Vagueness Glossary
Definition
A vague predicate is one that lacks precise criteria to demarcate the cases in which it applies from the cases in which it does not. Vague predicates give rise to vague propositions, whose truth conditions are similarly imprecise. The question of how to incorporate such propositions into formal logic remains a serious issue.
Comments
The sorites paradox illustrates the logical problem of vagueness: large changes in some respect make the difference between whether the vague predicate applies or not, but very small changes do not; yet the large change is made up of small ones.
One possible solution to the problem of vagueness is to weaken logic so that the problematic inferences are blocked. This gives rise to fuzzy logic, of which there are many varieties. We explore one a little in these notes.
See the link below for an introduction.