All abstract objects can always be classified. This is the foremost, necessary property upon which their very existence is predicated, and by which their very existence is made possible. There can't be such a thing as an unclassifiable abstract exactly like there can't be such a thing as a dimensionless cup of milk -- it's not that classification comes after abstraction anymore than dimensions come after the milk. They might've been observed later, as an artefact of historical accident, but that accident is irrelevant. Dimensions predate the milk and furthermore milk only exists as a mere function of whatever dimensions there are available ; classification predate abstracts and furthermore, any one abstract only exists as a mere function of whatever classifications there are available.i
All concrete objects are unclassifiable, again as a necessary, fundamental property of what concrete existence even is.ii Nevertheless, in a hopeless, desperate and ultimately doomed attempt to derive some of the benefits of classificationiii into the objective world, a hack's always invented. For instance -- living organisms, as eminently unclassifiable as any other concretes, are nevertheless classified into systematic taxonomy by use of the imaginary "typical representative", an item which neither exists nor could exist, but is useful.iv
Needless to say this hack is immensely expensive, and what's worse -- it's expensive in proportion of the use you make of it. It's like rent, basically, rent for existence in the world.
Which is, ultimately, the problem of classification : that while it's the only possible approach to anything, it is strictly speaking impossible in all useful contexts, and not so strictly speaking expensive enough to make the alternative tempting.
Yet... what alternative is there ?———
- This is why "creativity" as exhibited by they possessed of very few classification trees very sparsely populated is universally such sadness ; and this is why they say if you want to write well you'd better read a lot ; and this is why Roman numerals preclude serious astronomic or geometric work.
The only known substitute for these trees is a head full of cockroaches, simple bits of nonsense that process abstracts in some intrinsically limited* fashion, rather exactly like how genetics work in live cells : there's some "take all blue things with a red square and match them up with red squares touching" and such basic, localized processing. If you have a lot of time and a lot of resources you can of course wait for natural selection. Takes a while though.
Takes so long, in fact, that a perfectly reasonable notion of "Judgement Day" would be that all humans who ever lived are gathered up, the total variety of expression as actually expressed is compared to what variety of expression was meaningfully available in the first place through the simple mechanism of dividing it by the naturally occuring quantum of such variety. The factor separating Vmax from Vnatural is mindboggling infinity, but you (in the collective sense) are held to match a small threshold, say three. 3. That's it. If, from Begining to End you've not managed to reach at least three times as much as'd have naturaly flown out of things, you go straight to Heck -- and possibly wouldn't be the first set there, either.
* This link is a stand-in ; the actual item I wanted to link is a discussion of silicone fabrication, the production of CPUs and such cyberconsiderations relating the matter to the physics of the brain, the whole illustrated with a square of randomly distrubuted black dots (making the point that random walks are very slow to yield anything interesting by the workings of the very definition of "interesting"). [↩]
- Would "virus testing" even be a thing, if this weren't the case ?
Suppose you're paying for sex, so you pick up the phone, and order a whore. Now, did they send you a whore with or without some arbitrary virus you're thinking about ? And how would they know ? [↩]
- Which is readily the most powerful thing there is, ever was, or ever could be -- in fact, necessarily the only basis upon which any such thing as power can even exist, in any definition and to any degree. [↩]
- If you have trouble with the concept, think of a dog show. You know, like competitive.
What is is that they do at the dog show ?
If you're unhappy with how they scored your dog, and ask them to produce for your own inspection the model they compared it with, what are they likely going to do ? [↩]