An ancient philosopher once asked the following question: Take a million grains of sand and place them in a pile. Surely, it is a heap of sand. Now remove grains, one by one. Eventually, you have naught but a single grain of sand.

Obviously, this single grain of sand is not a heap of sand. But it also seems obvious that no heap of sand can be reduced to a non-heap by the removal of a single grain. Which grain of sand, precisely, demoted the heap?


Eubulides thought he had devised quite the paradox. Unfortunately, Eubulides had a poor grasp on the difference between his labels and the things they label.

The label “heap” is an arbitrary word that humans may or may not choose to apply to the grains of sand. Whether or not they choose to apply the label has no bearing upon how reality actually works. Reality does not care about your labels. Labels are prescriptive rules which you attach. There is no guarantee that reality matches your labels. Indeed, it often doesn’t.

The label “chair” does not describe a hard, well-defined, absolutely fundamental cluster of objects. There are many things which straddle the borderline – partially broken chairs, objects that are comfortable for sitting but were not intended for sitting, decorative chair-shaped objects, tall stools with small backs: and yet, it does no matter whether you count these borderline objects as chairs or non-chairs. There is not an intrinsic property of everything which is either “yes” (for chairs) or “no” (for non-chairs). When you argue over whether a broken chair counts as a chair, you are not trying to uncover the hidden chair-ness: you are deciding whether or not to apply your label.

The universe doesn’t care either way. The broken wood of the maybe-chair will act identically regardless of whether you call it a chair or not. The word “chair” is a fuzzy human label on a broad category of objects. The edge of that category has no meaning. You do not gain profound, deep insight by agreeing to count the broken chair as a chair. You do not learn anything about the splintered wood: you only learn something about your mind, and how it applies labels.

Similarly, it does not matter when you stop calling the heap of sand a “heap” – there is no hidden variable that reality has attached to the sand which changes from “yes it’s a heap” to “not a heap” when you remove that magical borderline grain. The properties of the sand do not change. There is no truth of reality to be uncovered: there is only the question of where you choose to place your labels, and it doesn’t really matter.

The philosophers of old imagined that the pile of sand itself, as an object, must instrinsically switch from heap to non-heap at some point. They also believed that removal of a single grain was never enough to cause a heap to become a non-heap. This was the root of their paradox.

They failed to realize that the sand itself does not posses it’s heapness – the label “heap” was applied within their own minds. The sand stopped being a heap whenever they no longer felt like it was a heap, and that’s all there is to it. They went looking for meaning in the boundaries of their labels, but the sand was none the wiser.

Do not look for meaning in the edges of your words: there is none to find.