Re: the Sorites paradox, I have a definition of a heap that I think is workable.
It's not a specific number; it's "a collection of items becomes a heap when some indeterminate number of items are obscured by other items on top of them, thus making the total number of items uncountable without disturbing the heap".
Therefore it depends on factors beyond just the number of grains of sand; if you have 1000 grains spread out on a surface so they are can all be distinctly counted, that's not a heap. But if you have 1000 grains gathered together, some on top of each other, then it becomes a heap.
It's not a specific number; it's "a collection of items becomes a heap when some indeterminate number of items are obscured by other items on top of them, thus making the total number of items uncountable without disturbing the heap".
Therefore it depends on factors beyond just the number of grains of sand; if you have 1000 grains spread out on a surface so they are can all be distinctly counted, that's not a heap. But if you have 1000 grains gathered together, some on top of each other, then it becomes a heap.