Part II: Examples
- Universal Affirmative:
- “All cats are animals”
- “All cats are albinos”
- “Socrates is a Philosopher.”
Propositions (1) – (3) are all examples of the Universal Affirmative. However, there is an important distinction between these propositions: the first and third are true, whereas the second is false. (1) is
true because all members of the category “cats” are in fact also members of the category “animals.” But (2) is false because there are members of the category “cats” that are not in the category “albino things”. In other words, some cats are not albino, and those cats are counterexamples to the (2). We can see from (2) that an affirmative statement is not the same thing as a true statement!
Now, it might seem counterintuitive that (3) is a Universal Affirmative proposition, but Aristotle treats propositions with singular subjects as universal. Why? Well, when we say that Socrates is a philosopher, we are saying that all of the members of the category “Socrates” are also members of the category “philosophers.” There is only one member of the category “Socrates”, so if he (Socrates) is also a philosopher, then (3) is a true Universal Affirmative proposition.
- Universal Negative:
- “No snakes are reptiles”
- “No snakes are birds”
- “Plato is not French”
Propositions (4) – (6) are all examples of the Universal Negative. But once again, there is an important distinction between these propositions: (4) is false, whereas (5) and (6) are true. We can see from (5) that a negative statement is not the same thing as a false statement! Finally, (6) is a Universal Negative proposition because no members of the category “Plato” have the property of being French. Plato was a Greek philosopher, so even though the category “Plato” has only one member (Plato himself), (6) is a Universal Negative proposition.
Activity: Fill out the box below with your own examples of a Universal Affirmative proposition that is true, a Universal Affirmative proposition that is false, a Universal Negative proposition that is true, and a Universal Negative proposition that is false. When you’re done, share your examples with at least two of your classmates so that you can check over each other’s work.
