[mewminator]

The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows:

1,000,000 grains of sand is a heap of sand. (Premise 1)

A heap of sand minus one grain is still a heap. (Premise 2)

Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand.

On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying 1,000,000 grains of sand makes a heap. But 1,000,000 is just an arbitrarily large number, and the argument will go through with any such number. So the response must deny outright that there are such things as heaps. Peter Unger defends this solution. Alternatively, one may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may accept the conclusion by insisting that a heap of sand can be composed of just one grain.

[Molly Mae]

The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows:

1,000,000 grains of sand is a heap of sand. (Premise 1)

A heap of sand minus one grain is still a heap. (Premise 2)

Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand.

On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying 1,000,000 grains of sand makes a heap. But 1,000,000 is just an arbitrarily large number, and the argument will go through with any such number. So the response must deny outright that there are such things as heaps. Peter Unger defends this solution. Alternatively, one may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may accept the conclusion by insisting that a heap of sand can be composed of just one grain.

I would say that it depends on the observer's definition of 'heap', as well. What one might call a heap another might not.

[mewminator]

I would say that it depends on the observer's definition of 'heap', as well. What one might call a heap another might not.

The point is that is it 1 grain of sand that seperates a heap from a no heap or is it 1000 and if it 1000 isn't a 1000 grains of sand

1000 x 1 grains of sand?

[Molly Mae]

The point is that is it 1 grain of sand that seperates a heap from a no heap or is it 1000 and if it 1000 isn't a 1000 grains of sand

1000 x 1 grains of sand?

I might consider 5 grains a heap. You might consider those 5 to not be a heap.

It's like saying "I have a lot of sand." If you keep taking one grain away, when do you no longer have "a lot of sand"?

[Guest]

it's basically what molly says. you're trying to compare an arbitary word with a fixed number, to determine when the arbitrary word no longer fits.

for example, if i said "1,000,000 grains of sand is precicely equal to 5 tons." removing a single grain of sand would change the wieght.

or if i said "1,000,000 grains of sand take up precicely 3 cubic meters of space." removing a single grain of sand would change the volume.

but if i say "1,000,000 grains of sand may be a large amount." its unclear whether removing a single grain would change that.