Vagueness: The Sorites Paradox

Sorites Paradox

Want to learn more about the Sorites Paradox? Check out my interview with philosopher and logician Graham Priest.

The “sorites paradox”, or paradox of the heap (“sorites” = “heap” in Greek), goes as follows: 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 light 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)

It’s easy to see that this type of argument allows us to prove that a 90-year-old woman is a child, a blade of grass is red, and Danny DeVito is tall.…

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