The Sorites Paradox

The Sorites Paradox also called a Sorites problem, is an argument that arises when a situation is presented in vague terms, or poorly defined circumstances. The name “sorites” derives from the Greek word “soros” meaning “pile” or “heap”.

Curiously, this paradox arose when trying to determine when an amount of grains of sand constitute a “heap of sand” or a “pile of sand” or when there are not enough grains to call it a heap. This paradox is attributed to the Greek philosopher Eubulides of Miletus.

The paradox goes like this: if a heap of sand is reduced by taking single grains of sand one after another, at what exact point does the pile of sand ceases to be considered “a heap”? Removing a single grain of sand at a time does not turn a heap into a non-heap, so the paradox is to find at what point repeating the process of taking away grains one by one turns the heap into a non-heap.

We can also study this paradox by going in an opposite direction; let's start with nothing of sand. Add a single grain of sand: this is obviously not a heap of sand. Adding one more grain is not enough to build a heap of sand; so, what about three grains of sand? How many grains do we need to make a heap?

Obviously, at some amount of grains, we will exclaim: “Now I have a heap of sand!” But if you go backward and extract just one grain of sand out of the heap you just created, can you still make the same exclamation? This is the paradox.