What Makes an Argument Good?

The Monty Python witch trial activator does several things at once: it is funny, it is genuinely fallacious, and it gives students a concrete case to apply vocabulary they learned the day before. The argument chain breaks down in multiple ways — undistributed middle errors compounding through the premises, then an affirming-the-consequent conclusion. Students who can identify each error specifically are demonstrating real understanding.

 

The key insight of Day 2 is worth stating to students directly before the notes: the fallacies are not new ideas. They are names for argument patterns you already understand — specifically, what happens when you use the wrong form of a conditional statement. The conditional and its contrapositive are the two equivalent forms and they generate the two valid argument patterns. The converse and the inverse are not equivalent to the conditional — they are equivalent to each other, but not to the original. Argument forms based on the converse or inverse are therefore fallacies. Students who see this do not need to memorize four separate patterns. They need to remember one thing from Lesson 2.2b.

 

The Venn diagram explanation of each fallacy is essential. Affirming the consequent: the p-circle sits inside the q-circle; a point inside q is not necessarily inside p. Undistributed middle: A and B are both inside C; that tells us nothing about whether A and B overlap. Draw these. The diagrams are more memorable than the symbolic forms.