Should I use a theory which I understand and which has an apparently necessary flaw, or a theory which is underspecified and therefore “avoids” this difficulty?
Saying your epistemology has a “necessary flaw” is an admission of defeat, that it doesn’t work. The “necessary flaw” is unavoidable if you are committed to the justificationist way of thinking. Popper saw that the whole idea of justification is wrong and he offered a different idea to replace it—an idea with no known flaws. You criticize Popper for being underspecified, yet he elaborated on his ideas in many books. And, furthermore, no amount of mathematical precision or formalism will paper over cracks in justificationist epistemologies.
Saying your epistemology has a “necessary flaw” is an admission of defeat,
In this case, its recognition of reality. I repeat that I would like to defer this conversation until we have something concrete to disagree about. Until then I don’t care about that difference.
The “necessary flaw” arises because all justificationist epistemologies lead to infinite regress or circular arguments or appeals to authority (or even sillier things). That you think there is no alternative to justificationism and I don’t is something concrete we disagree about.
It’s interesting how different Bayesians say different things. They don’t seem to all agree with each other even about their basic claims. Sometimes Bayesianism is proved, other times it is acknowledged to have known flaws. Sometimes it may be completely compatible with Popper, other times it is dethroning Popper. It seems to me that perhaps Bayesianism is a bit underspecified. I wonder why they haven’t sorted out these internal disputes.
Sometimes Bayesianism is proved, other times it is acknowledged to have known flaws. Sometimes it may be completely compatible with Popper, other times it is dethroning Popper. It seems to me that perhaps Bayesianism is a bit underspecified. I wonder why they haven’t sorted out these internal disputes.
There are disputes among the Bayesians. But you are confusing different issues. First, the presence of internal disputes about the borders of an idea is not a priori a problem with an idea that is in progress. The fact that evolutionary biologists disagree about how much neutral drift matters isn’t a reason to reject evolution. (It is possible that I’m reading an unintended implication here.)
Moreover, most of what you are talking about here are not contradictions but failure to understand. That Bayesianism has flaws is a distinct claim from when someone talks about something like Cox’s theorem which is the sort of result that Bayesians are talking about that you refer to as “Sometimes Bayesianism is proved”(which incidentally is a terribly unhelpful and vague way of discussing the point). The point of results like Cox’s theorem is that if one very broad attempts under certain very weak assumptions to formalize epistemology you must end up with some form of Bayesianism. At the same time it is important to keep in mind that this isn’t saying all that much. It doesn’t for example say anything about what one’s priors should be. Thus one has the classical disagreement between objective and subjective Bayesians based on what sort of priors to use (and within each of those there is further breakdown. LessWrong seems to mainly have objective Bayesians favoring some form Occam prior, although just what is not clear.) Similarly, when discussing whether or not Bayesianism is compatible with Popper depends a lot on what one means by “Bayesianism”, “compatible” and “Popper”. Bayesianism is certainly not compatible with a naive-Popperian approach, which is what many are talking about when they say that it is not compatible (and as you’ve already noted Popper himself wasn’t a naive Popperian). But some people use Popper to mean the idea that given an interesting hypothesis one should search out for experiments which would be likely to falsify the hypothesis if it is false (an idea that actually predates Popper) but what one means by falsify can be a problem.
Saying your epistemology has a “necessary flaw” is an admission of defeat, that it doesn’t work. The “necessary flaw” is unavoidable if you are committed to the justificationist way of thinking. Popper saw that the whole idea of justification is wrong and he offered a different idea to replace it—an idea with no known flaws. You criticize Popper for being underspecified, yet he elaborated on his ideas in many books. And, furthermore, no amount of mathematical precision or formalism will paper over cracks in justificationist epistemologies.
In this case, its recognition of reality. I repeat that I would like to defer this conversation until we have something concrete to disagree about. Until then I don’t care about that difference.
The “necessary flaw” arises because all justificationist epistemologies lead to infinite regress or circular arguments or appeals to authority (or even sillier things). That you think there is no alternative to justificationism and I don’t is something concrete we disagree about.
Adding a reference for this comment: Münchhausen Trilemma.
It’s interesting how different Bayesians say different things. They don’t seem to all agree with each other even about their basic claims. Sometimes Bayesianism is proved, other times it is acknowledged to have known flaws. Sometimes it may be completely compatible with Popper, other times it is dethroning Popper. It seems to me that perhaps Bayesianism is a bit underspecified. I wonder why they haven’t sorted out these internal disputes.
There are disputes among the Bayesians. But you are confusing different issues. First, the presence of internal disputes about the borders of an idea is not a priori a problem with an idea that is in progress. The fact that evolutionary biologists disagree about how much neutral drift matters isn’t a reason to reject evolution. (It is possible that I’m reading an unintended implication here.)
Moreover, most of what you are talking about here are not contradictions but failure to understand. That Bayesianism has flaws is a distinct claim from when someone talks about something like Cox’s theorem which is the sort of result that Bayesians are talking about that you refer to as “Sometimes Bayesianism is proved”(which incidentally is a terribly unhelpful and vague way of discussing the point). The point of results like Cox’s theorem is that if one very broad attempts under certain very weak assumptions to formalize epistemology you must end up with some form of Bayesianism. At the same time it is important to keep in mind that this isn’t saying all that much. It doesn’t for example say anything about what one’s priors should be. Thus one has the classical disagreement between objective and subjective Bayesians based on what sort of priors to use (and within each of those there is further breakdown. LessWrong seems to mainly have objective Bayesians favoring some form Occam prior, although just what is not clear.) Similarly, when discussing whether or not Bayesianism is compatible with Popper depends a lot on what one means by “Bayesianism”, “compatible” and “Popper”. Bayesianism is certainly not compatible with a naive-Popperian approach, which is what many are talking about when they say that it is not compatible (and as you’ve already noted Popper himself wasn’t a naive Popperian). But some people use Popper to mean the idea that given an interesting hypothesis one should search out for experiments which would be likely to falsify the hypothesis if it is false (an idea that actually predates Popper) but what one means by falsify can be a problem.