TRANSLATION INTO THE BASIC CATEGORICAL FORMS

Propositions with the specific A, E, I, and O forms do not appear often in everyday conversations. Normal people rarely say things like “All whales are mammals. All mammals breathe air. Therefore, all whales breathe air.” Most people talk more like this: “Whales breathe air, since they’re mammals.” Thus, if our logical apparatus could be applied only to propositions with the explicit forms of A, E, I, and O, then it would apply to few arguments in everyday life.

Fortunately, however, many common statements that are not explicitly in a categorical form can be translated into a categorical form. For example, when someone says, “Whales are mammals,” the speaker presumably means to refer to all whales, so this statement can be translated into “All whales are mammals,” which is an A proposition. We need to be careful, however. If someone says, “Whales are found in the North Atlantic,” the speaker probably does not mean to refer to all whales, because there are many whales in the Pacific as well. Similarly, if someone says, “A whale is a mammal,” this can usually be translated as “All whales are mammals,” which is an A proposition, but this translation would be inappropriate for “A whale is stranded on the beach,” which seems to mean “One whale is stranded on the beach.” Thus, we can be misled badly if we look only at the surface structure of what people say. We also need to pay attention to the context when we translate everyday talk into the basic categorical forms.

Despite these complications, it is possible to give some rough-and-ready guides to help in translating many common forms of expression into propo- sitions with the A, E, I, and O forms. Let’s begin with one problem that arises for all these categorical forms: They all require a class of things as a predicate. Thus, “All whales are big” and “No whales live on land” should strictly be reformulated as “All whales are big things” and “No whales are things that live on land” or “No whales are land dwellers.” This much is easy.