Continuing the discussion from On Distinguishing Science from Non-Science:
The word “sorites” derives from the Greek word for heap. The paradox is so named because of its original characterization, attributed to Eubulides of Miletus. 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 fewer grain) eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand.). Read (1995) observes that “the argument is itself a heap, or sorites, of steps of modus ponens”:
1,000,000 grains is a heap.
If 1,000,000 grains is a heap then 999,999 grains is a heap.
So 999,999 grains is a heap.
If 999,999 grains is a heap then 999,998 grains is a heap.
So 999,998 grains is a heap.
… So 1 grain is a heap.
There are a couple variants of this too. If we were talking about hair instead of sand, we would arrive at the bald man paradox, and the argument of the beard.
There is a common fallacy associated with this story. Just because we cannot draw a line of demarcation between heap and non-heap does not mean that heaps are an illusion. Arguing a distinction because the demarcation is difficult is common called the Continuum Fallacy.