vagueness part deux

Timothy Williamson, clearly the most exciting guy in the world, wrote a whole book called 'Vagueness' about some of the topics in my last post. His opening chapter is about the classical history of sorities problems - logical puzzles like the baldness problem i presented last post.

the general format of sorities problems is a series of questions, in which one begins with a clear case: "is this pile of 10,000 grains of corn a heap?" to which anyone would answer "yes." Then the questioner slowly works down: "if i remove one grain, is it still a heap?"; "yes". "If I remove one grain at a time, and no one grain should make a difference to the status of the object, is one grain a heap?" based on the logic of premises and conclusions, the answerer (usually a stoic) is left in the absurd position of having to answer that one or even zero grains are, in fact, a heap. The question has always been: is there a sharp cut off determining when something is no longer a heap? is there a certain number of grains required to make a heap?

I, possibly a skeptic, tried this line of questioning on a computer science major (dave, i think you know who you are). at first i thought i had failed utterly, because no matter how low the numbers got, he still considered it a heap. "alright, dave, what if there are no grains? is it still a heap?" dave: "yes, [laughter] it's just an empty heap."

but i found it hard to argue that he was wrong to hypothesize an empty heap. it was certainly an elegant way to buck a sorites problem. and it reminded us here at I.U. of a post scott wrote over the summer.

even with a c.s. major, pointing to an empty place on the ground and asking "is this a heap?" is unlikely to elicit a 'yes' response. but it's NOT hard to say that yes, after i've removed grain after grain, the empty spot left is a type of heap - namely, an empty one.

so, what's the difference? why are 5 grains sometimes a heap and sometimes not? as with most topics on this blog, we return to context. we are only inclined to call something a heap when salient that it is a heap - as opposed to anything else.

the same contextual issues are important in other circumstances - suppose i have 10,000 grains but they are spread out, for instance. suppose a heap is naturally formed by wind piling grains against a wall? is it a heap?

the neat thing about language is that we can match it effectively to these vaguenesses. i hesitate to say 'vaguenesses in the world', because vagueness isn't in the world - it's in the application of totalized terms like 'heap' to a world that isn't built out of totalized concepts. but language allows us to work around these gaps when we need to and say "it used to be a heap", "it's an empty heap"; "it's a group of grains, but not a heap".