"If you are certain of H no matter what evidence you see you should not change your belief in H, otherwise you are irrational" - I think the conclusion here is that either: (a) you are being irrational for having P(H)=1 or (b) P(H) is in fact 1 and you are correct about this (think of tautologies) and therefore "you are irrational if you stop believing H upon seeing ~H" is only true because the antecedent of this conditional is impossible, that is, you are not going to see ~H because H is the case and you correctly know that. Great series and channel btw, I don't know how you only have 32K subscribers.
In the second half where you are investigating what happens when either E or H is 0 or 1, you put the value 0.5 in the tables. Is this because we have no priors in these cases? Or is it something more subtle than that?
Harry Ray When we get to Types of Bayesianism, you will see that some will assign .5 with no priors. There's no particular reason that I put the .5's in the example. Just giving a possible interpretation of the priors.
The objection you offered indicates that it's counterproductive to be dogmatic, in other words, to assign a value of 0 or 1 about any H or E, based on assumed certainty. Instead, it seems the point of the Bayesian method is to hold degrees of belief and never reach absolute certainty because there is always new evidence to consider.
Potter Suppositionalist And yet, not being able to assign a value of 1 or 0 to any statement is going to cause some problems for the Bayesian in the future. More to come on that in the objection series.
Carneades.org I can't speak for the Bayesian, but when talking about probability values, it should all be provisional. Even if one could feel certain about a probability value, that doesn't mean it's true.
It would seem that unless you begin with a zero or one belief that there is no way to get there through Bayesian epistemology, but if you begin with zero or one, then why bother with Bayesian epistemology it at all? This seems very close to the problem of induction.
Andy B The problem of induction is a concern for Bayesian probability. The method _can_ be used to assign a value of one from a non-one position, but it doesn't seem reasonable to do so. What is a concern is that doing so entails issues such as the paradox of dogmatism. The entire point of the method is to reevaluate probability based on new evidence, but if you take a dogmatic position, then you can't change it later. As Voltaire said, "Doubt is not a pleasant condition, but certainty is absurd."
"If you are certain of H no matter what evidence you see you should not change your belief in H, otherwise you are irrational" - I think the conclusion here is that either:
(a) you are being irrational for having P(H)=1 or
(b) P(H) is in fact 1 and you are correct about this (think of tautologies) and therefore "you are irrational if you stop believing H upon seeing ~H" is only true because the antecedent of this conditional is impossible, that is, you are not going to see ~H because H is the case and you correctly know that.
Great series and channel btw, I don't know how you only have 32K subscribers.
In the second half where you are investigating what happens when either E or H is 0 or 1, you put the value 0.5 in the tables. Is this because we have no priors in these cases? Or is it something more subtle than that?
Harry Ray When we get to Types of Bayesianism, you will see that some will assign .5 with no priors. There's no particular reason that I put the .5's in the example. Just giving a possible interpretation of the priors.
Carneades.org Thanks!
The objection you offered indicates that it's counterproductive to be dogmatic, in other words, to assign a value of 0 or 1 about any H or E, based on assumed certainty. Instead, it seems the point of the Bayesian method is to hold degrees of belief and never reach absolute certainty because there is always new evidence to consider.
Potter Suppositionalist And yet, not being able to assign a value of 1 or 0 to any statement is going to cause some problems for the Bayesian in the future. More to come on that in the objection series.
Carneades.org I can't speak for the Bayesian, but when talking about probability values, it should all be provisional. Even if one could feel certain about a probability value, that doesn't mean it's true.
It would seem that unless you begin with a zero or one belief that there is no way to get there through Bayesian epistemology, but if you begin with zero or one, then why bother with Bayesian epistemology it at all? This seems very close to the problem of induction.
Andy B The problem of induction is a concern for Bayesian probability. The method _can_ be used to assign a value of one from a non-one position, but it doesn't seem reasonable to do so. What is a concern is that doing so entails issues such as the paradox of dogmatism. The entire point of the method is to reevaluate probability based on new evidence, but if you take a dogmatic position, then you can't change it later. As Voltaire said, "Doubt is not a pleasant condition, but certainty is absurd."