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 supervaluationism, fuzzy 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.

Next week: Bryan Caplan: The Case against Education

Visit http://williamnava.com or more info!

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

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.Click here for the full list of episodes!

Sources:Vagueness (Timothy Williamson)Tetralogue: I'm Right, You're Wrong (Timothy Williamson)"I Do Not Exist" (Peter Unger)"Vagueness Without Paradox" (Diana Raffman)

Topics discussed:

0:20 - Intro to Timothy Williamson1:01 - Teaser for "Tetralogue: I'm Right, You're Wrong"2:33 - The sorites paradox and vagueness9:14 - Is it really a problem?13:32 - Intro to epistemicism17:32 - Supervaluationism20:46 - Objections to supervaluationism28:58 - Limits of iteration?32:49 - Degrees of truth and fuzzy logic40:44 - Peter Unger's nihilism: there are no heaps, or people, or any everyday things or concepts44:43 - Vague claims aren't propositions?47:23 - Contextualism51:50 - Epistemicism: inexact knowledge and margins of error58:51 - Meaning and use1:03:01 - Knowledge sorites: not knowing what we know1:06:47 - Indiscriminate appearances sorites1:15:58 - A stipulated vague language?1:20:31 - The meaning formation process1:26:38 - Changes in the world and changes in language