Monty Python, ducks and witches.

As as fan of Monty Python and ducks, I’m keen to assess the logical integrity of the duck-witch segment in Monty Python and the Holy Grail:

• There are ways of telling whether she is a witch.
• Are there? What are they? Tell us. - Do they hurt?
• Tell me, what do you do with witches?
• Burn them!
• And what do you burn, apart from witches?
• More witches! - Wood!
• So why do witches burn?
• 'Cause they're made of wood? - Good!
• How do we tell if she is made of wood? - Build a bridge out of her.
• But can you not also make bridges out of stone?
• Oh, yeah.
• Does wood sink in water?
• No, it floats. - Throw her into the pond!
• What also floats in water?
• Bread. - Apples.
• Very small rocks. - Cider! Great gravy.
• Cherries. Mud. - Churches.
• Lead. - A duck!
• Exactly.
• So, logically--
• If she weighs the same as a duck...
• she's made of wood.
• And therefore?
• A witch!
• A duck! A duck! - Here's a duck.
• We shall use my largest scales.
• Burn the witch!

This dialog could be simplified into the following logical statements:

1. You burn witches.
2. You burn wood.
3. Witches burn because they are made of wood.
4. Bridges are made of wood.
5. However, bridges are also built from stone. Therefore building a bridge out of the woman will not determine that she is made of wood.
6. Wood floats in water.
7. A duck floats in water
8. If the woman weighs the same as a duck, then she is made of wood.
9. The woman weighs the same as a duck.
10. Therefore, the woman is a witch.

From here we can derive four distinct arguments. One of which is valid but unsound and three of which are invalid. Appalling!

First Argument:

P1. All witches are things that can be burned.

P2. All things that can be burned are made of wood.

C: Therefore, all witches are made of wood.

This is a valid argument but premise 2 is clearly unsound!

Second Argument:

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.

This is an invalid argument. It commits the fallacy of the undistributed middle.

Third Argument:

P1. All witches are made of wood.

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

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

This is an invalid argument. It commits the fallacy of the undistributed middle.

Fourth Argument:

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 is an invalid argument. It commits the fallacy of the undistributed middle.

Note - if you are looking for a key takeaway then this is it.