising nouns

Question

Can anybody come up with examples where a noun can be categorised twice, but neither of these categories is considered a complete subset of the other?
I'm looking for examples strictly in the form of two statements: 1) 'an X is a Y' and 2) 'an X is a Z', where these statements have the constraint that Y is not a subcategory of Z, nor Z a subcategory of Y. [X,Y,Z are always nouns preceded by an indefinite article]
Examples that don't work:

A cat is an animal. A cat is a creature.

This fails because an 'animal' is a 'creature' (we can categorise one category as a member of the other)

Running is a hobby. Running is a sport.

The constraint is satisfied because one wouldn't generally classify 'hobbies as sports', nor 'sports as hobbies'. However, the example doesn't work because it's not of the form 'an X is a Y' (we would need to write 'a running is a sport', which is wrong grammatically).
Note: in the second example, although some hobbies are sports and some sports are hobbies. one category doesn't fit fully into the other, so is considered to satisfy the constraint.

Avner Shahar-Kashtan · Answer

While some of your constraints seem a bit arbitrary, they can still be satisfied:

A restaurant is a business
A restaurant is a location

The two categories aren't subsets of each other, but a restaurant is both.

BoldBen · Answer

There are many of these, here are a few (with justifications)
A car is a machine / a car is a means of transport
(Not all machines are cars / riding animals are means of transport)
A house is a building / a house is a dwelling
(Not all buildings are houses / caravans {trailers if you're American}, caves, tents, bungalows and flats {apartments if you're American} are all dwelling places but not houses)
A walkie-talkie is an electronic device / a walkie-talkie is a means of communication
(Not all electronic devices are walkie-talkies / not all means of communication are walkie-talkies)
I could go on but I think that demonstrates the idea.
By the way there is another way of expressing your requirement: you could say that each pair of statements places the noun into two sets neither of which is a subset of the other but which have an intersection containing the noun.

Anton · Answer

Challenging question. My mind laboured over it. This is a combination of basic set theory and ambiguity. If X, Y and Z are all sets with one meaning and if X is in Y and X is in Z, then Y and Z intersect. If two sets intersect, one possibility is that they do so with non-empty complements, which means there may be a set Z that satisfies your criterion.

OK, so it should be easy to find a few examples of such sets but I did not find it so: gardens and plants both contain flowers but gardens do not contain all plants nor plants contain all gardens; apertures contain windows and houses contain windows but houses are not contained in apertures nor apertures in houses.
If you insist on the A is a B type of statement, I find it even more difficult. Water is a necessity; water is a liquid. Necessities and liquids overlap but neither includes the other. Sugar is a food; sugar is a hydrocarbon. Food and hydrocarbon do not overlap.
Added example: Hydrogen is a gas; Hydrogen is an element; not all gasses are elements nor all elements gasses.

Categorising nouns

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