Skip to main content

## Subsection7.5.2The Sorites Paradox

Suppose that we accept the following two premises:

[1] One grain of sand is not a heap.

[2] One grain of sand is too small to make a difference in determining whether something is or is not a heap.

Then, nothing, including this can be a heap:

But it clearly is a heap.

Thus we appear to have a logical paradox, classically called the Sorites Paradox.

The English word “heap” is vague: Are 75,000 grains enough? 120,000 grains? So we have a problem in deciding how to map English sentences about heaps into logic.

But we do not have a logical problem. The reason that we appeared, above, to get into trouble, is that we chose, as premises, to claims that don’t, in fact, do a good job of characterizing heapness.

### ExercisesExercises

#### Exercise Group.

Sometimes, a Sorites-like problem formulation may look reasonable (as in the case of the heap of sand). But sometimes it’s obvious that such a pair of premises doesn’t correspond to the situation. In these latter cases, it’s easy to see how to write premises that do clearly define the boundary between having some property P and not having it.

Mark each of the following pairs of premises as Sorites-like if, as in the sand example, it’s hard to decide how to get out of the apparent paradox. Mark it not Sorites-like if it is straightforward to write a more accurate set of premises.

##### 1.
1. A one word story isn’t a novel.

2. Adding one word to a short story won’t make it a novel.

Answer.

Correct answer is B - Sorites-like

Solution.

Explanation: There doesn’t seem to be a hard and fast boundary that separates novels from shorter works like novellas and short stories.

##### 2.
1. A one-year old is not old enough to drive.

2. Getting one year older doesn’t change whether or not you’re old enough to drive.

Answer.

Correct answer is A - Not Sorites-like

Solution.

Explanation: This one is easy. If age > 16 years (or whatever, in your state) then you are old enough to drive. Otherwise, you’re not.

##### 3.
1. A one gram package is easy to carry.

2. Adding one gram to a package doesn’t change how hard it is to carry.

Answer.

Correct answer is A - Sorites-like

Solution.

Explanation: There doesn’t seem to be a hard and fast boundary that separates packages that are too heavy from ones that are bearable.

##### 4.
1. (Part 4) One credit isn’t enough to get you a degree.

2. Getting one additional credit can’t make you degree-eligible.

Answer.

Correct answer is A - Not Sorites-like

Solution.

Explanation: For any specific degree, there is a clear definition of the number of credits that are required. If one credit takes you over that limit, you are degree-eligible.

##### 5.
1. (Part 5) One molecule of detergent won’t get the clothes clean.

2. Adding one additional molecule of detergent to the wash won’t change how clean the clothes get.

Answer.

Correct answer is A - Sorites-like

Solution.

Explanation: There doesn’t seem to be a hard and fast boundary that separates “enough detergent” from “not enough” detergent.