2 7 9H e a p sDespite its plausibility, everyone should agree that there is something
wrong with this argument. If we hand over enough pennies to Peter, previ-
ously poor Peter will become the richest person in the world. Another sign
of a problem is that a parallel argument runs in the other direction: Someone
with 100 billion cents is rich. For any number, n, if someone with n cents is
rich, then someone with n – 1 cents is also rich. Therefore, someone with no
cents at all is rich. This is absurd (since we are not talking about how rich
one’s life can be as long as one has friends).
We can see that these arguments turn on borderline cases in the follow-
ing 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
either 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 per-
son 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. Anyway, however
or whenever it occurs, the change does occur. Some people do cease to be fat
if they lose enough weight.
This tells us that conclusions of arguments from the heap, such as (3*), are
false, so these arguments cannot be sound. Almost everyone agrees to that
much. Moreover, if an appropriate starting point is chosen, then premises
like (1) and (1*) will also be accepted as true by almost everyone. So the
main debate focuses on premise (2*) and on whether the argument is valid.
Some philosophers reject premise (2*) and claim that there is a precise point
at which a person becomes rich, even though we don’t know where that
point is. Others try to avoid any sharp cutoff point by developing some kind
of alternative logic. Still others just admit that the premises seem true, and
the argument seems valid, but the conclusion seems false, so the argument97364_ch13_ptg01_273-290.indd 279 15/11/13 11:01 AM
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