5.2.2 Universal Statements

Another important type of statement is the universal affirmative statement. Aristotle included universal affirmative statements in his system of logic, believing they were one of only a few types of meaningful logical statements (On Interpretation). Universal affirmative statements take two groups of things and claim all members of the first group are also members of the second group: “All A are B.” These statements are called universal and affirmative because they assert something about all members of group A. This type of statement is used when classifying objects and/or the relationships. Universal affirmative statements are, in fact, an alternative expression of a conditional.

Universal Statements as Conditionals

Universal statements are logically equivalent to conditionals, which means that any conditional can be translated into a universal statement and vice versa. Notice that universal statements also express the logical relations of necessity and sufficiency. Because universal affirmative statements can always be rephrased as conditionals (and vice versa), the ability to translate ordinary language statements into conditionals or universal statements is helpful for understanding logical meaning. Doing so can also help you identify necessary and sufficient conditions. Not all statements can be translated into these forms, but many can.

Counterexamples to Universal Statements

Universal affirmative statements also can be disproven using counterexamples. Take the belief that “All living things deserve moral consideration.” If you wanted to prove this statement false, you would need to find just one example of a living thing that you believe does not deserve moral consideration. Just one will suffice because the categorical claim is quite strong—that all living things deserve moral consideration. And someone might argue that some parasites, like the protozoa that causes malaria, do not deserve moral consideration.