The Disappearing ‘Heap’ of Corn¹

Sorites Paradoxes and Vagueness Among Merchants

(by Andrew Greenwell)

Two merchants, Paul and Saul, entered into an agreement in which Saul agreed to sell, and the Paul agreed to purchase, a “heap” of corn, delivery to be at the end of that year’s harvest. The end of the harvest came and went, and Paul received only one kernel of corn from Saul.

So Paul sued Saul for breach of contract. In defense, Saul argued that he had complied with the contract.

“How so?” asked Paul? “You have not provided me a ‘heap’ of grain as you promised.”

“How much grain do you believe constitutes a ‘heap’ of grain?” asked Saul?

“Around 10,000 kernels,” responded Paul.

“Around 10,000 kernels. So, if I were to provide you with 9,999 kernels of corn, would you accept that amount to constitute a heap?”

“Yes, if around 10,000 kernels of corn is a ‘heap’ of corn, then 9,999 kernels of corn would still be a ‘heap,’” responded Paul."

“Would you agree that taking away one kernel of corn would not turn a ‘heap’ into a ‘non-heap?’” asked Paul?

“Yes.”

“If the difference of a kernel does not change a ‘heap’ into a ‘non-heap,’ then how about if I were to provide you with 9,998 kernels?”

“Yes,” answered Paul, “that would still be a ‘heap.’”

“And so if we continue with your premise—that the difference of a kernel cannot change a ‘heap’ into a ‘non-heap,’ then I can continue to deduct kernels from your ‘heap,’ and still have a ‘heap.’ So that we can apply that reasoning 9,997 more times so that one kernel remains a ‘heap.’ And even deducting that one kernel from the one-kernel ‘heap,’ since we have agreed that subtracting one kernel does not make a ‘heap’ into a ‘non-heap,’ it means I have a ‘heap’ with zero kernels. So, by providing you with one kernel, I have more than satisfied the contract with you.”

Endnotes

¹ Adapted from R.M. Sainsbury, Paradoxes (2nd ed.) (Cambridge: Cambridge University Press, 1995), 28-30.). ⇑