ABSTRACT
This chapter introduces some modifications of the traditional Venn diagram methods. In the traditional doctrine of the syllogism there are only two quantities involved— universal and particular. But additional quantifier words exist— "few", "many", and "most"— over and above expressions for universal and particular quantity. Traditionally, the validity of a syllogism could be determined by the application of four rules: two involving distribution and two involving quality. A formal system is inconsistent if its rules permit a formula and its denial to each be proved. Using syllogistic rules to produce valid syllogistic forms can be thought to parallel the way formulas are shown to be theorems in a formal system. To apply this syntactic concept of consistency to the syllogistic rules, then, would be to see if any syllogistic form and its denial were both deemed valid by the rules.
