Imagine we have 0 grains of sand. Do we have a heap of sand? Of course not! Well, what if we add one grain? We obviously still do not have a heap. Okay, what if we add one more? One more after that?

**No matter how many grains of sand we have, adding just one more will never turn a non-heap into a heap. **This is called the “tolerance principle,” and it is the defining feature of *vague* properties. It says that a small enough change can never alter the applicability of a vague property.

Say you have a red shirt. Change the frequency by an imperceptible amount. Obviously, the shirt is still red. Take someone who is sober. One ml of beer will not make that person drunk.

A problem appears when we compound these small increments. Here’s a version of the argument:

*1) 0 grains of sand is not a heap (premise)*

*2) 1 grain of sand is not a heap (by #1 & tolerance principle)*

*3) 2 grains of sand is not a heap (by #2 & tolerance principle)*

*…*

*10001) 10000 grains of sand is not a heap (by #10000 & tolerance principle)*

Welcome to the sorites paradox (“sorites” = “heap” in Greek), the argument that allows us to prove that a 90-year-old woman is a child, a blade of grass is red, and Danny DeVito is tall. It was invented by Eubilides sometime in the 4th century BCE, when he also invented the Liar and a few other paradoxes.…