Logical Analysis of Monty Python's Witch Scene from the Holy Grail.


The Skit

In which Bedevere (soon to be Sir Bedevere) uses logical inference to help the people figure out if a certain woman is indeed a witch, and therefore that they should burn her.

Basic rules of inference.

We will be using the following fundamental rules of inference:

Modus Ponens (MP)

Established ca. 370BC by Artistotle et al., clearly well known by the middle ages.
X.
X->Y.
------
Y.

Modus Bogus (MB)

This rule seems to have been developed prior to the middle ages, possibly by Bedevere himself, but clearly in common usage by the time of the witch-hunt depicted in the video. References to this rule of inference are notably lacking from the literature.
Y.
X->Y.
------
X.

The Analysis

We have the following premisses
W:
same_weight(woman,duck).
(according to the scale)
F:
same_weight(X,Y) and floats(Y) -> floats(X).
(false premiss, possibly acceptable in middle ages)
Df:
floats(duck).
(premiss - OK most ducks float)
Wf:
is_wood(X)->floats(X).
(premiss - OK most woods float)
Wob:
is_wood(X)->burns(X).
(premiss - OK most woods burn)
Wib:
is_witch(X)->burns(X).
(premiss - questionable...)


We can derive the following theorem
T1:is_wood(X)->is_witch(X).

Proof:
A1: is_wood(X).
P1: burns(X).  (A1 and Wob by Modus Ponens)
witch(X).  (P1 and Wib by Modus Bogus)


We can now prove the following propositions:
Prop1: floats(woman).
Proof:
F and Df and W using Modus Ponens

Prop2: is_wood(woman).
Proof:
Prop1 and Wf using Modus Bogus

Prop3: is_witch(woman).
Proof:
Prop2 and T1 using Modus Ponens

Burn!! Burn!!

Alternate Derivations


Last modified: Fri Jan 25 14:11:24 EST 2013