A word for something whose meaning is well known but defies definition

Question

Is there a word or phrase for:

A word whose meaning is well known within common knowledge but defies a consistent definition.

For instance, if you asked most people to point out an "a", or tell you if a thing is an "a" or a "b", they could easily tell you, but if you tried to define what attributes make up an "a" or a "b" you can not consistently pin down the definition.

An example:

Most people would have consensus on what is a game and what is a sport, but pinning down exactly what attributes makes something a game, and what attributes makes something a sport is difficult.

P.S. I am not asking to define game or sport (although that is interesting in itself). I'm sure there are plenty of clever enough people on this forum who can do so. You may be able to come up with a better example of what I mean, but hopefully you get the idea.

Answer 1

I think ineffable might work. From Merriam-Webster:

Definition of ineffable

1. a : incapable of being expressed in words : indescribable ineffable joy

It is used to describe situations similar to your example, as in

the ineffable difference between great music and that which is merely competent —Raymond Tallis, Reflections of a Metaphysical Flaneur: and Other Essays, 2014

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Edit—I've also found it specifically in the context of "what makes sport(s) special":

The affective claims made for sport, its allegedly ineffable qualities, routinely separate it from other areas —Toby Miller, Sport, Authenticity, Confession (PDF)