Something You Believe Is Wrong

No one is omniscient. No one knows everything. That means everyone believes something that is wrong (at least everyone who's not in a state of radical doubt). That includes me and you.

There is something I believe that is wrong. There is something you believe that is wrong. The problem is false beliefs feel just the same as true beliefs. Even something you know is true, might still be false.

And the only way to improve the situation, is to be willing to change your mind. Keep that in mind when you interact with someone who disagrees with you. They're probably not evil. They might not be stupid. They may not even be wrong. They have reasons for believing what they believe, just like you do. They might not be good reasons, but you can't determine that until you know what they are.

Note that I'm not saying you should blindly accept what someone who disagrees with you says. But nor should you blindly reject them either. You should be willing to listen to their arguments, and honestly evaluate them. Even for things you're absolutely sure are true, because those are the things you're least likely to question on your own.

So, always be willing to keep an open mind. Someone who disagrees with you might know something you don't.

Can You Choose What You Believe?

It's a simple yes or no question, right? Either you can choose what you believe in the same way you can choose what to have for breakfast, or you can't in the same way you can't choose to obey the law of gravity.

Well, no. Whether or not something is a choice is not a simple binary yes or no. It is, as nearly everything else is, a continuum. We don't normally notice it, because we usually only encounter examples at extreme ends of the continuum, like breakfast or gravity.

But there are examples of in-betweens. Consider a person with OCD. Does such a person choose to wash their hands over and over? To a degree, they do, but to a degree they don't.

It's the same with choosing what to believe. You form beliefs based on what you see and hear, and you can't really change that. But you can choose what to look at and who to listen to. And even when beliefs are deliberately chosen, it still takes a long time to really convince yourself of it.

Inferential Distance

Suppose you're trying to teach someone calculus. Before they can learn calculus, they have to learn algebra. Before they can learn algebra, they have to learn arithmetic. This is the basic idea of inferential distance - background knowledge needed the understand the matter at hand.

Put this way, it looks simple, maybe not even worth talking about. But it's more subtle than that. To start with, arithmetic, algebra and calculus aren't single subjects. They're a whole bunch of related but still different subjects, which need to be learned independently. The learn integration, you have to learn differentiation, before that you have to learn limits, before that functions, variables, division, mulitplication, subtraction, addition... And don't forget the really fundamental things like what a number is.

And that's the really tricky part of inferential distance. There are a lot of things you know that you don't know you know. That is to say, you know them so well, it doesn't even occur to you to that someone else might not know it. Things that are so fundamental to your point of view that they're invisible to it. And so when you try to explain something to someone, you accidentally skip over a bunch of inferential steps, resulting in misunderstanding and each party will walk away thinking the other is stupid or crazy.

Consider a biologist talking to a creationist. They might try to explain the evidence for evolution, but before the creationist can understand that, they have to understand what evidence means, how science works, maybe even something as simple as why truth is important...

Justified True Belief?

Epistemology is the branch of philosophy interested in the study of knowledge. One of the foundational questions of epistemology is "What does it mean to know something?". A common answer is that knowledge is justified true belief. In order to know something, you have to believe it, have a good reason for believing it and it has to actually be true.

That sounds pretty good, but there are problems with it. It's possible to construct scenarios in which all three conditions are apparently met, but it doesn't seem like anything was "known".

There's also the question of what counts as justification. But I think there's another, more fundamental, problem with this definition. One I don't think I've ever seen anyone else point out.

No definition of knowledge should include the condition of being true.

To do so is to make the term inapplicable in any situation remotely resembling real life. The reason for that is because of the answer to another fundamental question of epistemology: "Is it possible to be absolutely certain of something?". The answer to that is no. (Of course, others disagree, and I should probably write another post explaining why I think that.) All we can do is get more and more evidence for something, getting closer and closer to 100% certainty, but never actually reaching it.

In toy examples, whether a given fact is true or not is simply assumed/given. So if a hypothetical character has a justified belief, we can say whether that character knows it or not, because of our god-like omniscience. But in real life, no one has that omniscience.

Consider the same question - Is a belief knowledge or not - applied to yourself. Do I know the sun will rise tomorrow, or do I just believe it? Well, I certainly think it's true that the sun will come up. I wouldn't believe it if it I didn't think that, tautologically. But if that's the standard, then I ought to consider every belief I have to be knowledge. If I didn't believe they were true, I wouldn't believe them.

And if we apply that standard to other people, then our evaluations of whether someone else knows something or merely believes it, simply becomes a question of whether they agree with you or not.

I propose a simpler definition: Knowledge is belief that is held with a high degree of confidence.

This definition fits very well into a Bayesian framework. Degree of confidence is simply probability. If you believe something is true with a probability greater than, say, 99.9%, you can be said to know it. This also handily deals with the question of what counts as justification - that's just Bayesian evidence.