I. The Ladder Essay 2
Ten Cups, One Word
Abstract thinking
Put ten objects on a table in front of someone. A tea cup, a coffee mug, a tumbler, a bowl, a vase, a beaker, a jar, a mug with a chipped rim, a wine glass, a paper cup. Now ask: how many kinds of thing are there? Most people will say four or five, and they will group by size, by material, or by whether it has a handle. Almost nobody will say ten. Almost nobody will say one.
That middle answer, the four or five, is the one most of us think of as the world itself. The ten objects on the table are just examples of the four kinds that really exist. But watch what happened. The person sorting them had to make decisions. Which differences did not matter? Nobody said so, because the sorting felt like a recognition rather than a choice. It felt like the objects came pre-labelled and the person was just reading the labels off.
They were not reading labels off. They were writing them. A category is a decision about which differences do not matter for your purpose, and the decision is invisible exactly when it works well. The fewer words you need to cover a lot of things, the better the job the category is doing, and the harder it is to remember that you wrote it yourself.
Here is a school timetable. A school has ninety periods a week to fill and about sixty teaching groups. A rule says: no more than six periods of maths, no group above thirty-two students, no teacher in two places at once, every class must have a room. The timetable setter cannot think about every student every minute. They need a word, and the word is "section." A section is a group of students, a room, a teacher, a time slot, and a curriculum. That word lets you write "section 7B" in a column and stop thinking about it.
Now ask what the word "section" drops. It drops that this group of students has one student who works much better alone, one who needs the room to be moved nearer the door for a medical reason, and one whose parents speak a different first language at home. It drops that the room has bad acoustics and that this teacher's style suits a class who are not already behind. When the setter finishes and the timetable prints, all of that is inside the word. The word is doing real work. The word is also hiding a stack of decisions about which differences the timetable is allowed to ignore.
Abstraction is a lossy compression, and like all compressions it trades fidelity for speed. The word "cup" stands for ten objects, each of which you could hold. The word "student" stands for a person with a name and a temper and a grandfather who died in the spring. The word "revenue" stands for a number that was once a series of specific payments from specific people. Nothing is wrong with this. A photograph of a face is not the face. The point is that a compression is a tool, and a tool that is used without knowing what it discards eventually starts cutting in the wrong place.
It helps to think of the word as a contract. When you say "cup", you are promising that the thing in front of you will hold a drink, that it has a rim, that it can be picked up. Those promises are what make the word safe to use without checking. The chip on the rim does not break the contract. It just sits outside it, and once you have signed the contract you are not obliged to notice it at all. That is the bargain, and it is a good bargain, right up to the point where the chip matters.
Here is where abstraction earns its keep. Compression is not only a way of losing detail. It is a way of gaining reach. Once you have the word "cup," you can say things about cups that you could never say about any one of them. You can count them, price them, store them, compare them, predict what happens if you break one. The word is a variable, and a variable stands for many numbers. That is what makes it possible to reason about a shop that has never been visited, a class that has not been taught, a product that has not been made.
Without the word, you have ten cups and no way to talk about the eleventh. The word "cup" is what lets you order a thousand, or notice that the shop sells four kinds and never restocks the one that sells best. The category is a handle on a lot at once. That is a genuine gain in power, not a consolation prize for losing detail.
What if the ten objects had been given to a shopkeeper with two jobs? Job one: decide which ones go on the shelf for drinking. Job two: decide which ones go in the window as decoration. The shopkeeper will sort the same ten objects differently for each job, and both sorts will be right for their purpose. The tall narrow bottle is "drinkware" in one sort and "vase" in the other. Nothing about the bottle changed. The purpose did.
So if you change the purpose, you should expect to change the categories. If the purpose changes and the categories do not, that is a warning sign. A shop that reorganises its range for a new kind of customer but keeps the old shelf labels is going to mislead someone, and it will be hard to see why, because the labels look obviously correct on their own.
"Categories are given by nature." This sounds reasonable, and it is the source of most of the trouble. It is also hard to hold onto once you look. A ceramic dish with a handle is a mug if you are buying it to drink from, a bowl if you are buying it to hold soup, and a vase if you are buying it for a flower. The object does not change. The category does, because the category answers a question that has changed.
"Abstraction means being vague." It does not. A vague description is "a thing for holding stuff." An abstract description is "cup," which is precise, and the people who use it precisely have agreed on what it commits them to. Vagueness is not knowing what you said. Abstraction is knowing exactly what you gave up in order to say it.
Ten cups become one word, and the word is useful right up until you forget that it was made. This is why the error of treating the abstraction as the thing is so common. Once "cup" is in your mouth, it feels like a fact about the world rather than a tool in your hand. The chip on the rim stops being a chip and becomes a curiosity you noted once, in a different life.
There is a well known philosophical puzzle about this. Pull a duck, a rabbit, a beaver, and a flying duck out of a hat, one at a time, and show them to someone. Ask what they have in common. The duck and the rabbit and the beaver share the property of being animals. The flying duck shares that with the first three and also shares the property of being a duck, which the others do not. No single property is shared by all four. The family resemblance is a feature of how the categories are built, not something the objects possess on their own.
