I have a few comments on the critique of Bayesian epistemology, a lot of which I think is mistaken.
You say “It frames the search for knowledge in terms of beliefs (which we quantify with numbers, and must update in accordance with Bayes rule, else risk rationality-apostasy!” I don’t think anyone denies that Bayes theorem is true. It is mathematically proven. The most common criticism of Bayesianism is that it is “too subjective”. I don’t really understand what this means, but few sensible people deny Bayes theorem.
“It has imported valid statistical methods used in economics and computer science, and erroneously applied them to epistemology, the study of knowledge creation.” Economics and computer science are epistemic enterprises. If Bayesianism is the right approach in these fields, it will be difficult to show it is not the right approach in other domains, such as political science, forecasting, other questions that long-termists are interested in.
“It is based on confirmation as opposed to falsification”. Falsificationism is implausible as a philosophy of science. Despite his popularity among scientists who get given one philosophy of science class, Karl Popper was a scientific irrationalist who denied that scientific knowledge has increased over the last few hundred years - (on this, I would recommend David Stove’s Scientific Irrationalism). If you deny that observations confirm scientific theories, then you would have no reason to believe scientific theories which are supported by observational evidence, such as that smoking causes lung cancer.
“It leads to paradoxes”. Lots of smart philosophers deny that pascal’s mugging is a genuine paradox.
[redacted—sorry misread the quote]
“It relies on the provably false probabilistic induction”. Popper was a scientific irrationalist because he denied the rationality of induction. If you deny the rationality of induction, then you must be sceptical about all scientific theories that purport to be confirmed by observational evidence. Inductive sceptics must hold that if you jumped out of a tenth floor balcony, you would be just as likely to float upwards as fall downwards. Equally, do you think that smoking causes lung cancer? Do you think that scientific knowledge has increased over the last 200 years? If you do, then you’re not an inductive sceptic. Inductive scepticism can’t be used to ground a criticism that distinguishes uncertain long-termist probability estimates from probability estimates based on “hard data”. e.g. GiveWell’s estimates on the effectiveness of bednets are based on induction—they use data from studies showing that bednets have reduced the incidence of malaria
“(ironically, it’s precisely this aspect of Bayesianism which is so dubious: its inability to reject any hypothesis). ” This isn’t true. Bayesianism rejects some hypotheses. e.g. it assigns zero probability to some hypotheses, such as those that are logically or analytically false, like “smoking does and does not increase the risk of lung cancer”. It also assigns very low probability to some hypotheses that are not logically or analytically false but have little to no observational support, such as “smoking does not increase the risk of lung cancer”. If ‘reject’ means “assigns <0.001% probability to”, then Bayesianism obviously does reject some hypotheses.
I think you’re mistaking Bayesian epistemology with Bayesian mathematics. Of course, no one denies Bayes’ theorem. The question is: to what should it be applied? Bayesian epistemology holds that rationality consists in updating your beliefs in accordance with Bayes’ theorem. As this LW post puts it:
Core tenet 3: We can use the concept of probability to measure our subjective belief in something. Furthermore, we can apply the mathematical laws regarding probability to choosing between different beliefs. If we want our beliefs to be correct, we must do so.
Next, it’s not that “Bayesianism is the right approach in these fields,” (I’m not sure what that means) it’s that Bayesian methods are useful for some problems. But Bayesianism falls short when it comes to explaining how we actually create knowledge. (No amount of updating on evidence + Newtonian mechanics gives you relativity.)
Despite his popularity among scientists who get given one philosophy of science class.
Love the ad hominem attack.
If you deny that observations confirm scientific theories, then you would have no reason to believe scientific theories which are supported by observational evidence, such as that smoking causes lung cancer.
Smoking causes lung cancer is a hypothesis, smoking does not cause lung cancer is another. We then discriminate between the hypotheses based on evidence (we falsify incorrect hypotheses). We slowly develop more and more sophisticated explanatory theories of how smoking causes lung cancer, always seeking to falsify them. At any time, we are left with the best explanation of a given phenomenon. This is how falsification works. (I can’t comment on your claim about Popper’s beliefs—but I would be surprised if true. His books are filled with examples of scientific progress.)
If you deny the rationality of induction, then you must be sceptical about all scientific theories that purport to be confirmed by observational evidence.
