The paradox

Suppose that your height is 6′3″. Clearly, you are tall. Your friend Tom, however, is only 5′4″ and is concerned about his height. You offer him the following philosophical argument. If two people differ in height by only 0.1″, you point out, then either both are tall or neither is. A difference in height of 0.1″ cannot make the difference between being tall and not being tall. So a person who is 0.1″ shorter than you are (6′3″ - 0.1″) is tall. But then a person who is 0.1″ shorter than that (6′3″ - 0.2″) is also tall. You continue in this way until you reach 5′4″, and can reassure Tom that he is indeed tall. Your friend is neither comforted nor amused.

This sort of paradoxical reasoning can be traced back to the logician Eubulides, a contemporary of Aristotle. It is sometimes referred to as “the paradox of the heap”, since it is commonly illustrated in terms of a heap of sand. (“Sorites” derives from “soros”, the Greek term for “heap”.) Suppose you have a heap of sand consisting of 10,000 grains. Removing one grain surely cannot turn a heap into something that is not a heap. So 10,000 - 1 grains constitute a heap. But then so do 10,000 - 2 grains. Continuing with this reasoning will eventually lead to the absurd conclusion that one grain of sand suffices for a heap.