How to Diagram Categorical Propositions
(1) Decide what the universe of discourse is. Then draw a box to represent it.
(2) Determine what the subject term and predicate term is. Then assign them letters.
(3) Divide your universe of discourse using your subject term and predicate term. For instance, suppose that your subject term is ‘cat’ and your predicate term is ‘feline’. Then your universe of discourse box needs to include four smaller boxes: a [cat & feline] box, a [cat & nonfeline] box, a [noncat & feline] box, and a [noncat & nonfeline] box.
(4) Determine what the proposition is including in the universe of discourse, what it is excluding, and what it is leaving unknown. For instance, if the proposition is expressed by the sentence, ‘Some cats are felines’, that includes cats that are felines. If it instead tells us that no cats are felines, that excludes cats that are felines. Then we’ll put an O in boxes that are included, an X in boxes that are excluded, and leave blanks where it doesn’t tell us. ‘Some cats are felines’ would have an O in the [cats & felines] box.
