Borderline Cases

We can see that these arguments turn on borderline cases in the following way: The argument would fail if we removed borderline cases by laying down a ruling (maybe for tax purposes) that anyone with a million dollars or more is rich and anyone with less than this is not rich. A person with $999,999.99 would then pass from not being rich to being rich when given a single penny, so premise (2*) would be false at that point under this ruling. Of course, we do not usually use the word “rich” with this much precision. We see some people as clearly rich and others as clearly not rich, but in be- tween there is a fuzzy area where we are not prepared to say that people ei- ther are or are not rich. In this fuzzy area, as well as in the clear areas, a penny one way or the other will make no difference.

That is how the argument works, but exactly where does it go wrong? This question is not easy to answer and remains a subject of vigorous de- bate. Here is one way to view the problem: Consider a person who is 80 pounds overweight, where we would all agree that that person would pass from being fat to not being fat by losing over 100 pounds. If he or she lost an ounce a day for five years, this would be equivalent to losing just over 114 pounds. An argument from the heap denies that this person would ever cease to be fat. (So what is the point of dieting?) Anyone who accepted that conclusion, or (3*), would seem to claim that a series of insignificant changes cannot be equivalent to a significant change. Surely, this is wrong. Here we might be met with the reply that every change must occur at some particular time (and place), but there would be no particular day on which this person would pass from being fat to not being fat. The problem with this reply is that, with concepts like this, changes seem to occur gradually over long stretches of time without occurring at any single moment. Any- way, however or whenever it occurs, the change does occur. Some people do cease to be fat if they lose enough weight.