Unlike children, and some adults, I don’t eat sand, be it in a heap or not, so I’m not entirely convinced that’s the right model either.
Interesting “paradox” though, as the initial premise of one million grains of sand being a heap falls over as it doesn’t specify the structure of the sand: which is what defines a heap of anything.
You think that’s a worse fit than: If I replace parts of a thing with SOMETHING ELSE is it still the same thing? The ship of theseus is more well known, but you would need to eat sand to think it’s a good fit IMO.
As an aside, the structure of the heap has nothing to do with it. The point is simply “when does a heap stop being a heap if I remove one grain at a time?” That is the same is the same as when does food stop being food if you make it poop one bit at a time. If you don’t like “heap” you can call it a pile WLOG.
If I spread a million grain heap of sand out evenly over a plane such that the grains are still touching it’s no longer a heap. Therefore the heap is a structure not a numeric quantity.
Unlike children, and some adults, I don’t eat sand, be it in a heap or not, so I’m not entirely convinced that’s the right model either.
Interesting “paradox” though, as the initial premise of one million grains of sand being a heap falls over as it doesn’t specify the structure of the sand: which is what defines a heap of anything.
You think that’s a worse fit than: If I replace parts of a thing with SOMETHING ELSE is it still the same thing? The ship of theseus is more well known, but you would need to eat sand to think it’s a good fit IMO.
As an aside, the structure of the heap has nothing to do with it. The point is simply “when does a heap stop being a heap if I remove one grain at a time?” That is the same is the same as when does food stop being food if you make it poop one bit at a time. If you don’t like “heap” you can call it a pile WLOG.
If I spread a million grain heap of sand out evenly over a plane such that the grains are still touching it’s no longer a heap. Therefore the heap is a structure not a numeric quantity.
I said no such thing.