Postby Sounder » Thu Oct 09, 2008 7:16 pm
From Wikipedia:
The name '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 less number of grains), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand (and if you follow premise 2 again, composed of no grains at all! (and then a heap of zero grains minus one will have to be a heap too...)).
On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying 1,000,000 grains of sand makes a heap. But 1,000,000 is just an arbitrarily large number, and the argument will go through with any such number. So the response must deny outright that there are such things as heaps. This is Unger's proposal. Alternatively, one may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may accept the conclusion by insisting that a heap of sand can be composed of just one grain.
Alternatively, one may define a heap inductively instead of by reduction, and make the rules as follows:
100,000 grains of sand is a heap of sand.
A heap of sand plus one grain is still one heap of sand.
and adjust the number in the first premise to an arbitrary, but well-defined value for a heap.
[edit] Variations
This paradox can be reconstructed for a variety of predicates, for example, with "tall", "rich", "old", "blue" and so on. Bertrand Russell argues, in his paper titled 'Vagueness', that all of natural language, even logical connectives, are vague; most views do not go that far, but it is certainly an open question.