It first occurred to me that human intuitions were making a qualitative distinction between "No chance" and "A very tiny chance, but worth keeping track of." You can see this in the OB lottery debate, where someone said, "There's a big difference between zero chance of winning and epsilon chance of winning," and I replied, "No, there's an order-of-epsilon difference; if you doubt this, let epsilon equal one over googolplex."The problem is that probability theory sometimes lets us calculate a chance which is, indeed, too tiny to be worth the mental space to keep track of it - but by that time, you've already calculated it. People mix up the map with the territory, so that on a gut level, tracking a symbolically described probability feels like "a chance worth keeping track of", even if the referent of the symbolic description is a number so tiny that if it was a dust speck, you couldn't see it. We can use words to describe numbers that small, but not feelings - a feeling that small doesn't exist, doesn't fire enough neurons or release enough neurotransmitters to be felt. This is why people buy lottery tickets - no one can feel the smallness of a probability that small.
But what I found even more fascinating was the qualitative distinction between "certain" and "uncertain" arguments, where if an argument is not certain, you're allowed to ignore it. Like, if the likelihood is zero, then you have to give up the belief, but if the likelihood is one over googol, you're allowed to keep it.
Now it's a free country and no one should put you in jail for illegal reasoning, but if you're going to ignore an argument that says the likelihood is one over googol, why not also ignore an argument that says the likelihood is zero? I mean, as long as you're ignoring the evidence anyway, why is it so much worse to ignore certain evidence than uncertain evidence?
I have often found, in life, that I have learned from other people's nicely blatant bad examples, duly generalized to more subtle cases. In this case, the flip lesson is that, if you can't ignore a likelihood of one over googol because you want to, you can't ignore a likelihood of 0.9 because you want to. It's all the same slippery cliff.
Consider his example if you ever you find yourself thinking, "But you can't prove me wrong." If you're going to ignore a probabilistic counterargument, why not ignore a proof, too?