Tom Griffiths

And so your classic logical arguments are arguments that are telling you, oh, the information you have gives you enough constraints on the worlds that you might be in that this is a reasonable conclusion that you can draw about that world.

Probability theory takes one more step, which is to say, for those possible worlds, we're also going to assign a number to them.

And that number reflects our degree of belief about the probability that that world is true.

And then as soon as you do that and you start following the rules of probability theory, you're then updating your beliefs about what world is it that we're likely to be in based on the information that I've got so far.

And so the logical arguments still work, right?

So you can think about a logical argument as telling you that something is true with probability one, that with certainty, it has to be the case that you're in a world where this thing is true.

But it's generalized by probability theory in allowing us to say, oh, we don't have enough information to determine that this thing is true with certainty.

But we can say, oh, well, there's like a 70% chance this thing is true.

But the same kind of idea of as you get information, you're maybe ruling out some possible worlds, and as a consequence of that, you're changing the probabilities of the other worlds that you could be in, or you're

getting information that changes the chances that you think you're in one world or another, and then you're just doing the same kind of thing.

It's just that you're now doing it in this much more graded way.

No, it's a tool at that abstract computational level of saying, what is it that we should be doing?

What's the solution, the ideal solution to the problem that our minds face?

And so when our minds face inductive problems, probability theory tells us what the ideal solution to those problems look like.

And of course, there's lots of ways that that doesn't line up with the things that people actually do.

And in the 20th century, we started to explore those.

Some of those are things that we can explain from this sort of Bayesian perspective, but where we have to think about people doing something slightly different from the thing that they've been told to do.

I can talk a little more about that.

And then some of them are...

in between these different levels of analysis.