Topics Logic

Question Is the Sorites paradox really a paradox, or is it more properly considered to be a logical fallacy? By definition, the term "heap" is indeterminate. Yet the Sorites paradox tries to force a specific definition on what is by design an indeterminate concept: the very idea of defining the term "heap" as a specific number of grains of sand is fallacious, is it not? I don't see a paradox here as much as I see confusion about how terms are defined. How many grapes are in a bunch of grapes? How many leaves are in a head of lettuce? How many grains are in an ear of corn? How many chips are in a bag of potato chips? in each of the above questions, the answer will vary from one example to the next, the exact number is not particularly germane to the concept. So what makes a heap different from a bunch or any of the other examples?

Accepted:
August 2, 2018

Comments

I see the sorites paradox as

I see the sorites paradox as a very serious problem, not a logical fallacy that's easy to diagnose and fix. The paradox arises whenever we have clear cases at the extremes but no known line separating the cases where a concept applies from the cases where the concept doesn't apply.

Clearly, 1 grape isn't enough to compose a bunch of grapes. Just as clearly, 100 grapes is enough to compose a bunch of grapes. So which number between 2 and 100 is the smallest number of grapes sufficient to compose a bunch of grapes? If there's no correct answer, then the sorites paradox shows that the concept enough grapes to compose bunch of grapes is an inconsistent concept. But inconsistent concepts, such as the concept colorless red object, necessarily never apply to anything, in which case it would be impossible for anything to be a bunch of grapes.

One might reply, "Okay, fine. Necessarily there are no bunches of grapes. Life goes on." The problem, however, is that the sorites paradox applies to every vague concept, including the concept human body, and presumably we don't want to deny the logical possibility that our own bodies exist: who would be doing the denying in that case? The lesson is that classical logic requires the existence of an arbitrarily precise cutoff falling somewhere in between the clear cases, even if we can't hope to know where the cutoff falls. Many philosophers have tried non-classical logic or non-classical semantics to avoid the need for sharp cutoffs, but all of the attempts I know of either fail to eliminate sharp cutoffs or come to grief in some other way.

Yes, the number of leaves in a head of lettuce varies from one case to the next, but there are limits. A head of lettuce can't have zero leaves, whereas this year's prize-winning head of lettuce at the state fair clearly has enough leaves. To repeat: Logic requires there to be a sharp cutoff in between those clear cases -- a line that separates having enough leaves to be a head of lettuce from having too few leaves to be a head of lettuce. Or else there couldn't possibly be heads of lettuce.

Incidentally, I don't think it's true that "heap," "bunch," etc., are defined as indeterminate. Instead, we learn to apply those words by being shown only clear cases of heaps and bunches. Our teachers simply don't bring up the words in unclear cases (or, I think, in clearly negative cases either). So the indeterminacy results from omission rather than from any deliberate definition.