*Introductory Logic* formally teaches two methods for determining the validity of a syllogism: rules of validity, and counterexamples. The rule that tells us that any AAO-4 syllogism is invalid is this: “A valid syllogism cannot have two affirmative premises and a negative conclusion.” But can we show the invalidity of AAO-4 with a counterexample? Here is the schema:

All P is M

All M is S

∴ Some S is not P

I contend that there is only one way to write a counterexample for a syllogism of that form. **I challenge you to write a counterexample to AAO-4.** Remember that a counterexample must be the same form, and have true premises and a false conclusion.

Good luck!

I seem to be having difficulty with this one. Any hints, Mr. Nance?

Here is a hint. Try drawing circle diagrams to represent the premises. For example, for “All P is M” draw a circle labeled P inside a circle labeled M. Similarly for “All M is S.” How could you draw these such that “Some S is not P” is false.