The Sorting Machine Is Not a Thinking Machine

In 1955, George Kelly wrote something that turned out to be useful seventy years later in a way he couldn't have anticipated.

He was making a point about statistics. He said that before any mathematical operation can happen, before sorting or counting or calculating, someone has to perform a prior step. Someone has to decide what counts as data. What gets grouped together. What the relevant similarity is. What is being measured. He called this the concept-formation task and argued it is basic to any conclusion you reach through computation. The math tests your construing. The math does not replace your construing.

This sounds technical. It is actually one of the more important things ever said about thinking. And in 2026, it names with surprising precision what is going wrong in how we are using AI.

What Kelly actually said

Kelly's claim is developed across several pages in The Psychology of Personal Constructs. He returns to it with different illustrations: cows and horses, chi-square tests, simple counting. The point throughout is the same. Every statistical or mathematical operation rides on top of a prior decision about what counts as same and what counts as different. The numbers can only sort the categories you give them. The numbers cannot create the categories.

He illustrates this with a passing line about a sorting machine. A machine, however sophisticated, can sort what you put into it. It cannot decide what to sort by. That decision is the concept-formation task. It is the prior step.

The illustration was throwaway in 1955. In 2026, the sorting machine is no longer a thought experiment. It is the thing on your laptop.

What an LLM actually is

A large language model takes a massive amount of human-written text, converts it to numerical tokens, builds a statistical map of which tokens tend to co-occur, and generates output by predicting the most probable next token. That is the entire mechanism. There is no thinking step. There is no point at which the model decides what counts as data, what is similar, what is being measured. It sorts.

The training data, which is to say every book and paper and website written by humans, was created by people who had already done the concept-formation task. They decided what to write about. What mattered. What was similar to what. What contrasted with what. The model inherited the output of their construing and sorts it statistically. The concept formation happened upstream, in the writing. The model does not perform it.

This is description, not polemic. What follows is the polemic.

What this means for the user

Everyone can see the symptoms of how LLMs are being used. Declining critical thinking in students. Executives accepting confident nonsense from AI tools. Junior workers losing the skill of slow reading because they ask the model for summaries. The now-familiar pattern of someone using AI to write an email that says less than they would have said in three sentences themselves. Kelly's framework gives us the mechanism underneath the symptoms.

The mechanism is this. People are outsourcing the concept-formation task to a machine that does not perform it. The machine performs the computation at extraordinary scale. What gets skipped is the operation before the computation. The step where you decide what's relevant, what counts, what the abstraction is, what makes one thing the same as another and one thing different. That step is, in Kelly's framework, where thinking actually happens.

When you hand that step to a sorting machine, the step does not happen faster or more efficiently. It does not happen at all. The machine sorts. You receive sorted output. The operation Kelly placed at the foundation of cognition gets skipped. Nobody performs it.

The output looks like thinking because it is composed of thinking-shaped tokens, statistically arranged. The fluency of the output is mistaken for the quality of the construing underneath. Construing was never performed.

What this means for learning

Kelly was specific about something most learning theorists were not. He said his theory offered, in his words, "a learning theory in which learning is considered so universal that it appears in the postulate rather than as a special class of phenomena." Learning, for Kelly, is not a separate thing that happens in classrooms or training programs. Learning is construing. The Fundamental Postulate of his framework, "a person's processes are psychologically channelized by the ways in which they anticipate events," describes a creature whose entire ongoing existence is the formation and revision of constructs.

This means that when people outsource concept formation to AI, they are skipping the operation Kelly placed at the foundation of being a person who learns at all. The construing does not happen faster. It does not happen.

What you have instead is a person who receives sorted text, anchors their next thought to that sorted text, and slowly loses the practice of doing the prior step on their own. The construing muscle atrophies. The person becomes increasingly unable to perform the operation that, in Kelly's framework, is the operation that makes them a thinking person.

This applies everywhere construing happens, which in Kelly's framework is everywhere. In school. At work. In relationships. In making sense of daily experience. The same person who lets the model write the email is the person who, over time, stops noticing things that needed naming.

The obvious pushback

The likely objection to all of this is: obviously LLMs don't do concept formation. Everyone knows that. They are statistical models. This is not news. Nobody actually thinks the machine is thinking.

