ABSTRACT
The propositional logic we have developed puts us in a position to rigorously evaluate only a very limited class of arguments, arguments the validity of which turns on the role of truth-functional operators. This means that attention has been limited to arguments that depend for their validity on the relation between simple and compound propositions. We have as yet no tools for investigating arguments the validity of which depends on what is going on inside simple propositions; that is, propositions that do not contain other propositions. For instance, consider the following valid arguments: All persons are mortal. Socrates is a person. Therefore, Socrates is mortal. All Balliol students are clever. Icabod is a Balliol student. Therefore, Icabod is clever. All zemindars are powerful. Icabod is a zemindar. Therefore, Icabod is powerful.