Yes. Theories are not confirmed by evidence (there’s no number of white swans you can see which confirms that all swans are white. “Swans are white” is a hypothesis, which can be refuted by seeing a black swan), they are falsified by it. Evidence plays the role of discrimination, not confirmation.
Inductive sceptics must hold that if you jumped out of a tenth floor balcony, you would be just as likely to float upwards as fall downwards.
No—because we have explanatory theories telling us why we’ll fall downwards (general relativity). These theories are the only ones which have survived scrutiny, which is why we abide by them. Confirmationism, on the other hand, purports to explain phenomenon by appealing to previous evidence. “Why do we fall downwards? Because we fell downwards before”. The sun rising tomorrow morning does not confirm the hypothesis that the sun rises every day. We should not increase our confidence in the sun rising tomorrow because it rose yesterday. Instead, we have a theory about why and when the sun rises when it does (heliocentric model + axis-tilt theory).
Observing additional evidence in favour of the theory should not increase our “credence” in it. Finding confirming evidence of a theory is easy, as evidenced by astrology and ghost stories. The amount of confirmatory evidence for these theories is irrelevant, what matters is whether and by what they can be falsified. There are more accounts of people seeing UFOs than there are of people witnessing gamma ray bursts. According the confirmationism, we should thus increase our credence in the former, and have almost none in the existence of the latter.
If you haven’t read this piece on the failure of probabilistic induction to favour one generalization over another, I highly encourage you to do so.
Anyway, happy to continue this debate if you’d like, but that was my primer.
This is a very strange criticism—he says the proposition is provably false but also has nonzero probability.
He said it has zero probability but is still useful, not nonzero probability.
“It relies on the provably false probabilistic induction”. Popper was a scientific irrationalist because he denied the rationality of induction. If you deny the rationality of induction, then you must be sceptical about all scientific theories that purport to be confirmed by observational evidence. Inductive sceptics must hold that if you jumped out of a tenth floor balcony, you would be just as likely to float upwards as fall downwards. Equally, do you think that smoking causes lung cancer? Do you think that scientific knowledge has increased over the last 200 years? If you do, then you’re not an inductive sceptic. Inductive scepticism can’t be used to ground a criticism that distinguishes uncertain long-termist probability estimates from probability estimates based on “hard data”.
I think you’re overinterpreting the claim (or Ben’s claim is misleading, based on what’s cited). You don’t have to give equal weight to all hypotheses. You might not even define their weights. The proof cited shows that the ratio of probabilities between two hypotheses doesn’t change in light of new evidence that would be implied by both theories. Some theories are ruled out or made less likely in light of incompatible evidence. Of course, there are always “contrived” theories that survive, but it’s further evidence in the future, Occam’s razor or priors that we use to rule them out.
It also assigns very low probability to some hypotheses that are not logically or analytically false but have little to no observational support, such as “smoking does not increase the risk of lung cancer”. If ‘reject’ means “assigns <0.001% probability to”, then Bayesianism obviously does reject some hypotheses.
This depends on your priors, which may be arbitrarily skeptical of causal effects.
I have a few comments on the critique of Bayesian epistemology, a lot of which I think is mistaken.
You say “It frames the search for knowledge in terms of beliefs (which we quantify with numbers, and must update in accordance with Bayes rule, else risk rationality-apostasy!” I don’t think anyone denies that Bayes theorem is true. It is mathematically proven. The most common criticism of Bayesianism is that it is “too subjective”. I don’t really understand what this means, but few sensible people deny Bayes theorem.
“It has imported valid statistical methods used in economics and computer science, and erroneously applied them to epistemology, the study of knowledge creation.” Economics and computer science are epistemic enterprises. If Bayesianism is the right approach in these fields, it will be difficult to show it is not the right approach in other domains, such as political science, forecasting, other questions that long-termists are interested in.
“It is based on confirmation as opposed to falsification”. Falsificationism is implausible as a philosophy of science. Despite his popularity among scientists who get given one philosophy of science class, Karl Popper was a scientific irrationalist who denied that scientific knowledge has increased over the last few hundred years - (on this, I would recommend David Stove’s Scientific Irrationalism). If you deny that observations confirm scientific theories, then you would have no reason to believe scientific theories which are supported by observational evidence, such as that smoking causes lung cancer.
“It leads to paradoxes”. Lots of smart philosophers deny that pascal’s mugging is a genuine paradox.
