The Story
"Come on, Harry! The cave should only be a few minutes away!"
Harry, Ron and Hermione were in a dense forest, picking their way through the underbrush as they slowly but inexorably made their way towards their objective.
"Wait, hang on a moment," said Ron. "Did you hear that?"
"Hear what?" asked Harry
"It sounded like a snort, or something."
"I didn't hear anything" said Harry.
"No, Harry, I heard it too," said Hermione. "In fact, it almost sounded like -"
"- a dragon!" shouted Ron.
It was true. Having reached a clearing in the forest, they discovered that they had reached the cave that was their destination. Most inconveniently, however, their way to the cave was blocked by a sleeping dragon.
"That's it," said Ron. "We can't handle a dragon. We'd better go back."
"We can't go back, Ron!" said Harry. "We've got to get the horcrux!"
"I thought we were searching for the hallows," said Hermione.
"Whatever plot device, Hermione! It's in the cave!"
"Alright, well not leave then," said Ron, "but maybe see if the cave opens up somewhere else. Perhaps there's another entrance?"
"...wait, hang on," said Hermione. "Something isn't right."
"What do you mean?"
"Well, think about it. If Voldemort had a dragon, why would he leave it around just guarding a cave?"
"Uh, gee, I don't know, maybe because he's got a piece of his soul in there?"
"Right, Ron, but he doesn't know that we're looking for them. I mean, if he had something as powerful as a dragon under his control, wouldn't he be doing something else with it other than leaving it around on guard duty in case someone were to happen to come around? I mean, think about it. Having a dragon here would draw a lot of unnecessary attention to this cave. If the last thing he wants is for people to know about this cave, why guard it with something that soon half the countryside would know about? For that matter, if he had a dragon around here, wouldn't we have heard something about it? I mean, in a forest this small, you can't keep a dragon the size of a house secret. And what would it eat? I haven't seen anything in here other than a few squirrels, have you? There isn't enough food around here for something that big. And look! It's not tied to anything. There's nothing keeping it here. If Voldemort could make dragons do what he wanted, without taking them prisoner, wouldn't he have already won the war?"
"That's great, Hermione, but none of that changes the fact that there's a great, massive dragon right in front of us!"
"I don't know Ron, I think maybe it does."
There was silence for a moment before Harry asked "What are you saying, Hermione?"
"I'm saying that it doesn't add up. Nothing about Voldemort keeping a dragon here makes any sense. I'm saying that there's no dragon here. It's some sort of magical illusion."
Harry and Ron were quiet as they digested this. Finally -
"You're bloody mental!" Ron erupted. "Look, Hermione, what you're saying is great and everything, really it is, but there's still a great big dragon in front of us! I can see it! I can hear it! I can smell it, and believe me, I really wish I couldn't do that."
"Okay, so it's a really clever illusion, but we're talking about one of the greatest wizards who ever lived!"
"You can say whatever you want. You can stay here and talk about reasons why the dragon isn't real until the sun comes up, for all I care. All I know is that, right here, right now, there's a dragon directly in front of me. Sure, maybe you're right. Maybe it is an illusion. But do we really want to bet our lives on that?"
"Well, Ron, can you refute my arguments?"
"Do I really need to? I mean, like I said, you can go on all you want, but there's still a dragon. It's still here. I don't know how else to put this. Here, look!"
"Ron, wait!" Harry cried, but it was too late. Ron had already pitched a stone out into the clearing. It bounced off the dragon's tail with a thump before rolling away into the grass. The dragon did not stir.
"There, see? The dragon's real. If it were an illusion, the stone would've gone through it or something."
"Oh, yes Ron, real convincing. It's not as though we learned how to make illusions solid back in third year, or anything!"
"Well what do you think we should do, then, Hermione? If you're wrong and the dragon's real, it will kill us as soon as we get near enough to wake it up!"
"Well? If you're wrong, Ron, and we go away and start searching for another entrance - that may not even exist, I might add - we'll lose days, if not weeks, and Voldemort will end up killing us anyway!"
"That's mental! You're mental!"
"Mental? I'll show you mental!"
"Stop it, both of you," Harry said sharply. He needed to think. The time to make a decision had come.
What's Going On
This time, Ron and Hermione are bickering over something called epistemology. Epistemology basically asks the question: How do we know what we know? Or put another way, what is truth? Hermione and Ron both embodied two major perspectives here.
Hermione was arguing for something called rationalism. Rationalism is the notion that the best path to truth is logic. Ultimately, our minds are the most important tool for determining what's true and what isn't. If something doesn't make sense, then it can't really be true. Perhaps the most well-known example of rationalism is the French philosopher Rene Descartes. His famous statement "cogito ergo sum," or "I think, therefore I am," was brought forth as an answer to the problem he posed, how can we have absolute knowledge? His answer: The only thing we can claim to have absolute knowledge of is the fact that we are thinking. Our senses could all be deceived, the evidence could be misleading, but the one thing we can know with absolute certainty is that we think. To say "I think that I don't think" is a contradiction, an impossibility. So to the rationalist, the surest source of truth comes through what our thoughts can logically determine to be true.
