To avoid this paradox you can make the following rule:
(“The heap of sand minus one grain is still a heap ” is true) if and only if (The heap of sand minus one grain still constitutes a heap) in the style suggested in this lesswrong post
But there’s also another route, the non-inductive route: can you give me a single example of a heap of sand that becomes a non-heap when you remove a grain?
Yes that’s pretty easy, since it’s only a question of what you call a heap. The paradox is basically feeding you a bait by asking you to think of a million grains of sand, which you obviously can’t quantitatively visualize and that could result into abandoning trying to find definitive criteria.
As I’m not a native speaker of english I’m not sure if my idea of a “heap” corresponds to what it’s generally used to refer to, but I’d draw the mininum boundary at 1 grain always not being a heap of grains. In my opinion a heap refers to a count of objects above 1. In addition I think it also refers to a geometric structure where objects are arranged in such a fashion that some objects are supporting other objects on top of them. You could also try and make a distinction between stacks and heaps.. Anyway I think you should just drop suggested the million grains and start from “3 grains” and ask yourself “if I remove one grain, is what’s remaining a heap?”
To avoid this paradox you can make the following rule:
(“The heap of sand minus one grain is still a heap ” is true) if and only if (The heap of sand minus one grain still constitutes a heap) in the style suggested in this lesswrong post
Yes that’s pretty easy, since it’s only a question of what you call a heap. The paradox is basically feeding you a bait by asking you to think of a million grains of sand, which you obviously can’t quantitatively visualize and that could result into abandoning trying to find definitive criteria.
As I’m not a native speaker of english I’m not sure if my idea of a “heap” corresponds to what it’s generally used to refer to, but I’d draw the mininum boundary at 1 grain always not being a heap of grains. In my opinion a heap refers to a count of objects above 1. In addition I think it also refers to a geometric structure where objects are arranged in such a fashion that some objects are supporting other objects on top of them. You could also try and make a distinction between stacks and heaps.. Anyway I think you should just drop suggested the million grains and start from “3 grains” and ask yourself “if I remove one grain, is what’s remaining a heap?”
This gets quickly to “This plucked chicken has two legs and no feathers—therefore, by definition, it is a human!” that is it’s hard to find a really solid definitive criterion and so you should instead just try and imagine a situation where you would no longer call the the remaining grains of sand a heap
http://answers.yahoo.com/question/index?qid=20100805132521AAcGBqs
:)