Existence

"Unique" is surely an absolute. Something either is different to anything else or it isn't. So, suppose I have a collection of 100 CDs (and I'm referring to titles, rather than the physical objects). If someone else had 99 of the same CDs in their collection, then mine would only be 1% different, but it would still be unique (obviously assuming that no-one else had the exact same collection). However, if I again have a collection of 100 CDs and the closest anyone could get to having the exact same collection is to just match with one of my CDs - my collection would be 99% different, and would be unique. Both collections are unique, but is one more unique than the other? If so, surely being 'unique' isn't an absolute but a question of degree. If neither are more unique than the other, how can they both be equally unique if it would only take 1 changed CD to match someone elses collection (and lose the unique status), but with the other it would take 99 changed CDs to match another collection.

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We use language to draw distinctions of various kinds. Some suchdistinctions are binary -- such as that between prime and nonprimenatural numbers or that between pregnant and nonpregnant female personsand animals. Other such distinctions are scalar -- such as that betweenobjects called long or short, fast or slow, North or South, suggestinga scale along which things can be ordered. Yet other such distinctionsare plural -- such as the distinctions we draw by means of colorpredicates.

As your example brings out, distinctions ofdifferent kinds can sometimes be applied within the same space. In thespace of colors, for instance, we might operate with a simple binarydistinction (blue/nonblue) or with a scalar distinction (bright/dark)or with a plural distinction (mauve/crimson/turquois/...). Similarly,in regard to CD collections, we might operate with a simple binarydistinction (unique/nonunique) or with a more complex scalar or pluraldistinction.

Which kind of distinction we employ typicallydepends on the purpose at hand. A guy locked out of his apartment maywant to distinguish among keys in a simple binary way according towhether they do or do not fit his door. An avid key collector, bycontrast, may draw much more complex distinctions among keys.

The air ofparadox in your example arises from the fact that you place a word --"unique" -- used to mark a binary distinction into a context in which amore complex distinction would seem more appropriate. When assessing aCD collection as indicative of her owners taste, we are typically notsimply interested in whether her collection does or does not matchsomeone else's precisely. As you suggest, we are usually interested also in thedegree of overlap between her collection and its closest match -- aswell as (I would add) in how her collection compares to yet furthercollections.

This being so, we can nonetheless avoid yourparadoxical (or revisionist) talk of CD collections being more or lessunique. We can instead make the point in different language, with aword like "distinctive," for example. A CD collection is the lessdistinctive the more overlap there is with its closest match and themore overlap there is with other CD collections more generally.

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