The Sorite paradox (or heap paradox) is one of the oldest and most important paradoxes known. Its origin is attributed to Eubulides of Miletus, the ancient Greek philosopher to whom we also owe the Liar’s paradox. The paradox can be informally described as follows. First of all, it is commonly accepted that a collection of 100,000 grains of sand is a heap. Furthermore, it appears that if a set with a given number of grains of sand is a heap, then a set with one less grain of sand is also a heap. Given these premises, it follows that a set with one grain of sand is also a heap. Indeed, if a set with 100,000 grains of sand is a heap, it follows that a set with 99999 grains of sand is a heap; and the same applies to a set with 99998 grains of sand, then 99997, 99996, 99995, …, and so on, down to a single grain of sand. The paradox arises from the fact that the corresponding reasoning appears to be perfectly valid, while the conclusion that follows is unacceptable.
The different steps leading to the Sorite paradox can be detailed as follows:
(1) a set with 100,000 grains of sand is a heap
(2) if a set with n grains of sand is a heap, then a set with n – 1 grains of sand is a heap
(3) if a set with 100000 grains of sand is a heap, then a set with 99999 grains of sand is a heap
(4) ∴ a set with 99999 grains of sand is a heap
(5) if a set with 99999 grains of sand is a heap, then a set with 99998 grains of sand is a heap
(6) ∴ a set with 99998 grains of sand is a heap
(7) if a set with 99998 grains of sand is a heap, then a set with 99997 grains of sand is a heap
(8) ∴ a set with 99997 grains of sand is a heap
(9) …
(10) ∴ a set with 1 grain of sand is a heap
(excerpt from) Franceschi P. An Introduction to Analytic Philosophy: Paradoxes, Arguments and Contemporary Problems, 2nd edition, March, 2010
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