The Labyrinth and Logic

There is a great scene in the movie The Labyrinth (that doesn’t involve David Bowie in purple tights, thank you) in which a logic puzzle is presented to Sarah (the main character). There are two guards (really four, but two play no real role other than to look weird). One of them tells Sarah that one of them always tells the truth, and one of them always lies. Each guard (we will refer to them as A and B) stands in front of separate doors (we will refer to them as 1 and 2); one leads to the castle and one leads to certain death. She is permitted to ask one question and then make her choice. The following is her reasoning:

A (1)                                                                                        B (2)

Question to A: Would B tell me 1 leads to the castle?

Answer from A: Yes

Sarah’s conclusion: Then door 2 leads to the castle, and 1 leads to certain death.

Is this logical?

If A is telling the truth, then B is lying.

If A is telling the truth, then B would tell Sarah door 1 leads to the castle.

But then it is the case that door 1 does not lead to the castle, but instead to certain death.

If A is lying, then B is telling the truth.

If A is lying, then B would not tell Sarah door 1 leads to the castle.

But then it is the case that door 1 does not lead to the castle, but instead to certain death.

However, can we not question the premise in the first place?

B is the one who tells us “one of us always tells the truth, and one of us always lies.” But suppose he is lying? Then it is the case that either of them could tell the truth or lie. But for the sake of argument suppose it is true. In that case, we know B is the one who tells the truth, and A lies. However, even this is not certain, for it seems that both A and B agree to the rules, which are: she can only ask one of them the question, and one of them always tells the truth while the other always lies. In this case, it seems “always” is within the context of the puzzle itself (else the proposition is plainly false, as both A and B agree these are the rules).

What’s the point? Logical entailment. This will sharpen one’s thinking in understanding deduction and entailments of certain positions. If one understands an entailment of certain logical givens or premises, he may better undertake a refutation (or even an acceptance) of those propositions. Thinking rationally and clearly is the only way we will be able to evaluate critically our own proffered arguments. This is what we must do in order to present the best case for the Christian God as possible.

-----------------------------------------------------

All posts, and the blog Possible Worlds, are the sole intellectual property of Randy Everist. One may reprint part or all of this post so long as: a) full attribution is given (Randy Everist, Possible Worlds), b) all use is non-commercial, and c) one is in compliance with the Creative Commons license at the bottom on the main page of this blog.