Solution to the Puzzle (11/1/2006): Several puzzlers pointed out that the puzzle is similar to an argument known as "Pascal's wager". The philosopher and mathematician Blaise Pascal argued that you should "bet" on God's existence because you stand to gain an infinite value if He exists, while only losing a finite amount if He doesn't. The Boojum argument presents a negative version of this argument, where you stand to lose an infinite amount if the Boojum exists and you don't pray to him, but only lose a finite amount if you do pray. It wasn't part of the puzzle proper, so the following readers deserve extra credit for pointing out this similarity: Dan Adams, Lee Randolph, Matt Turner, and Kyle Wilkinson.

So, what's wrong with the argument? Christopher S. Moore identified the fallacy committed:

The logical fallacy of false dilemma―also known as falsified dilemma, fallacy of the excluded middle, black and white thinking, false dichotomy, false correlative, either/or fallacy and bifurcation―involves a situation in which two alternative points of view are held to be the only options, when in reality there exist one or more other options which have not been considered.

Christopher also deserves extra credit for giving the fallacy some aliases that I hadn't heard before!

John Congdon explains why the argument commits the fallacy:

"…[Y]ou must agree that either it [the Boojum] exists or it doesn't" assumes that, if the Boojum exists, it exists only in the manner described. This ignores a number of possibilities: that the Boojum exists but that praying to it won't help you, that the Boojum exists but is purely benign, that the Boojum exists but praying to it will only help if you pray to it sincerely and not merely out of fear or calculation, or―irrespective of the Boojum's existence―that praying to it will certainly offend the Snark, against whose retribution the anger of the Boojum is a mere bagatelle. Since the calculation of possible outcomes does not indicate the full range of possibilities, it is therefore useless as a guide to what action to take.

Dan Adams sums it up nice and concise:

The problem is that only two possibilities are presented: Boojum exists and the claims are true; Boojum doesn't exist. There could be a third option: Gorjack exists and detests prayers to Boojum and will torture all who pray to Boojum, which changes the face of the whole gambit. There could also be this option: Boojum exists and he hates being prayed to and will torture all who pray to him.

In other words, the chart oversimplifies the situation in the following ways: The "Boojum exists" column conceals many alternatives in addition to the one listed, including that the Boojum exists but doesn't like to be prayed to, the Boojum exists but an anti-Boojum monster also exists who hates people who pray to the Boojum, etc. Similarly, the "Boojum Doesn't Exist" column should include the alternatives of an anti-Boojum existing, or a jealous Yahweh who punishes all those who pray to false gods, etc. One needs to take into account the full range of possibilities since they affect the bottom line value of the decision. The possibilities of a Boojum and an anti-Boojum cancel each other out, leading to the correct conclusion that we really have no good reason to pray to the Boojum. When applied to Pascal's Wager, this is known as the "many gods" objection.

Other readers who correctly identified the mistake are: James Knobbs, Mike McKay, and Wade Wesolowsky. Congratulations to them all!

A few readers suggested, not surprisingly, that the argument was an appeal to fear, or more generally, an appeal to consequences. However, it isn't a fallacious appeal, because it doesn't conclude that the Boojum exists, or even that you should believe in it. Rather, the conclusion is that you should pray to the Boojum. It isn't necessarily fallacious to use fear of bad consequences to motivate people to change their behavior, though it may often be better to use a carrot rather than a stick.

Resource: Alan Hájek, "Pascal's Wager", Stanford Encyclopedia of Philosophy




Now if somebody could just break this down so that small children and World Leaders could understandit.....

Cheers ozylynx

Good one Bill

I see where you're coming from and I too am a devout but untraditional Christian. My faith makes perfectly logical sense to me and I agree that people must find it themselves and unless one is ready for that it's better not to challenge it. No further correspondence will be entered into on faith as it is a certain flame war and if that even begins I ask that this entire thread be removed.

However I placed this as a pure logic problem and had things like WMD and flawed perception in general in mind rather than a religious aspect. Funny how ones personal perspective can colour what one sees as key points. OR is that what it's really all about anyway?

I know I just mentioned a specific political aspect too, only an example people... off the soap box. It's about flawed perception not religion or politics please..

Cheers. ozylynx