On the semantics of uniqueness

I've mused occasionally for a while about the semantics of the concept of “uniqueness”. I've seen it asserted that uniqueness is essentially a boolean quality: something is either unique or it isn't. There's no comparative or superlative form of unique: uniquer, uniquest (although having written that, those sound pretty cool!). And the first two definitions from Merriam-Webster seem to agree with this: “being the only one : sole; being without a like or equal : unlike anything or anyone else : unequaled”.

But when I find myself pondering the concept, it feels like there should be degrees of uniqueness. For one thing, if we're talking about real objects, then every thing larger than a single molecule is technically unique at some scale. But that renders the concept rather useless as a word. If have a set of five “identical” rubber ball, four white balls and one blue one (⚪⚪⚪⚪🔵), it makes sense to describe the blue one as unique compared to the set of all of them, even if they technically are not all perfectly identical (and thus are all technically “unique”). So there's some tolerance built-in, within which we consider things to be identical for the sake convenience. That's fine – we live in the real world, not an ideal one.

Now consider a set of five balls, all of different colors. ⚪🔵🟢🟠🟣 It makes sense to describe each one (within the set) as being unique: they're all different from each other member of the set in terms of color, which is a concept we generally attach importance to. (Though I just realized I haven't considered color-blind people in this example; I should remember that for the future.)

But what if we add an elephant to that set? ⚪🔵🟢🟠🟣🐘

Every item in the set is still technically unique – but it certainly feels as if the elephant is somehow more unique than the other items. It's more different from all of them than any of them are from each other. Remove any one item from the set and the diversity (in pretty much any metric) will be at a global minimum when that item is the elephant. Calling any of the balls unique – while technically true – seems somewhat understated in the face of the literal elephant in the room set.

I was prepared to argue this point more, until as I was looking unique up in the online Merriam-Webster dictionary I noticed a third definition, and a usage guide. The third definition reads “very special or notable : unusual”, and the usage guide notes that:

Unique is often cited as a word that should never be modified by terms like somewhat or very. The thinking is that unique properly only describes what is unequaled or otherwise distinct from all others. Just as something cannot be more "only" than another, it cannot be more unique than another. This logic fails, however, when we consider that unique can also mean "unusual" or "rare," as in "a unique opportunity" or "a unique feature." In these cases, phrases like "very unique" are standard.

 “Very”, I would argue, is just an intensifier adverb like “more” is, so I think it's ultimately fine to consider something more or less unique; it's expressing something about the ratio of how similar it is to other things in whatever set we're including it in vs. how similar those other set members are to each other. (You could probably come up with a mathematical definition for this in terms of set theory, but I'm not sure I know enough about it to do so.) But that's just my take on it, and it is, ultimately, semantics. Feel free to chime in in the comments! A hui hou!