ABSTRACT
The theory of logical consequence constructed so far is powerful and useful. It is elegant in its simplicity, but far-reaching in its power and its breadth. There are also some important problems for interpreting and using this account. In this chapter, we will look at one class of problems, which stem from the assumption that each proposition is assigned either the value ‘true’ or the value ‘false’. This is the doctrine of bivalence (‘bivalent’ means ‘has two values’). The first problem stems from the vagueness inherent in our use of language.