That objection is half right. At an intellectual level, most people would agree the machine isn't doing what humans do. But the gap between what people intellectually acknowledge and how they actually use the technology is where Kelly's argument has teeth.

A few examples of the gap.

Why do people call model failures "hallucinations"? The word implies the machine is trying to represent reality and occasionally getting it wrong. Kelly's framework suggests it was never representing reality. It was sorting. Calling the failure a hallucination locates the problem in a deviation from accuracy, when the actual issue is the absence of the operation that produces accuracy in the first place. The misnomer matters because it shapes how we try to fix the problem. We train the model to hallucinate less, meaning we try to make the sorting more accurate. The structural issue is that there is no concept formation happening anywhere in the loop.

Why do people use AI output as a "starting point" for their own thinking? A starting point implies the concept-formation task has been performed and you are now refining the result. If the machine didn't perform it, what you are receiving isn't a starting point. It is sorted text. Using it as a starting point means anchoring your own construing to an output that was never construed. You are revising a draft that no one wrote.

Why do people feel more confident in their answers after consulting an AI, even when the AI is wrong? If they fully understood the machine was sorting, this wouldn't happen. The confidence comes from treating the fluency of the output as evidence that careful thinking went into it. The output is articulate, so the underlying operation must have been good. But the operation was sorting, which is articulate by design and uninformative about whether anything was construed.

Why are AI companies investing heavily in making models sound more thoughtful, more cautious, more "reasoning"? Because the market value depends on the perception that the concept-formation task is being performed. If everyone genuinely understood the machine sorts but does not construe, the product would be positioned very differently and priced very differently.

The argument is not that people don't know LLMs are statistical. It is that people know it abstractly and behave as if it isn't true. The behavior is what matters. Kelly's framework gives us precise language for the operation that is missing, which makes the behavioral inconsistency harder to maintain.

Is Kelly even talking about this?

Fair to ask. The sorting machine line is a passing remark in a passage about statistics. Kelly was not writing about AI. Am I building too much on an illustration?

The illustration is passing. The argument the illustration belongs to is the central point of that section of his book. Kelly develops the same claim across several paragraphs and several examples: that the concept-formation task precedes and is basic to any mathematical or statistical conclusion. The sorting machine is one of several ways he makes the point concrete. The argument is the principle. The line is just where he gets compact about it.

That the illustration became literal seventy years later does not make the argument anachronistic. It makes the argument testable against a case Kelly couldn't have anticipated. The argument holds. The principle of concept formation as a prior, irreducible operation is exactly what is missing from current AI use, named precisely, by a framework developed before computers existed.

This is what happens when someone identifies a structural feature of cognition at a level deep enough that the description survives every change in the medium.

What already exists in the literature

Two published papers connect PCP to AI. Pavlović (2025) uses constructivist principles to design better human-AI collaboration, focusing on the interaction rather than the structural question of what the AI is doing underneath. Raj et al. (2023) use Kelly's framework to build more inclusive construct definitions for AI training data, essentially doing the concept-formation task for the model, which inadvertently demonstrates the exact point Kelly made.

Neither paper makes the premathematical argument. Neither says: Kelly identified the specific operation that LLMs don't perform, named it in 1955, and explained why no amount of computational sophistication compensates for its absence. That argument is what this essay is.

Why this matters for what comes next

The argument is not "AI is bad" or "people are using AI wrong." Both are familiar claims and largely beside the point. The argument is that we have, as a culture, started outsourcing an operation Kelly identified as the operation in which thinking actually happens. The mechanism of that outsourcing is invisible to most users because the output looks like the result of thinking. The machine is genuinely good at producing thinking-shaped output. It is also, by design, not doing the thing the output looks like the result of.

What follows from naming this operation precisely is that you can decide, deliberately, when to let the machine sort for you and when to insist on performing the concept-formation task yourself. There are situations in which sorting is exactly what you need. There are also situations in which the work demanded the prior operation, and accepting sorted output instead is the difference between learning and not learning, thinking and not thinking, growing and not growing.

The fluency of LLM output is going to keep getting better. The mechanism is not going to change. Whether the people using it are still performing the concept-formation task is the question. Kelly gave us, decades early, the vocabulary to ask it.