THE LOGIC NOTES

Sorites paradox Glossary

Definition

Suppose P is a predicate whose applicability is a matter of degree, and suppose a1...an are in order of decreasing value of P, so that P(a1) is true, P(an) is false, and the difference between P(ai) and P(ai+1) is nowhere enough to make a significant difference. Then we have

P(a1) IMP P(a2)
P(a2) IMP P(a3)
P(a3) IMP P(a4)
etc.

from which it follows by ordinary propositional logic that

P(a1) IMP P(an)

This is paradoxical since all of the premises apear to be true but the conclusion is false.

Comments

The sorites paradox arises whenever vague predicates are allowed in the language of logic. Such predicates are widespread in natural languages.

Examples

  1. A series of coloured patches shading gradually from red to not red. This example is discussed in the link below.
  2. A pile of sand grains. If there are enough grains, it can constitute a heap; if there are not, it cannot be a heap; being a heap or not is insensitive to the addition or removal of a single grain.
  3. Chickens and eggs. Each generation of chickens is the offspring of the previous generation; members of successive generations belong to the same species; yet millions of years ago there were no chickens.

Links