Logical Fallacies In Monty Python and The Holy Grail

Following the rules of logic is the key to making a good argument for any proposition. Logic is something of a science, which with practice, can be mastered. The following is meant to be an amusing demonstration of logic by using an example of bad logic from a scene in the classic British comedy Monty Python and the Holy Grail (1975).

You may watch the clip here and then see my analysis of the logical reasoning below:

An Inductive Argument:

At the beginning of the scene, the mob attempts to use inductive reasoning, which means they attempt to arrive at a conclusion ("She's a witch!") by way of empirical evidence. What evidence do they provide? A witch's nose, witch's clothing, a witch's hat, and a wart. The nose, clothing, and hat all fail to lead to the conclusion, because, as it turns out, they forced her to dress in such a way. Therefore, they are false premises (see the argument below). The wart alone, then, is insufficient to declare her a witch, because non-witches have warts. This is the problem with inductive arguments--they are not conclusively true with absolute certainty. Inductive arguments, at their best, can only suggest the truth of their conclusion with a high degree of probability. [1] Inductive arguments may be strong and cogent. If the given premises lead to the conclusion with a high degree of probability, it is strong. If the given premises are true and they lead to the conclusion, the argument is cogent. In this case, the argument is strong, but not cogent (because three of the premises are false).

The failed inductive argument:

1. The woman has a witch's nose,           (false premise)
2. and [she is wearing] witch's clothing,  (false premise)
3. and [she is wearing] a witch's hat.       (false premise)
4. She has a wart.                                    (insufficient for the conclusion)
5. Only witches have witches' noses, clothing, hats, and warts.
6. Therefore, she's a witch!

The task of proving her witchy ways is not over, however. Due to Sir Bedevere's superior rationalist wisdom, he seeks to guide them through Socratic questioning down a deductive path, rather than an inductive one.

A Deductive Argument:

The transcript of the scene is below, but I have attempted to recompose the narrative as a deductive syllogism. [2] However, I have reconstructed the argument in reverse order, relative to the film, because Sir Bedevere seems to work backwards from the conclusion to the premises. [3]

1. If she weighs the same as a duck, she'll float. (false, confuses weight with density)
2. she does weigh the same as a duck; (true in this case, if the scales are to be trusted)
3. [conclusion #1] Therefore, she'll float. (valid but unsound)
4. If she floats, she is made of wood. (false, many other things float)
5. She does float; (false/based on conclusion #1)
6. [conclusion #2] Therefore, she's made of wood. (valid but unsound)
7. If she's made of wood, she's a witch. (assumed by all in the scene to be true)
8. She is made of wood; (false/based on conclusion #2)
9. [conclusion #3] Therefore, she's a witch! (valid but unsound)

Deductive arguments may be valid and sound. "Valid" means that the given premises logically lead to the given conclusion because they follow a good form. [4] "Sound" means that the premises lead to the conclusion, and all of the premises are actually true. In this case, according to the way in which I have modeled the argument, the three sections of the argument are all valid. However, they are unsound, because a number of the premises are clearly false.

Unfortunately for the young lady accused, this crowd of peasants and their dim-witted leader, Sir Bedevere, do not understand that arguments can be valid but still untrue.
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[1] Scientific data and evidence presented in court are empirical data meant to construct an inductive argument. Scientific theories and verdicts in court can't be proven 100%; however, they can be demonstrated to be true beyond a "reasonable doubt."
[2] A syllogism is merely a form of argument in which a conclusion is inferred from two or more premises.
[3] I attempted to compose the argument in the same order as the film, but I couldn't make sense of it. Reworking it in reverse made it work.
[4] Each of the three deductive arguments that make up the larger argument that she is a witch are valid forms. The logical form that they are follow is called modus ponens, which means that the second line affirms the antecedent of the first first line. An explanation of the four valid deductive forms is beyond the scope of this post.
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Transcript:

Mob: "We've found a witch. May we burn her?"
Sir Bedevere: "How do you know she is a witch?"
Mob: "She looks like one!"

...

Man: "She turned me into a newt (pause)... I got better"
Mob: "Burn her anyway!"
Sir Bedevere: "Quiet, Quiet, there are ways of telling if she is a witch. Tell me, what do you do with witches?"
Mob: "Burn 'em"
Sir Bedevere: "And what do you burn apart from witches?"
Mob: "More witches ... (silence and pondering) ... wood."
Sir Bedevere: "So, why do witches burn?"
Mob: " (pondering) because they're made of wood?"
Sir Bedevere: "Good ... So, how do we well whether she is made of wood?"
Mob: "Build a bridge out of her."
Sir Bedevere: "Ah, but can you not also make bridges out of stone?"
Mob: "Oh yeah..."
Sir Bedevere: "Does wood sink in water?"
Mob: "No, it floats. Throw her into the pond!"
Sir Bedevere: "What also floats in water?"
Mob: "apples...cider...cherries...nuts...churches...very small rocks...lead..."
King Arthur: "A duck!"
Sir Bedevere: "Exactly. So, logically ....
Mob: "If she weighs the same as a duck, she's made of wood."
Sir Bedevere: "And, therefore ...."
Mob: "A witch!"