Paradox Compilation

The Sorites Paradox

Sometimes known as The Paradox of the Heap, The Sorites Paradox 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? (Or are even no grains at all 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:

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 (and consequently, if one grain of sand is still a heap, then removing that one grain of sand to leave no grains at all still leaves a heap of sand; indeed a negative number of grains must also form a heap). Read (1995) observes that "the argument is itself a heap, or sorites, of steps of modus ponens(Placing mode)"

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. If ...... So 1 grain is a heap.