initial reaction to your several replies today: I feel like writing several replies that would be quite long, but a) I don’t have time to do that within the next few days and b) I don’t want to spam you with walls of text you’re not interested in. I’ll try and refine my thoughts down to something more short and focused, but, how interested are you in reading the longer less-focused version? This is a “I wrote you a long letter because I didn’t have time to write you a short one” situation—longer is easier, but potentially less useful.
“Does Bayesianism say X” is a complex question to answer—there are a cluster of ideas that are implemented among the group here, that I personally have noticed, but I don’t have a canonical source for what “Bayesianism” says or does not say, so I’d be sharing my current impressions and understandings, and as I’ve said before, I’m not an expert Bayesian, and what I think might not be representative of the group.
As for “What kind of event would cause you to update your prior about Bayesism?”… well at the core of this set of ideas is a mathematical formula. And I understand why that formula is what it is (I walked through the reasoning once, years ago, and it made sense). So if the question was “what kind of event would make my believe Bayes’ formula is incorrect” then it would have to be the same sort of thing that would cause me to question the validity of math more generally—something that would make me think “maybe the Pythagorean theorem doesn’t reliably describe characteristics of triangles”. There are things that could do that, but it’d be a pretty fundamental questioning of the nature of reality. Or, I guess if some mathematician found some fundamental flaw in Bayes’ formula and I could walk through their reasoning? But “Bayesianism” and “Bayes’ formula” are not the same thing, and I could give up on various ideas that cluster around Bayes’ formula much more easily. If I saw this group systematically making errors in thinking that I could trace back to a Bayes-adjacent idea, I’d update my thinking based on that evidence fairly easily. What I’ve seen instead is that members of this group using this form of reasoning have reached conclusions that turned out correct, well ahead of society in general coming to the same conclusions. if that changed, I’d learn from that.
When I said “Bayesianism says”, a few messages above, I was just running with your conceptual frame for the sake of discussion—and there are certain things that are implied by Bayes’ formula which I think everyone would agree on, like “if you have a high prior on something happening that doesn’t happen as expected, that causes a big update, and similarly for low priors on something that happens”. Inputting certain numbers into Bayes’ formula means other numbers come out, and in that sense “Bayesianism says/Bayes’ formula says” consistent things. But there are other ideas that kind of come along for the ride and might be grouped under the label “Bayesianism” while being less directly connected to the formula, and it’s there where I go “I may not be the best person to comment on that/it’s a bit fuzzy/complex”.
I’d suggest picking something you think we disagree about to focus on if we want to make some progress (helps keep discussion tree width small). But you’re also welcome to write down your thoughts with less structure—I’m still interested in that and I get that it can be easier sometimes. If you do, it might be good to, at the end, point out what you think the strongest or most important point / disagreement is, and I’ll focus on that and/or suggest something of my own.
FWIW, I’m already familiar-in-passing with more modern retreats from like hardcore bayesianism. IMO it’s a bit unprincipled but necessary because bayesianism isn’t complete (eg hypothesis generation, evidence modelling, etc). One thing I don’t like about the state of bayesianism is everyone seems to have their pet theory about how to handle the problems. IMO this is a sign that bayesianism is failing (but doesn’t mean it’s irredeemable). If b-ism weren’t failing, we’d know of a more consistent integrated position that people point to and say ‘see X’s book/essays for the gold standard’.
If there is one thing in particularly that I take issue with, it’s the idea that Bayesianism is the logic of science. I disagree with that wholeheartedly. The problem is the leap from applying a statistics method epistemologically. Bayes has no epistemic insights that aren’t covered elsewhere, and the domains where it works aren’t useful for getting to the truth and understanding the world proper. It doesn’t help us to explain how and why scientific progress happens and is possible.
Edit/Addendum: to (loosely and reductively) analogize to pythagoras: bayesianism is to bayes what pyramid power is to pythagoras.
