You don’t get an infinite regress if you use a universal prior.
The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p.
Actually you still do… You simply have to ask: what is the probability that the universal prior idea is correct? And whatever you say, ask the probability that is correct. And so on.
The regress works no matter what you say, even if you say something about universal priors.
“Correct” in what sense? In the actual agent using it, it’s a probability distribution over statements, not a statement itself! Do you mean “What is the probability that the universal prior has [certain property that we consider a reason to use it]?”
A probability distribution over statements is itself a statement (one states that the probability distribution is X). Maybe you use the word “statement” in a fancy way but I include anything.
And the property I was talking about is truth. But another one could be used.
No, because the universe has a state/law, not a probability distribution over states. A theory/universe/statement is either true or false, a probability distribution over theories is not, though it can be scored for accuracy in various ways. A probability distribution over theories is not a statement about the actual state of the universe.
Similarly, the universal prior is in no way “true”; it’s a distribution, not a statement at all. You shouldn’t even expect it to be “true” since it’s meant to be updated. What is important about it is that it has various nice properties such as eventually learning any computable distribution.
The first prior is where the regress bottoms out. Bayesian reasoning has to stop somewhere—and it stops at the first prior.
This area is known as “The problem of the priors”. For most agents it is no big deal—since they are rapidly swamped by evidence that overwhelms their priors, so there is little sensitivity to their exact values.
You don’t get an infinite regress if you use a universal prior.
Actually you still do… You simply have to ask: what is the probability that the universal prior idea is correct? And whatever you say, ask the probability that is correct. And so on.
The regress works no matter what you say, even if you say something about universal priors.
“Correct” in what sense? In the actual agent using it, it’s a probability distribution over statements, not a statement itself! Do you mean “What is the probability that the universal prior has [certain property that we consider a reason to use it]?”
A probability distribution over statements is itself a statement (one states that the probability distribution is X). Maybe you use the word “statement” in a fancy way but I include anything.
And the property I was talking about is truth. But another one could be used.
No, because the universe has a state/law, not a probability distribution over states. A theory/universe/statement is either true or false, a probability distribution over theories is not, though it can be scored for accuracy in various ways. A probability distribution over theories is not a statement about the actual state of the universe.
Similarly, the universal prior is in no way “true”; it’s a distribution, not a statement at all. You shouldn’t even expect it to be “true” since it’s meant to be updated. What is important about it is that it has various nice properties such as eventually learning any computable distribution.
The first prior is where the regress bottoms out. Bayesian reasoning has to stop somewhere—and it stops at the first prior.
This area is known as “The problem of the priors”. For most agents it is no big deal—since they are rapidly swamped by evidence that overwhelms their priors, so there is little sensitivity to their exact values.
My bayesian reasoning finishes with a posterior. It starts at the first prior. I’m backwards like that.
So, you simply refuse to question the prior. Is this a matter of faith, or what? Why stop there?
More often a matter of birth. Agents usually start somewhere.
A few details about the process.