Monty Python Witch Trial: Validity, Soundness, and the Fallacy of the Undistributed Middle

In the film Monty Python and the Holy Grail (1975), there is a scene involving a Witch Burning Trial that I use in my critical thinking course to analyze valid and sound arguments. It is great for teaching students to recognize the fallacy of the undistributed middle.

In the scene, the townspeople accuse a woman of being a witch, and then a knight leads them through a hilariously flawed line of reasoning.

First, we try to informally map the structure of the argument. One can do this in many different ways but this is the way I break down the structure of the script:

1. We know this woman is a witch because she looks like one.
2. We know this woman is a witch because she dresses like one.
3. We know this woman is a witch because she has a wart.
4. We know this woman is a witch because she turned someone into a newt.
5. One burns witches.
6. One burns wood.
7. Witches burn because they are made out of wood.
8. Bridges are made of wood.
9. However, bridges are multiply realizable. They can be built from stone. [Implied] Building a bridge out of the woman will not determine that she is made of wood.
10. Wood floats in water.
11. A duck floats in water [bread, apples, very small rocks, cider, gravy, cherries, mud, churches, lead].
12. If the woman weighs the same as a duck, then she is made of wood.
13. The woman weighs the same as a duck.
14. Therefore, the woman is a witch.

After going through the script and helping the students find this basic structure (or something similar), we then turn to a logical analysis of this argument. The students will likely be able to identify the argument as unsound very quickly, though they will be slower to understand why it’s invalid.

This argument is clearly unsound. However, we can try to clean up and analyze the argument itself. I break the class up into groups. I provide the students the script and suggest there are four separate arguments in it. I give them the conclusion of each argument below and ask them to try to find the premises in the script that might lead to that conclusion. I warn them ahead of time that they should find the fallacy of the undistributed middle.

The following are the four arguments I they will usually find:

First Argument: Valid. Unsound.

P1. All witches are things that can be burned.

P2. All things that can burn are made of wood.

C: Therefore, all witches are made of wood.

Second Argument: Invalid. Commits Fallacy of the Undistributed Middle.

P1. All things that are made out of wood are also things that can float.

P2. All things that weigh the same as a duck are things that can float.

C: Therefore, things that weigh the same as a duck are things that are made of wood.

Third Argument: Invalid. Commits Fallacy of the Undistributed Middle.

P1. All witches are made out of wood.

P2. All things that weigh the same as a duck are things that are made out of wood.

C: Therefore, all witches are things that weigh the same as a duck.

Fourth Argument: Invalid. Commits Fallacy of Undistributed Middle.

P1. All witches are things that weigh the same as a duck.

P2. This thing weighs the same as a duck.

C: Therefore, this thing is a witch.

This clip is particularly helpful in introducing students to how to break down arguments in everyday usage and figure out what has gone wrong with them. Depending on the class level, the instructor may want to go over each argument with the class as a whole rather than in groups. I find that using Venn diagrams on the board with this assignment can be helpful.

This clip allows students to gain a deeper understanding of the fallacy of the undistributed middle. This analysis also allows for a productive discussion about the difference between validity and soundness. In particular, the first argument is valid but unsound. The students find this a great example to flesh out their intuitions.

Sources and other resources:

• Witch Scene Script.
• “The Undistributed Middle.” Fallacy Files. (4/24/19)
• Yount, David. “Monty Python and The Holy Grail: The Witch Argument in Logical Form and Why it is Fallacious” (2015). (4/24/19)
• “Monty Python and the Quest for the Perfect Fallacy. Teacher’s Guide: The Witches Trial Argument.” Annenberg Classroom. (4/24/19)
• Hoë, Jesse. “Logical Analysis of Monty Python’s Witch Scene from the Holy Grail.” (4/24/19)

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