[redacted—sorry misread the quote]
“It relies on the provably false probabilistic induction”. Popper was a scientific irrationalist because he denied the rationality of induction. If you deny the rationality of induction, then you must be sceptical about all scientific theories that purport to be confirmed by observational evidence. Inductive sceptics must hold that if you jumped out of a tenth floor balcony, you would be just as likely to float upwards as fall downwards. Equally, do you think that smoking causes lung cancer? Do you think that scientific knowledge has increased over the last 200 years? If you do, then you’re not an inductive sceptic. Inductive scepticism can’t be used to ground a criticism that distinguishes uncertain long-termist probability estimates from probability estimates based on “hard data”. e.g. GiveWell’s estimates on the effectiveness of bednets are based on induction—they use data from studies showing that bednets have reduced the incidence of malaria
“(ironically, it’s precisely this aspect of Bayesianism which is so dubious: its inability to reject any hypothesis). ” This isn’t true. Bayesianism rejects some hypotheses. e.g. it assigns zero probability to some hypotheses, such as those that are logically or analytically false, like “smoking does and does not increase the risk of lung cancer”. It also assigns very low probability to some hypotheses that are not logically or analytically false but have little to no observational support, such as “smoking does not increase the risk of lung cancer”. If ‘reject’ means “assigns <0.001% probability to”, then Bayesianism obviously does reject some hypotheses.
Thanks for the engagement!
I think you’re mistaking Bayesian epistemology with Bayesian mathematics. Of course, no one denies Bayes’ theorem. The question is: to what should it be applied? Bayesian epistemology holds that rationality consists in updating your beliefs in accordance with Bayes’ theorem. As this LW post puts it:
Next, it’s not that “Bayesianism is the right approach in these fields,” (I’m not sure what that means) it’s that Bayesian methods are useful for some problems. But Bayesianism falls short when it comes to explaining how we actually create knowledge. (No amount of updating on evidence + Newtonian mechanics gives you relativity.)
Love the ad hominem attack.
Smoking causes lung cancer is a hypothesis, smoking does not cause lung cancer is another. We then discriminate between the hypotheses based on evidence (we falsify incorrect hypotheses). We slowly develop more and more sophisticated explanatory theories of how smoking causes lung cancer, always seeking to falsify them. At any time, we are left with the best explanation of a given phenomenon. This is how falsification works. (I can’t comment on your claim about Popper’s beliefs—but I would be surprised if true. His books are filled with examples of scientific progress.)
Yes. Theories are not confirmed by evidence (there’s no number of white swans you can see which confirms that all swans are white. “Swans are white” is a hypothesis, which can be refuted by seeing a black swan), they are falsified by it. Evidence plays the role of discrimination, not confirmation.
No—because we have explanatory theories telling us why we’ll fall downwards (general relativity). These theories are the only ones which have survived scrutiny, which is why we abide by them. Confirmationism, on the other hand, purports to explain phenomenon by appealing to previous evidence. “Why do we fall downwards? Because we fell downwards before”. The sun rising tomorrow morning does not confirm the hypothesis that the sun rises every day. We should not increase our confidence in the sun rising tomorrow because it rose yesterday. Instead, we have a theory about why and when the sun rises when it does (heliocentric model + axis-tilt theory).
Observing additional evidence in favour of the theory should not increase our “credence” in it. Finding confirming evidence of a theory is easy, as evidenced by astrology and ghost stories. The amount of confirmatory evidence for these theories is irrelevant, what matters is whether and by what they can be falsified. There are more accounts of people seeing UFOs than there are of people witnessing gamma ray bursts. According the confirmationism, we should thus increase our credence in the former, and have almost none in the existence of the latter.
If you haven’t read this piece on the failure of probabilistic induction to favour one generalization over another, I highly encourage you to do so.
Anyway, happy to continue this debate if you’d like, but that was my primer.
He said it has zero probability but is still useful, not nonzero probability.
I think you’re overinterpreting the claim (or Ben’s claim is misleading, based on what’s cited). You don’t have to give equal weight to all hypotheses. You might not even define their weights. The proof cited shows that the ratio of probabilities between two hypotheses doesn’t change in light of new evidence that would be implied by both theories. Some theories are ruled out or made less likely in light of incompatible evidence. Of course, there are always “contrived” theories that survive, but it’s further evidence in the future, Occam’s razor or priors that we use to rule them out.
This depends on your priors, which may be arbitrarily skeptical of causal effects.
Yes thanks my mistake—edited above