This isn’t exactly a fair analogy, but the point I want to make is that the belief that bayes’ theorem applies to epistemological matters is a massive leap. I can see how it’s tempting and it’s much easier to see how intelligent people would fall into the trap. I don’t mean to be insulting or offensive btw, and I’m sorry if I am, but I don’t want to lie about what I think and am a little short on time.
initial reaction to your several replies today: I feel like writing several replies that would be quite long, but a) I don’t have time to do that within the next few days and b) I don’t want to spam you with walls of text you’re not interested in. I’ll try and refine my thoughts down to something more short and focused, but, how interested are you in reading the longer less-focused version? This is a “I wrote you a long letter because I didn’t have time to write you a short one” situation—longer is easier, but potentially less useful.
“Does Bayesianism say X” is a complex question to answer—there are a cluster of ideas that are implemented among the group here, that I personally have noticed, but I don’t have a canonical source for what “Bayesianism” says or does not say, so I’d be sharing my current impressions and understandings, and as I’ve said before, I’m not an expert Bayesian, and what I think might not be representative of the group.
As for “What kind of event would cause you to update your prior about Bayesism?”… well at the core of this set of ideas is a mathematical formula. And I understand why that formula is what it is (I walked through the reasoning once, years ago, and it made sense). So if the question was “what kind of event would make my believe Bayes’ formula is incorrect” then it would have to be the same sort of thing that would cause me to question the validity of math more generally—something that would make me think “maybe the Pythagorean theorem doesn’t reliably describe characteristics of triangles”. There are things that could do that, but it’d be a pretty fundamental questioning of the nature of reality. Or, I guess if some mathematician found some fundamental flaw in Bayes’ formula and I could walk through their reasoning? But “Bayesianism” and “Bayes’ formula” are not the same thing, and I could give up on various ideas that cluster around Bayes’ formula much more easily. If I saw this group systematically making errors in thinking that I could trace back to a Bayes-adjacent idea, I’d update my thinking based on that evidence fairly easily. What I’ve seen instead is that members of this group using this form of reasoning have reached conclusions that turned out correct, well ahead of society in general coming to the same conclusions. if that changed, I’d learn from that.
When I said “Bayesianism says”, a few messages above, I was just running with your conceptual frame for the sake of discussion—and there are certain things that are implied by Bayes’ formula which I think everyone would agree on, like “if you have a high prior on something happening that doesn’t happen as expected, that causes a big update, and similarly for low priors on something that happens”. Inputting certain numbers into Bayes’ formula means other numbers come out, and in that sense “Bayesianism says/Bayes’ formula says” consistent things. But there are other ideas that kind of come along for the ride and might be grouped under the label “Bayesianism” while being less directly connected to the formula, and it’s there where I go “I may not be the best person to comment on that/it’s a bit fuzzy/complex”.
Heh, I know what you mean.
I’d suggest picking something you think we disagree about to focus on if we want to make some progress (helps keep discussion tree width small). But you’re also welcome to write down your thoughts with less structure—I’m still interested in that and I get that it can be easier sometimes. If you do, it might be good to, at the end, point out what you think the strongest or most important point / disagreement is, and I’ll focus on that and/or suggest something of my own.
FWIW, I’m already familiar-in-passing with more modern retreats from like hardcore bayesianism. IMO it’s a bit unprincipled but necessary because bayesianism isn’t complete (eg hypothesis generation, evidence modelling, etc). One thing I don’t like about the state of bayesianism is everyone seems to have their pet theory about how to handle the problems. IMO this is a sign that bayesianism is failing (but doesn’t mean it’s irredeemable). If b-ism weren’t failing, we’d know of a more consistent integrated position that people point to and say ‘see X’s book/essays for the gold standard’.
If there is one thing in particularly that I take issue with, it’s the idea that Bayesianism is the logic of science. I disagree with that wholeheartedly. The problem is the leap from applying a statistics method epistemologically. Bayes has no epistemic insights that aren’t covered elsewhere, and the domains where it works aren’t useful for getting to the truth and understanding the world proper. It doesn’t help us to explain how and why scientific progress happens and is possible.
Edit/Addendum: to (loosely and reductively) analogize to pythagoras: bayesianism is to bayes what pyramid power is to pythagoras.
This isn’t exactly a fair analogy, but the point I want to make is that the belief that bayes’ theorem applies to epistemological matters is a massive leap. I can see how it’s tempting and it’s much easier to see how intelligent people would fall into the trap. I don’t mean to be insulting or offensive btw, and I’m sorry if I am, but I don’t want to lie about what I think and am a little short on time.