Subscribe to Elucidations:

This month, we are delighted to make our return to the topic of vagueness, this time in conversation with Stewart Shapiro, Professor of Philosophy at The Ohio State University. Click here to listen to our discussion.

You may remember from our previous episode on vagueness that most of the adjectives, common nouns, verbs, and prepositions we use are vague.  To illustrate the idea, think of the adjective blue.  In the philosophical setting, to say that the adjective blue is vague is to say a couple of things. First, although some things clearly are blue (like bluejays) and some things clearly aren’t (like lemons), some things are right at the border (like this).  Should we call that last borderline case blue or not?  It’s not particularly clear.

Second, words like blue lead to an old philosophical problem called the sorites paradox.  Consider the adjective tall. Danny DeVito is clearly not tall, and LeBron James is clearly tall. Imagine that Danny DeVito were one millimeter taller. Surely that wouldn’t make him tall. In fact, it seems obvious that no matter how tall he is, his being one millimeter taller couldn’t ever suffice to make him tall. But on the other hand, if he were as tall as LeBron James, he obviously would be tall. Uh-oh. These two statements are logically inconsistent. Why? Well, LeBron James is a finite number of millimeters taller than Danny DeVito–510, to be exact. So if we played the game of supposing his height to be one millimeter greater than it is, then supposing it to be one millimeter greater than that, then supposing it to be one millimeter greater than that, etc., then at some point he is going to have to cross over from not being tall to being tall. Oops.

Shapiro argues that the reason we get into this paradox is that the standards for what counts as tall (or blue, or whatever) can shift within the same conversation, as the context changes. So maybe earlier on in our imagined conversation, I claim that being 1770 mm in height wouldn’t be enough to make Mr. DeVito tall. We continue playing this game, and then at a certain point, I flip–let’s say around 1830 millimeters. Shapiro thinks that at that point, I am committed to retracting my last few judgments. If I decide that being 1830 millimeters (about 6’) in height would make him tall, then I am thereby committed to retracting my previous claim that being 1829 millimeters in height wouldn’t make him tall. Working this basic idea out in detail allows Shapiro to explain why we have the intuitions we do about the sorites paradox while holding onto our intuitions about what is or isn’t logically consistent to say.

Tune in to hear our guest explain how his theory works!

Matt Teichman