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 grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand. 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. Peter Unger defends this solution. 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.
Posted on: Sat, 10 Aug 2013 23:50:12 +0000
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