Bayesian updating, as a method of learning in general, is induction. It’s trying to derive knowledge from data.
Only in a sense so broad that Popper can rightly be accused of the very same thing. Bayesians use experience to decide between competing hypotheses. That is the sort of “derive” that Bayesians do. But if that is “deriving”, then Popper “derives”. David Deutsch, who you know, says the following:
But, in reality, scientific theories are not ‘derived’ from anything. We do not read them in nature, nor does nature write them into us. They are guesses – bold conjectures. Human minds create them by rearranging, combining, altering and adding to existing ideas with the intention of improving upon them. We do not begin with ‘white paper’ at birth, but with inborn expectations and intentions and an innate ability to improve upon them using thought and experience. Experience is indeed essential to science, but its role is different from that supposed by empiricism. It is not the source from which theories are derived. Its main use is to choose between theories that have already been guessed. That is what ‘learning from experience’ is.
I direct you specifically to this sentence:
Experience is indeed essential to science, but its role is different from that supposed by empiricism. It is not the source from which theories are derived. Its main use is to choose between theories that have already been guessed.
This is what Bayesians do. Experience is what Bayesians use to choose between theories which have already been guessed. They do this using Bayes’ Theorem. But look back at the first sentence of the passage:
But, in reality, scientific theories are not ‘derived’ from anything.
Clearly, then, Deutsch does not consider using the data to choose between theories to be “deriving”. But Bayesians use the data to choose between theories. Therefore, as Deutsch himself defines it, Bayesians are not “deriving”.
The point of this criticism is that to even begin the Bayesian updating process you need probability estimates which are created unscientifically by making them up
Yes, the Bayesians make them up, but notice that Bayesians therefore are not trying to derive them from data—which was your initial criticism above. Moreover, this is not importantly different from a Popperian scientist making up conjectures to test. The Popperian scientist comes up with some conjectures, and then, as Deutsch says, he uses experimental data to “choose between theories that have already been guessed”. How exactly does he do that? Typical data does not decisively falsify a hypothesis. There is, just for starters, the possibility of experimental error. So how does one really employ data to choose between competing hypotheses? Bayesians have an answer: they choose on the basis of how well the data fits each hypothesis, which they interpret to mean how probable the data is given the hypothesis. Whether he admits it or not, the Popperian scientist can’t help but do something fundamentally the same. He has no choice but to deal with probabilities, because probabilities are all he has.
The Popperian scientist, then, chooses between theories that he has guessed on the basis of the data. Since the data, being uncertain, does not decisively refute either theory but is merely more, or less, probable given the theory, then the Popperian scientist has no choice but to deal with probabilities. If the Popperian scientist chooses the theory that the data fits best, then he is in effect acting as a Bayesian who has assigned to his competing theories the same prior.
Do you understand DD’s point that the majority of the time theories are rejected without testing which is in both his books? Testing is only useful when dealing with good explanations.
Do you understand that data alone cannot choose between the infinitely many theories consistent with it, which reach a wide variety of contradictory and opposite conclusions? So Bayesian Updating based on data does not solve the problem of choosing between theories. What does?
Do you understand DD’s point that the majority of the time theories are rejected without testing which is in both his books? Testing is only useful when dealing with good explanations.
Bayesians are also seriously concerned with the fact that an infinity of theories are consistent with the evidence. DD evidently doesn’t think so, given his comments on Occam’s Razor, which he appears to be familiar with only in an old, crude version, but I think that there is a lot in common between his “good explanation” criterion and parsimony considerations.
We aren’t “seriously concerned” because we have solved the problem, and it’s not particularly relevant to our approach.
We just bring it up as a criticism of epistemologies that fail to solve the problem… Because they have failed, they should be rejected.
You haven’t provided details about your fixed Occam’s razor, a specific criticism of any specific thing DD said, a solution to the problem of induction (all epistemologies need one of some sort), or a solution to the infinity of theories problem.
Only in a sense so broad that Popper can rightly be accused of the very same thing. Bayesians use experience to decide between competing hypotheses. That is the sort of “derive” that Bayesians do. But if that is “deriving”, then Popper “derives”. David Deutsch, who you know, says the following:
I direct you specifically to this sentence:
This is what Bayesians do. Experience is what Bayesians use to choose between theories which have already been guessed. They do this using Bayes’ Theorem. But look back at the first sentence of the passage:
Clearly, then, Deutsch does not consider using the data to choose between theories to be “deriving”. But Bayesians use the data to choose between theories. Therefore, as Deutsch himself defines it, Bayesians are not “deriving”.
Yes, the Bayesians make them up, but notice that Bayesians therefore are not trying to derive them from data—which was your initial criticism above. Moreover, this is not importantly different from a Popperian scientist making up conjectures to test. The Popperian scientist comes up with some conjectures, and then, as Deutsch says, he uses experimental data to “choose between theories that have already been guessed”. How exactly does he do that? Typical data does not decisively falsify a hypothesis. There is, just for starters, the possibility of experimental error. So how does one really employ data to choose between competing hypotheses? Bayesians have an answer: they choose on the basis of how well the data fits each hypothesis, which they interpret to mean how probable the data is given the hypothesis. Whether he admits it or not, the Popperian scientist can’t help but do something fundamentally the same. He has no choice but to deal with probabilities, because probabilities are all he has.
The Popperian scientist, then, chooses between theories that he has guessed on the basis of the data. Since the data, being uncertain, does not decisively refute either theory but is merely more, or less, probable given the theory, then the Popperian scientist has no choice but to deal with probabilities. If the Popperian scientist chooses the theory that the data fits best, then he is in effect acting as a Bayesian who has assigned to his competing theories the same prior.
Where do you get the theories you consider?
Do you understand DD’s point that the majority of the time theories are rejected without testing which is in both his books? Testing is only useful when dealing with good explanations.
Do you understand that data alone cannot choose between the infinitely many theories consistent with it, which reach a wide variety of contradictory and opposite conclusions? So Bayesian Updating based on data does not solve the problem of choosing between theories. What does?
Bayesians are also seriously concerned with the fact that an infinity of theories are consistent with the evidence. DD evidently doesn’t think so, given his comments on Occam’s Razor, which he appears to be familiar with only in an old, crude version, but I think that there is a lot in common between his “good explanation” criterion and parsimony considerations.
We aren’t “seriously concerned” because we have solved the problem, and it’s not particularly relevant to our approach.
We just bring it up as a criticism of epistemologies that fail to solve the problem… Because they have failed, they should be rejected.
You haven’t provided details about your fixed Occam’s razor, a specific criticism of any specific thing DD said, a solution to the problem of induction (all epistemologies need one of some sort), or a solution to the infinity of theories problem.