Pascal’s Wager

I personally find Pascal’s Wager to be an immensely entertaining example of just how wrong you can go with logic.

If you’re not familiar with it, it’s the idea that we should believe in God whether or not we think he exists, because that way if we’re right, we get to go Heaven. Wikipedia has a pretty good page on it here, which outlines two major objections to it. You should go read it, because what I’ve got to say here won’t make a huge amount of sense unless you’re familar with it.
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