Wittgenstein used “game” as an example of a word that we can use effectively even though the examples are highly various. Some games are competitive, some are fun, and some have rules– but some have none of these features. Indeed, Wittgenstein thought that there was no defining feature of “games,” but there were many individual games that were similar to many others. The word marked a cluster of cases that one could learn to “see” without being able to identify a common denominator. It might be right or wrong to call a given object a “game,” but the test would not be whether the game met any particular criterion.
My favorite example of such words is not “game,” but “curry”–a kind of hobson-jobsonism derived from a Tamil word meaning “sauce or relish for rice.” But there are plenty of curries served without rice, and plenty of rice sauces that aren’t curries. Webster’s defines the English word “curry” as “a food, dish, or sauce in Indian cuisine seasoned with a mixture of pungent spices.” But there are millions of curries that don’t come from India, and some Indian curries are not particularly pungent.
Here are the ingredients for two curries, taken from cookbooks in our house. 1) Whole chicken, onions, blanched almonds, coriander seeds, cardamom pods, pepper, yogurt, salt. 2) Flank steak, peanut butter, coconut milk, basil leaves, fish sauce, sugar, cumin, white pepper, paprika, galanga root, kaffir lime leaves, cumin, coriander, peppercorns, lemon grass, garlic, shallots, salt, and shrimp paste. These recipes both contain coriander and salt, but it is not hard to find other curries without the coriander, and you can leave out the salt. It is hard to find any two curries that share absolutely no common ingredient. Yet the ingredients that any two share may not be found in a third.
If “curry” cannot be defined by its components, perhaps it refers to some cooking method? Many curries involve pastes or thick sauces composed of ground ingredients. But that’s also a good description of romesco sauce from Catalonia, pesto from Italy, or chile con carne. No one would call a minestrone with pesto a curry. We could try to define “curry” by listing countries of origin. But there are dishes from India that aren’t curries. “Country captain” is arguably a curry of English origin. And what about adobo from the Philippines or a lamb stew from Iran? Curries or not?
In short, you can teach or learn the correct meaning of “curry” (albeit with some controversial borderline cases), but you cannot define it in a sentence that will communicate its meaning. Learning requires experience. I believe the same is true of “love,” “happiness,” and “virtue”–but that’s another story.