To Hermione, it is completely illogical that a dragon could be there. So, since reason is saying one thing, and the evidence is saying something different, the evidence must be flawed, and our senses must be deceived - in this case, by a magic spell.
Ron, on the other hand, was arguing more for something called empiricism. Empiricism is the notion that the best path to truth is experience. Logic can be flawed, and reasoning can be faulty, but the facts are the facts, and nothing can change that. One of the most prominent empiricists is British philosopher John Locke, who is often associated with the Aristotelean idea of "tabula rasa" - that is to say, that we come into this world as blank slates, and everything we know has to be taught to us. In other words, we develop knowledge through experience of the world around us: contrast this with the rationalist perspective that we come into this world with the ability to know all sorts of things, all we've got to do is use our brains to puzzle those things out logically.
Ron claimed that he had knowledge of the dragon because he was experiencing the dragon's presence: He saw it, he smelt it, he heard it, and eventually he, in a way, touched it. He observed the dragon. To Ron, all the logic in the world isn't going to change any of that - you can't just logic away what your senses experience. You can't just logic away facts.
Now, taken to extremes, both of those positions seem a bit silly. Rationalism, when taken to the extreme, claims that we can never really know or trust anything outside of what we can determine using logic alone; empiricism, when taken to the extreme, means that we can never believe anything that isn't directly communicated to us by our senses. So on one end, we've got a sort of extreme skeptic who constantly questions her senses; on the other end, we've got a sort of robot who just constantly observes and never draws conclusions. Immanuel Kant managed to synthesize the two positions - he looked at rationalism and said "Listen, logic is important, but if you never bother to root it in empirical evidence, it's all just going to seem fantastical. You can talk all you want about some grand theory that's logically airtight, but if the theory doesn't play out in practice, then you've got to revisit it," and he looked at empiricism and said "Evidence is awesome, really, it is, but if it's the only thing you trust, then you can never actually say anything meaningful. All evidence says is that every time you drop something from a tower, it falls. If you want to start talking about why it falls, or whether it will fall again next time, you've got to go beyond evidence and start using reason and logic."
And this, of course, is the position most people take today. Hermione's logical conclusions were still based on empirical evidence (e.g. there weren't enough animals around to sustain a dragon's appetite), while Ron was still drawing logical conclusions from his evidence. So why bother discussing it? Well, because as we saw above, there's going to come a time when what is logically true and what the facts indicate to be true contradict each other - and which one you trust is going to have a huge impact on how you reason and interact with the world around you.
A great place where this sort of conversation comes up is in crime dramas - think CSI, Sherlock, Law and Order, that sort of thing. A fairly common episode premise is that a crime is committed, but the evidence gathered doesn't make sense - the person who it's pointing to has no motive, nothing to gain from the crime, and everything to lose. Sometimes in the show, we'll see a rationalist. This might happen more in a show like Sherlock - the investigator might look at all the facts and say "Okay, these are the facts, but they're stupid facts," and go about investigating. Sure enough, by the end of the episode we've discovered that the person was framed - the facts point to them because the real killer specifically arranged it to look that way. On the other hand, we might see an empiricist. This might happen more in a show like CSI - the investigator looks at all the reasons why the suspect couldn't be the killer, but then looks at the evidence and says "It doesn't add up, but the evidence doesn't lie. He must be hiding something." Sure enough, by the end of the episode, we've discovered that the person with no motive and nothing to gain was actually the victim's ex.
The point is that in the first scenario, the investigator says "If the facts don't make sense, then there's something wrong with the evidence," while in the second scenario, the investigator says "If the facts don't make sense, then there's something wrong with our line of reasoning." Ultimately, when push comes to shove, most of us will fall into one of those two categories: Do we trust what seems to make sense over what the facts indicate to be true? Or do we trust what the facts indicate to be true over what seems to make sense?
Asking and answering these questions reveal a great deal about how we view the world around us.
As a final note, sometimes empiricism is associated with the hard sciences, while rationalism is associated with things like mathematics and philosophy. It's very important that we have both in either camp! The hard sciences need people who are willing to stand up and say "I don't care what the evidence says, it doesn't make any sense! You need to reconsider your theory!" just as fields like mathematics or philosophy need people who are willing to stand up and say "I don't care how logical it is, it doesn't play out in reality! There's zero evidence to support it!" When we don't do this and cordon off rationalists and empiricists to separate disciplines, all of humanity is poorer for it.
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