Heap paradox

The sorites paradox (/soʊˈraɪtiːz/; 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 of sand from which grains are individually removed. One might construct the argument, using premises, as follows:

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":

Then tension between small changes and big consequences gives rise to the Sorities 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 turn it into a heap. Inductively, this process can be repeated as much as one wants without ever constructing a heap. A more natural formulation of this variant is to assume a set of colored chips exists such that two adjacent chips vary in color too little for human eyesight to be able to distinguish between them. Then by induction on this premise, humans would not be able to distinguish between any colors.

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