Sorites paradox

The sorites paradox (soʊ'raɪtiːz; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a single grain does not cause a heap to become a non-heap, the paradox is to consider what happens when the process is repeated enough times that only one grain remains: is it still a heap? If not, when did it change from a heap to a non-heap? The word sorites (σωρείτης) derives from the Greek word for 'heap' (σωρός). The paradox is so named because of its original characterization, attributed to Eubulides of Miletus. The paradox is as follows: consider a heap of sand from which grains are removed individually. 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. Read (1995) 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. Then tension between small changes and big consequences gives rise to the sorites Paradox...There are many variations...[some of which allow] consideration of the difference between being...(a question of fact) and seeming...(a question of perception). Another formulation is to start with a grain of sand, which is clearly not a heap, and then assume that adding a single grain of sand to something that is not a heap does not cause it to become a heap. Inductively, this process can be repeated as much as one wants without ever constructing a heap.