Emphasis on low-level. Thinking “hmm, the probability of this outcome is 1/3” is high-level, conscious cognition. The sense in which we’re “Bayesians” is like the sense in which we’re good at calculus: catching balls, not (necessarily) passing written tests.
The conjunction fallacy is a closer to being a legitimate counterargument, but I would remind you that “Bayes-like” does not preclude the possibility of deviations from Bayes.
Perhaps some general perspective would be helpful. My point of view is that “inference = Bayes” is basically an analytic truth. That is, “Bayesian updating” is the mathematically precise notion that best corresponds to the vague, confused human idea of “inference”. The latter turns out to mean Bayesian updating in the same sense that our intuitive idea of “connectedness” turns out to meanthis. As such, we can make our discourse strictly more informative by replacing talk of “inference” with talk of “Bayesian updating” throughout. We can talk about Bayesian updating done correctly, and done incorrectly. For example, instead of saying “humans don’t update according to Bayes”, we should rather say, “humans are inconsistent in their probability assignments”.
An idea becomes “non-confused” when it is turned into math. “Inference” may be a confused notion, but Bayesian updating isn’t.
If Popper has better math than Bayes, so much the better. That’s not the impression I get from your posts, however. The impression I get from your posts is that you meant to say “Hey! Check out this great heuristic that Karl Popper came up with for generating more accurate probabilities!” but instead it came out as “Bayes sucks! Go Popper!”
If the math is non-confused, and the idea is confused, then what’s going on is not that the idea became non-confused but the math doesn’t correspond to reality.
If Popper has better math than Bayes, so much the better.
He doesn’t have a lot of math.
No matter how much math you have, you always face problems of considering issues like whether some mathematical objects correspond to some real life things, or not. And you can’t settle those issues with math.
“Bayes sucks! Go Popper!”
You guys are struggling with problems, such as justificationism, which Popper solved. Also with instrumentalism, lack of appreciation for explanatory knowledge, foundationalism, etc
If the math is non-confused, and the idea is confused, then what’s going on is not that the idea became non-confused but the math doesn’t correspond to reality.
What? Only confused ideas correspond to reality? That makes no sense.
No matter how much math you have, you always face problems of considering issues like whether some mathematical objects correspond to some real life things, or not. And you can’t settle those issues with math.
You settle those issues by experiment.
You guys are struggling with problems, such as justificationism, which Popper solved. Also with instrumentalism, lack of appreciation for explanatory knowledge, foundationalism, etc
I’m not sure I see the problem, frankly. As far as I can tell this would be like me telling you that you’re “struggling with the problem of Popperianism”.
If you take a confused idea, X. And you take some non-confused math, Y. Then they do not correspond precisely.
No matter how much math you have, you always face problems of considering issues like whether some mathematical objects correspond to some real life things, or not. And you can’t settle those issues with math.
You settle those issues by experiment.
Can’t be done. When you try to set up an experiment you always have to have philosophical theories. For example if you want to measure something, you need a theory about the nature of your measuring device. e.g. you’ll want to come up with some mathematical properties and know if they correspond to the real physical object. So you run into the same problem again.
I’m not sure I see the problem, frankly.
How are theories justified?
How are theories induced? If you say using the solomonoff prior, then are the theories it offers always best? If not, that’s a problem, right? If yes, what’s the argument for that?
Emphasis on low-level. Thinking “hmm, the probability of this outcome is 1/3” is high-level, conscious cognition. The sense in which we’re “Bayesians” is like the sense in which we’re good at calculus: catching balls, not (necessarily) passing written tests.
The conjunction fallacy is a closer to being a legitimate counterargument, but I would remind you that “Bayes-like” does not preclude the possibility of deviations from Bayes.
Perhaps some general perspective would be helpful. My point of view is that “inference = Bayes” is basically an analytic truth. That is, “Bayesian updating” is the mathematically precise notion that best corresponds to the vague, confused human idea of “inference”. The latter turns out to mean Bayesian updating in the same sense that our intuitive idea of “connectedness” turns out to mean this. As such, we can make our discourse strictly more informative by replacing talk of “inference” with talk of “Bayesian updating” throughout. We can talk about Bayesian updating done correctly, and done incorrectly. For example, instead of saying “humans don’t update according to Bayes”, we should rather say, “humans are inconsistent in their probability assignments”.
I agree with you that “inference” is a vague and confused notion.
I don’t agree that finding some math that somewhat corresponds to a bad idea, makes things better!
Popper’s approach to it is to reject the idea and come up with better, non-confused ideas.
An idea becomes “non-confused” when it is turned into math. “Inference” may be a confused notion, but Bayesian updating isn’t.
If Popper has better math than Bayes, so much the better. That’s not the impression I get from your posts, however. The impression I get from your posts is that you meant to say “Hey! Check out this great heuristic that Karl Popper came up with for generating more accurate probabilities!” but instead it came out as “Bayes sucks! Go Popper!”
If the math is non-confused, and the idea is confused, then what’s going on is not that the idea became non-confused but the math doesn’t correspond to reality.
He doesn’t have a lot of math.
No matter how much math you have, you always face problems of considering issues like whether some mathematical objects correspond to some real life things, or not. And you can’t settle those issues with math.
You guys are struggling with problems, such as justificationism, which Popper solved. Also with instrumentalism, lack of appreciation for explanatory knowledge, foundationalism, etc
What? Only confused ideas correspond to reality? That makes no sense.
You settle those issues by experiment.
I’m not sure I see the problem, frankly. As far as I can tell this would be like me telling you that you’re “struggling with the problem of Popperianism”.
If you take a confused idea, X. And you take some non-confused math, Y. Then they do not correspond precisely.
Can’t be done. When you try to set up an experiment you always have to have philosophical theories. For example if you want to measure something, you need a theory about the nature of your measuring device. e.g. you’ll want to come up with some mathematical properties and know if they correspond to the real physical object. So you run into the same problem again.
How are theories justified?
How are theories induced? If you say using the solomonoff prior, then are the theories it offers always best? If not, that’s a problem, right? If yes, what’s the argument for that?