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Uncharted 4: A Thief's End (2016)

Duration: 0:22

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The sorites paradox sometimes known as the paradox of the heap) is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?

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:

1000000 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. Observes that "the argument is itself a heap, or sorites, of steps of modus ponens":

1000000 grains is a heap.
If 1000000 grains is a heap then 999999 grains is a heap.
So 999999 grains is a heap.
If 999999 grains is a heap then 999998 grains is a heap.
So 999998 grains is a heap.
If ...
... So 1 grain is a heap.

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