An Economic Paradox: The Sophism of the Heap of Wheat and Statistical Truths

Abstract

[688/2197] In many economic matters there arises a paradox that may be related to what in logic courses is called the ‘‘sophism of the heap of wheat’’. Among the sophisms bequeathed to us by the Greeks, none is worthier to have come down through the centuries than this ‘‘sophism of the heap of wheat’’; indeed this no mere puzzle, but a topical example of a frequent difficulty, as much in practical life as in pure speculation. One grain of wheat does not make a heap; neither do two grains; nor do three grains; . . . on the other hand, if a million grains are gathered, we can agree that they constitute a heap. What is the exact limit? Should we say that 2,342 grains, for instance, do not make a heap, whereas 2,343 grains do? This is obviously ridiculous. There appears no logical way out of this dead-end; it is therefore not possible to know what a heap of wheat is. The expression of the sophism can be varied in many ways; a classification of these expressions will not be unhelpful. A first category is very similar to the original sophism: at what time of his life can a child be called a man? What is the limit that separates a shack from a house, a house from a palace? At what instant does a series of hues cleverly shaded turn from grey to white, or from green to blue? One possible attitude toward these questions [689/2198] is to declare them totally devoid of any interest, given that it is only a matter of how words are defined, something one is entitled to consider as purely