How would you describe the sand in this picture: as a collection of grains or a heap?

This short article is the last of a three-article series on paradoxes in philosophy. You can read the other two, on Russell's paradox and Moore's paradox, here and here.

Today we travel back to Ancient Greece to the times of Eubulides of Miletus, who is usually credited with ‘sorites paradox’, which goes like this.

Picture a single grain of something—say, rice, wheat, or sand. Let’s go with sand. Start with one grain. Then add one grain at a time to your collection. Here’s the paradox.

In our description, when does the collection of grains become a heap? It never seems to. According to the language we used to describe the collection—through ‘grain’—the sand always remains granular, no matter how many grains we add.

We can work in reverse, too: if we start with a heap of sand and take one grain away at a time, we are always left with a heap.

Thus, howsoever we start in our description, sand always remains as either a collection of grains or a heap: it cannot change from one to the other. Intuitively, this doesn’t sit well: we ordinarily put so much trust into language—and then it goes and lets us down like this!

‘Heap’, then, is a ‘lazy term’; and, with it, sorites paradox exposes the vagueness of language (whereas the last two paradoxes we discussed expose limitations of mathematics and epistemology). Like ‘old’, ‘tall’, ‘bald’, ‘grey’, and many other terms, ‘heap’ is used in predicates (e.g. ‘is a heap’ or ‘is heap-ish’). But in doing so we elicit the blurred boundaries of our descriptions—we aren’t describing anything properly!

To conclude, ‘sorites’ derives from ‘soros’ and translates from Greek to English as ‘heap’; but turning a description of grains of sand into a heap of sand, or vice versa, isn’t so easy a translation.

So next time you describe something, TRY NOT TO BE SO LAZY and just say exactly how many grains there are!