The paradox of the heap, also known as the Sorities Paradox (from the Greek word for heap), is a paradox revolving around the problem of vagueness.

In its classical formulation, the paradox is expressed as follows:

One grain of sand is not a heap.
If one grain of sand is not a heap, adding one grain of sand will not make it a heap.
So two grains of sand are not a heap.
So three grains of sand do not make a heap.
…
X grains of sand do not make a heap.
Therefore, 10,000 grains of sand do not make a heap.

The form of this argument boils down to:

X grains of sand are not a heap.
If X grains of sand are not a heap, adding 1 grain of sand will not make it a heap.
(Some arbitrary large number of grains of sand) do not make a heap.

Read more »