Timothy Williamson: Vagueness | Who Shaves the Barber? #33

Download this episode / Watch on YouTube / RSS Feed / iTunes


The problem of vagueness stems from the sorites paradox. A heap of sand cannot be turned into a non-heap by removing a single grain of sand. A short person cannot become tall by growing one millimeter. Someone who is sober cannot become drunk by ingesting one-tenth of a milliliter of alcohol. These conditionals hold regardless of what we take as our starting conditions. But if this is true, we can iterate the conditionals many times over, until we can prove that one grain of sand makes a heap, an 8-ft. tall man isn’t tall, and someone who’s just ingested a liter of alcohol is sober.

This ancient paradox has become one of the toughest puzzles in contemporary metaphysics and philosophical logic. During our conversation, Professor Timothy Williamson explains and rejects a few approaches, including supervaluationismfuzzy logic, nihilism, and contextualism. His preferred solution, known as epistemicism, is much simpler: all vague predicates have a precise cutoff point – we just can’t know where it is. Williamson supports this counterintuitive view with compelling accounts of meaning and knowledge. Meaning, he explains, is determined in part by aggregate use; since we cannot know all of the factors of aggregate use, we cannot know the exact meanings of vague terms. From this, we can infer that there are many cases in which we know something but do not know that we know it.

Interested in vagueness? Check out my interview with Graham Priest on the sorites paradox.…

Continue Reading →

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.…

Continue Reading →