There is a practical version of the same puzzle in any small business. A workshop that sells hand-thrown pottery starts with a single glaze and a single shape. The word "mug" does the work for a while. Then someone asks for a taller version that holds a pencil, and the maker makes one, and it is not a mug, and it does not fit under the shelf label. Now there are two products. The maker calls them both "cups" because "cups" is what the customers say, and the shelf label says "cups", and the inventory system has a field called "cup". The word has been stretched until it no longer tells anyone anything, and the stretching happened one request at a time, each individually reasonable.
Notice what the maker did not do. The maker did not decide to widen the category. The maker decided, in each case, to keep using the nearest word because switching to a new one would have required new labels, a new count, and a conversation with the person who handles the stock. The category drifted, and the drift was the sum of small conveniences. By the time anyone noticed, the word had stopped being a tool and become a place where information went to be lost.
So the edges are drawn. Somebody drew them, for some purpose, and the drawing is usually forgotten. This is not a flaw in the categories. It is what makes them usable. You could not pour a drink if you had to re-derive the boundary between cup and bowl every time you picked one up. The edge has to be settled and stable, and settledness looks like naturalness from the inside.
The interesting failures are not in the categories you settled. They are in the categories you have not revisited. A shop adds a new product line and files it under the nearest old category, because filing it under a new one would require relabelling the shelf labels and rethinking the count of how many kinds they stock. The label says "kitchenware" and now it holds a thing that is not for the kitchen. Nobody notices for a year.
There is a second kind of failure, which is more interesting. A category that was drawn for one purpose gets borrowed for another. The school timetable "section" is fine as a unit of timetabling. It becomes a problem when the school counts sections, and the count of sections becomes a target, and now the school has an incentive to create sections that are easy to count rather than sections that work. The word "section" was doing fine. The word "number of sections" was built on top of it, and the new word never asked what it had given up. This is the subject of Perfectly Optimized, Pointless.
Category edges are not the only thing abstraction decides. It also decides what counts as an instance at all. In a small workshop that makes and sells ceramic pieces, the maker sorts the work into cups, bowls, and "other." That third pile is where the experiments go, and it is the pile that is hardest to defend to a customer. Yet the pile is doing something valuable. It is holding the things that have not yet found their category, which is where new categories come from.
Every category was once an "other." That is worth sitting with. The category you use most fluently was invented by someone who was once in the awkward position of having a thing that fit nowhere. The person who put the first tea cup on a shelf in a coffee shop made a category, and the category then looked obvious to everybody who came after. This is not an argument against categories. It is an argument for keeping one eye on the pile marked "other," because that is where the next one comes from.
There is a test for this, and it is slightly uncomfortable. Ask what your category would look like if it had been drawn by somebody whose purpose was different from yours. Take "meeting." Drawn for the purpose of sharing information, a meeting is a group of people with a topic. Drawn for the purpose of making a decision, a meeting is a procedure with a chair and a deadline. Drawn for the purpose of letting people who work together like each other, a meeting is a ritual. The word is the same. The category is not. Once you see that the word is doing several jobs at once, you can ask which job you are actually using it for, and you can check whether the others are quietly costing you something.
Limits
Abstraction cannot tell you whether your category is the right one. It can only tell you what your category commits you to. You can reason perfectly inside a category and still have chosen badly. The tool cannot inspect itself, which is a real limit and not a minor one.
Abstraction also cannot be the last step. A category is a compression of things you have already looked at. If you compress before you have looked, you compress nothing. An inspector who has never seen the product and only knows the category name has a name, not a judgment. This is the failure the site keeps circling: each level is built from the one below, so skipping down leaves the one above standing on air.
And abstraction carries a hidden cost that is hard to price. Every compressed decision is a rule you will not think to revisit. The category does not just describe what you see. It changes what you can notice next, because you will notice what fits and fail to notice what does not.
There is a fair objection to all of this. If every category is a decision and every decision can be wrong, then nothing can be relied on, and the whole apparatus collapses into permanent doubt. That is not what is being claimed. Most categories are good. The shelf label is right about most of the things on the shelf. The point is narrower and more useful: a category is a bet, and bets should be held consciously enough that you can collect on them when they pay off.
Stuck
You are stuck in abstraction when your category starts doing the work that looking should do. The tell is a sentence like "that's just a cup" or "it's really a standard case" that ends a conversation. It means the word has become a wall instead of a handle.
The way out is to make the decision visible again. Write down what your category is for. Then find one object that your category handles badly, and look at that object for five minutes without using the word. If you cannot find one, you are not using a category. You are using a word as a wall, and you have stopped seeing with it.
Sources
- The family resemblance puzzle appears in Wittgenstein's later work on category boundaries; the general idea is widely discussed in philosophy of language.
- Reification, treating an abstraction as a concrete thing, is a standard term in the social sciences and in continental philosophy.
- No specific studies are cited; all examples here are hypothetical or ordinary operational situations.