What's a heap?
Stanford Encyclopedia of Phlosophy puts the paradox this way: 1 grain of wheat does not make a heap. If 1 grain of wheat does not make a heap then 2 grains of wheat do not. If 2 grains of wheat do not make a heap then 3 grains do not. … If 9,999 grains of wheat do not make a heap then 10,000 do not.10,000 grains of wheat do not make a heap.
That is we can't make a heap of wheat from a non heap of wheat by adding one grain at a time.
Similarly if you start with a heap, you can't make it a non heap by taking away a single grain of wheat. Therefore you can never get a non heap from a heap by removing one grain at a time.
This paradox pops up in all sorts of contexts. In general there is a situation moving from one state of affairs to another by steps that are too small to count as the move in itself. For instance, if you start at yellow on the color wheel and go around 30 degrees you move from yellow to red. If you move 1 degree you move from yellow to yellow. Where is the dividing line between yellow and red? It can't be orange because a dividing line would have yellow on one side and red on the other. At orange you have just orange on either side of the line - no line is apparent.
Or consider how a new species evolves from an ancestral one. At what sharp point in time can we say when the new species arose? We can't. It is always true that all children are the same species as the parent.
Situations where the sorites paradox arises involve a certain sort of vagueness. Its sort of like porn - we all know heaps when we see them but they are hard to define precisely . Philosophers relate to vagueness like nature supposedly related to a vacuum - with abhorrence. But perhaps this abhorrence is misplaced.
One approach to resolving the paradox is to first look at the extreme cases. One grain of wheat isn't a heap, A truck load of wheat on the floor is a heap. And there are boundary cases where we can't really say one way or the other.
This morning Elaine suggested an interesting variation on this: say you took the truckload of wheat and spread it out so it was only a single grain thick.
Would that be a heap?
How about two layers thick? Or three . . . - get the idea?
Vagueness might have more than semantic significance. Not only is the distinction between heap and non heap vague but the heap itself is sort of vague. It has many members but very little is known of those as individuals - they are all part of this vague structure called a heap. Since the structure is vague there aren't strong forces maintaining a certain state of affairs.
And this has practical results. It's fun to jump from a height into a pile of wheat because the grains can move to absorb the energy of your fall without affecting the heap as a whole very much. Which interestingly might give us a way to define a heap. If small changes in the members make a big difference then that's not a heap. If small changes don't make a big difference then that's a heap.
Or we might try a more pragmatic definition: If you'd be comfortable leaping into it then it's a heap.
What do you think?