07.10.2026 Diary XXXVII Sorites: how many make a heap?

07.10.2026 Diary Page XXXVII

Not knowing where the boundary is does not mean not knowing that the two sides are different.

Wednesday. After dinner I looked at the kitchen and for a moment I was undecided: is it messy?

There were three plates in the sink. A pot on the counter. Onion skins next to the stove. At a glance none of them was a problem by itself. But all together they looked like a different place from last night, and I could not say exactly when that difference had begun.

We have been asking this question for two thousand three hundred years.

The paradox of the heap

Sorites comes from the Greek "soros," that is, heap. The paradox is attributed to Eubulides of Megara and it is built like this. One grain of wheat is not a heap. If it is not a heap, adding one more grain does not make it a heap. This rule is applied a hundred times, a thousand times, ten thousand times. In the end you have ten thousand grains and it is still not a heap.

The conclusion is plainly false. Ten thousand grains are a heap. But no step of the argument looks wrong. Adding one grain really does change nothing.

It looks like a game but behind it lies a serious question: words like "heap," "bald," "tall," "messy," "late" have no sharp boundary and we keep thinking with these words. How?

The philosophers' answers

There are a few answers and none of them convinces everyone.

The Stoic Chrysippus' proposal says something in itself: to stop answering questions after a certain point. Cicero reports this. Stopping and falling silent after a point is a way of not entering the paradox.

One of the modern answers says that the boundary actually exists but we cannot know it. According to this view, defended by Timothy Williamson, the heap begins at a certain grain; we just do not know where.

The second says that the meaning of the word stays indeterminate in that region. In the gray zone "heap" is neither true nor false; or it is a matter of degree, half true.

I cannot say which of them is right. But what helped me this morning in the kitchen was what they all share: not being able to find the boundary does not mean the two sides are the same.

No boundary but there is a difference

This is the strangest side of the sorites. Between one grain of wheat and ten thousand grains of wheat there is definitely a difference. The difference does not appear at a single point but the difference itself cannot be denied.

Daylight is like this too. Between night and day there is no sharp boundary; but nobody mixes the two up.

My kitchen is like this too. Mess does not begin between one plate and two plates. But between one plate and twenty plates it has begun, and somewhere between the two there is a transition. Not knowing the exact place of the transition does not stop me from knowing that the kitchen was messy that evening.

Why it matters so much in ADHD

Because my problem is exactly the boundary not being visible.

Mess accumulates slowly and every step is reasonable by itself. Leaving one plate is not a crime. The second is not either. The accumulation grows at a speed nobody notices, and one day, suddenly, it becomes a heap.

In the visible place article I spoke of an upper limit for things left out in the open: for me around seven, more than seven blends into the background. I cannot say why that number is exactly seven.

This is exactly what the sorites says. There is no natural boundary, so I have to set one. Seven, eight or six could do. There is no right number; but having no number is worse than having a number.

What an arbitrary boundary is good for

This sounds like a contradiction: obeying a boundary while knowing it is arbitrary.

But in law we know this very well. There is nothing natural about the age limit of eighteen. Between someone seventeen years eleven months twenty-nine days old and the next day there is no difference in maturity. Still we have to draw a line, because without a line no decision can be made.

An arbitrary boundary does not have to be the right boundary; it has to be a usable boundary. For it to be usable three things are enough. That it be simple, that it be visible, and that everyone, in this case I, can apply it in the same way.

The boundary I found for the kitchen is this: when there are four plates in the sink, they get washed. Not three, not five. Four. Why four? There is no reason. Its being a number is enough.

The trap of the small step

The second face of the sorites is more uncomfortable, and I have to write it too.

The same logic works in the direction of recovery as well. Washing one plate does not make the kitchen clean. The second does not either. None of the small steps makes a difference by itself, and so it feels as if none of them is worth taking.

This is the silent argument of not being able to start. If I wash one plate nothing will change. This sentence is true. And this sentence, like the sorites itself, is true at every step and false at the end.

The way out is to judge the set, not the step. Instead of asking whether one plate changes the kitchen, asking whether the habit of washing changes the kitchen. The answer is clear.

I suppose that is why the two-minute rule works: it takes the single step out of calculation and turns it into a starting movement.

Law lives with vagueness

The field that lives most comfortably with this paradox is law. Statutes are full of words like "reasonable time," "immediately," "serious fault," "without delay," and none of them has a numerical definition.

The reason for this is not neglect. Drawing the boundary with a number would produce an unjust result in every case. For the breach of a contract, is a "reasonable time" five days or ten days? It changes with the situation, and someone who knows this does not try to draw the boundary with a ruler.

But in some areas law chooses to draw an arbitrary line: limitation periods, the age of majority, forfeiture periods. In these the cost of uncertainty is very high. That the line is sharp matters more than that the line is right.

This double stance is, I suppose, the practical solution of the sorites: where things stay vague we trust judgment, where uncertainty does harm we trust the arbitrary line.

The boundary of being late

On the ADHD side the concept that produces the most sorites is time. How many minutes late counts as "being late"?

Two minutes nobody cares about. Fifteen minutes is a problem in most settings. Somewhere in between, the boundary is unclear but the effect is real. In the other person there is a moment when they say "this is now being late," and that moment changes from person to person.

As I described in the chronic lateness article, my problem is not that I do not know the boundary; it is that I do not feel when I have crossed it. Time blindness does not tell me at which point I am while walking inside a blurry boundary.

The solution is again an arbitrary line: writing the departure time backward from the arrival, setting the alarm to the departure time. The line is not natural, it is a necessity.

The inbox

Though not as concrete as the kitchen plates, email too is a heap.

One message going unanswered is not a problem. The second is not either. But at some point the inbox turns into a room that is not opened, and I never notice that point. I described the emotional side of this in the email paralysis article.

The sorites says the same thing here: if you cannot find the boundary, set one. When the number of unread messages passes twenty, set aside a day. Twenty is not the right number but it is a line.

Whether the line works depends less on the number than on there being something to make you notice it: if the number sits in a visible place the line works, if it is left to calculation it does not.

What I listened to today

Arvo Pärt: Pari intervallo.

The title is Latin, it means at equal intervals. The piece was written for organ, in his first period of the tintinnabuli method. The notes move in small and equal steps, no step bigger than another.

While listening I cannot say at what moment it changes. There is something at the beginning, something else at the end. I cannot find the boundary between them and I am sure the two are not the same.

Tomorrow

Tomorrow is Thursday. I will keep trying the four-plate limit in the kitchen. I know the number is not right; it is enough that it exists.