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Forgive me for stealing the gusto of your post, but it seems I can't make a comment on an old post. I am new here, and I can't help but think that some things are being over looked here.
Maybe everyone is already thinking this, so everyone feels that no one needs to say it (but isn't that exactly the "problem" this is discussing).
I absolutely disagree that generalizing from one example is a bad thing. I do agree that people tend to make that idea permanent, rather than just taking it as a starting point.
We are human. We are living, remember, reactional beings. We are able to make quick decision because we are able to come to quick conclusions. Let me give you an example. You see someone pick up a mushroom, eat it, and then die. What do you think? "If I eat that mushroom, then I will die to." But isn't that exactly the problem you discussed? Generalizing based on one example?
So then you go on to do science and prove that this particular mushroom is bad and not ALL mushrooms; you find out that some (not all) people have allergies to some (not all) mushrooms; but in the mean time you were spared from trial by fire. It is important for people to be able to make a snap decision, it is important for them to be able to figure out what is "going on" from very limit examples. The problem is that people are stubborn; once a person makes up their mind, they stick to it so stead-fast, it takes extra-ordinary measures to change their mind - something like a 95% confidence at minimum (I jest).
Sorry if the explanation is hard to follow. I am bad a setting up / introducing my ideas, so my meaning tends to get lost.
Let me reiterate: You speak as though generalizing is bad. I disagree. You need to have a basis to get started from. You need to be able to start making intelligent decision about the world around you based on what you see. But, you cannot assume that a) you are right or b) that you have accounted for all the variables.
A) Just because you are able to act on knowledge doesn't mean that knowledge is right. It means some of it is right, but not all of it. You need to be open to situations where that knowledge is wrong, and figure out how the situations are different.
B) A good place to start is that XKCD comic that was referenced: http://xkcd.com/385/ When the main character sees the male at the board, he is able to see the male for who he is. He perceives that the male is bad at math. When the female is at the board, the main character only perceives that she is female. I could give any number of explanations for this from Freud to pheromones to National Geographic, but there is no way of know which may be right. The point is he just perceives that "she" is bad at math. And I think that is perfectly acceptable. I DO think that if the main character perceives another female who proves to be good at math, then he needs to overturn his original assumption.
Make assumptions! Do it! But be open to being wrong.