sorites, or paradox of the heap
Consider the following two apparently true statements:
(1) If someone has only $1, they are not rich.
(2) If someone is not rich, then one more dollar won't make them rich.
These statements seem reasonable enough, but they can be used to show that one can never become rich by getting additional dollars, no matter how many one gets. By premise (1), if one has only one dollar, one isn't rich. By (2) it follows that getting one more dollar won't make one rich. So with $2 you aren't rich. But then by (2) again, getting one more dollar won't make you rich, so with $3 you aren't rich. If we keep repeating this process, we can get to any amount whatsoever, say one billion dollars. It follows that with one billion dollars you aren't rich.
The name "sorites" is derived from the ancient Greek word for "heap", since the first version of this paradox involved a heap of sand (one grain of sand is not a heap; if something is not a heap, then adding one grain of sand will not make it into a heap; therefore, there are no heaps of sand). All such paradoxes rely on some vague word, such as "rich", "heap", "tall", etc. And although the solution obviously depends in some way on the concept of vagueness, it is by no means easy to explain exactly what is wrong with this kind of argument.
Sorites paradoxes may seem silly, but they sometimes appear in serious arguments, even if in a somewhat subtler form. Perhaps the most common example is found in the debate over abortion. There is no non-arbitrary way of determining exactly when a fetus becomes a human being. It is therefore sometimes claimed that the fetus should be regarded as a human being from the moment of conception. (Of course, someone might also have other reasons for regarding the fetus as human.)
©2000 Franz Kiekeben