So Bayes teaches: do not disobey the laws of logic and math.
Still wondering where the assigning probabilities to truths of theories is.
OK. So what? There’s more to life than that. That’s so terribly narrow. I mean, that part of what you’re saying is right as far as it goes, but it doesn’t go all that far. And when you start trying to apply it to harder cases—what happens? Do you have some Bayesian argument about who to vote for for president? Which convinced millions of people? Or should have convinced them, and really answers the questions much better than other arguments?
Still wondering where the assigning probabilities to truths of theories is.
Well the Dutch books make it so you have to pick some probabilities. Actually getting the right prior is incomplete, though Solomonoff induction is most of the way there.
OK. So what? There’s more to life than that. That’s so terribly narrow. I mean, that part of what you’re saying is right as far as it goes, but it doesn’t go all that far.
Where else are you hoping to go?
And when you start trying to apply it to harder cases—what happens? Do you have some Bayesian argument about who to vote for for president? Which convinced millions of people? Or should have convinced them, and really answers the questions much better than other arguments?
In principle, yes. There’s actually a computer program called AIXItl that does it. In practice I use approximations to it. It probably could be done to a very higher degree of certainty. There are a lot of issues and a lot of relevant data.
Well the Dutch books make it so you have to pick some probabilities.
Can you give an example? Use the ice cream flavors. What probabilities do you have to pick to buy ice cream without being dutch booked?
Where else are you hoping to go?
Explanatory knowledge. Understanding the world. Philosophical knowledge. Moral knowledge. Non-scientific, non-emprical knowledge. Beyond prediction and observation.
In principle, yes.
How do you know if your approximations are OK to make or ruin things? How do you work out what kinds of approximations are and aren’t safe to make?
The way I would do that is by understanding the explanation of why something is supposed to work. In that way, I can evaluate proposed changes to see whether they mess up the main point or not.
So Bayes teaches: do not disobey the laws of logic and math.
Still wondering where the assigning probabilities to truths of theories is.
OK. So what? There’s more to life than that. That’s so terribly narrow. I mean, that part of what you’re saying is right as far as it goes, but it doesn’t go all that far. And when you start trying to apply it to harder cases—what happens? Do you have some Bayesian argument about who to vote for for president? Which convinced millions of people? Or should have convinced them, and really answers the questions much better than other arguments?
Well the Dutch books make it so you have to pick some probabilities. Actually getting the right prior is incomplete, though Solomonoff induction is most of the way there.
Where else are you hoping to go?
In principle, yes. There’s actually a computer program called AIXItl that does it. In practice I use approximations to it. It probably could be done to a very higher degree of certainty. There are a lot of issues and a lot of relevant data.
Can you give an example? Use the ice cream flavors. What probabilities do you have to pick to buy ice cream without being dutch booked?
Explanatory knowledge. Understanding the world. Philosophical knowledge. Moral knowledge. Non-scientific, non-emprical knowledge. Beyond prediction and observation.
How do you know if your approximations are OK to make or ruin things? How do you work out what kinds of approximations are and aren’t safe to make?
The way I would do that is by understanding the explanation of why something is supposed to work. In that way, I can evaluate proposed changes to see whether they mess up the main point or not.