I love the amount of effort that went into this, and find it very amusing. I've had similar forays into defining sandwiches, ravioli, soups, and so on, but never in such meticulous detail.

But taking it seriously, a word like "salad" is best understood, IMO, as a family resemblance [0]: a group of inconsistently overlapping properties. Or, you could understand it functionally/pragmatically (a salad is what I order when I want a salad), where the meaning is not derived from an internal property but from the social system that produced it.

For salad or sandwich, it's all rather unimportant, naturally. But I do think taking this step back and questioning what it even means for an utterance to have meaning can help dissolve some serious and otherwise contentious philosophical issues. ("Intelligence" seems to be a rather relevant example.)

Mathematical definition is enchanting to those of us with an inclination towards abstraction. But just because it's a noun doesn't mean it's a thing --- or at least, not a thing independently of the speaker and their community of speakers.

[0] https://en.wikipedia.org/wiki/Family_resemblance

Yes, I actually think this sort of self-aware silliness (also hot dog sandwich, etc) could be looked at as kind of “koans” of rationality. Ultimately the goal might be to recognise that pure rationality is incompatible with the inherent nebulosity of applying “meanings” to the world, and to embrace that interplay!

Or more likely i’m overthinking it and they’re just a way to have a funny argument with friends.