That is the criterion which the Bayesian idea of evidence lets you relax. Instead of saying that “you need to be able to define experiments where at least one result would be completely impossible by the theory”, a Bayesian will tell you that “you need to be able to define experiments where the probability of one result under the theory is significantly different from the probability of another result”.
Look at, say, the theory that a coin is weighted towards heads. If you want to be pedantic, no result can “definitely prove” that it is not (unusual events can happen), but an even split of heads and tails (or a weighting towards tails) is much more unusual given that theory than a weighting towards heads.
Edit PS: I am totally stealing the meme that “Bayes is a generalization of Popper” from SilasBarta.
Fair point, and it was EY’s essay that showed me the connection. But keep in mind, the point of the essay is, “Bayesian inference is right, look how Popper is a crippled version of it.”
My point in saying “my” meme is different: “Popper and falsificationism are on the right track—don’t shy away from the concepts entirely just because they’re not sufficiently general.” It’s a warning against taking the failures of Popper to mean that any version of falsificationism is severely flawed.
Steal the meme, and spread it as far and as wide as you possibly can! The sooner it beats out “Popper is so 70 years ago”, the better. (Kind of ironic that Bayes long predated Popper, though the formalization of [what we now call] Bayesian inference did not.)
Example of my academically-respected arch-nemesis arguing the exact anti-falsificationist view I was criticizing.
As Robin’s explained below Bayesianism doesn’t do that. You should also see the works of Lakatos and Quine where they discuss the idea that falsification is flawed because all claims have auxiliary hypotheses and one can’t falsify any hypothesis in isolation even if you are trying to construct a neo-Popperian framework.
Yes, but that still doesn’t show falsificationism to be wrong, as opposed to “narrow” or “insufficiently generalized”. Lakatos and Quine have also failed to show how it’s a problem that you can’t rigidly falsifiy a hypothesis in isolation: Just as you can generalize Popper’s binary “falsified vs. unfalsified” to probabilistic cases, you can construct a Bayes net that shows how your various beliefs (including the auxiliary hypotheses) imply particular observations.
The relative likelihoods they place on the observations allow you to know the relative amount by which those various beliefs are attenuated or amplified by any particular observation. This method gives you the functional equivalent of testing hypotheses in isolation, since some of them will be attenuated the most.
If I remember rightly, that’s where poor old Popper came unstuck: having thought of the falsifiability criterion, he couldn’t work out how to rigorously make it flexible. And as no experiment’s exactly 100% uppercase-D Definitive, that led to some philosophers piling on the idea of falsifiability, as JoshuaZ said.
The key idea is “severe testing”, where a “severe test” is a test likely to expose a specific error in a model, if such an error is present. Those models that pass more, and more severe, tests can be regarded as more useful than those that don’t. This approach also disarms the “auxiliary hypotheses” objection JoshuaZ paraphrased; one can just submit those hypotheses to severe testing too. (I wouldn’t be surprised to find out that’s roughly equivalent to the Bayes net approach SilasBarta mentioned.)
Isn’t it an essential criteria of falsifiability to be able to design an experiment that can DEFINITIVELY prove the theory false?
That is the criterion which the Bayesian idea of evidence lets you relax. Instead of saying that “you need to be able to define experiments where at least one result would be completely impossible by the theory”, a Bayesian will tell you that “you need to be able to define experiments where the probability of one result under the theory is significantly different from the probability of another result”.
Look at, say, the theory that a coin is weighted towards heads. If you want to be pedantic, no result can “definitely prove” that it is not (unusual events can happen), but an even split of heads and tails (or a weighting towards tails) is much more unusual given that theory than a weighting towards heads.
Edit PS: I am totally stealing the meme that “Bayes is a generalization of Popper” from SilasBarta.
I’m pretty sure that was handily discussed in An Intuitive Explanation of Bayes’s Theorem and A Technical Explanation of Technical Explanation.
Fair point, and it was EY’s essay that showed me the connection. But keep in mind, the point of the essay is, “Bayesian inference is right, look how Popper is a crippled version of it.”
My point in saying “my” meme is different: “Popper and falsificationism are on the right track—don’t shy away from the concepts entirely just because they’re not sufficiently general.” It’s a warning against taking the failures of Popper to mean that any version of falsificationism is severely flawed.
Ehhcks-cellent!
Steal the meme, and spread it as far and as wide as you possibly can! The sooner it beats out “Popper is so 70 years ago”, the better. (Kind of ironic that Bayes long predated Popper, though the formalization of [what we now call] Bayesian inference did not.)
Example of my academically-respected arch-nemesis arguing the exact anti-falsificationist view I was criticizing.
As Robin’s explained below Bayesianism doesn’t do that. You should also see the works of Lakatos and Quine where they discuss the idea that falsification is flawed because all claims have auxiliary hypotheses and one can’t falsify any hypothesis in isolation even if you are trying to construct a neo-Popperian framework.
Yes, but that still doesn’t show falsificationism to be wrong, as opposed to “narrow” or “insufficiently generalized”. Lakatos and Quine have also failed to show how it’s a problem that you can’t rigidly falsifiy a hypothesis in isolation: Just as you can generalize Popper’s binary “falsified vs. unfalsified” to probabilistic cases, you can construct a Bayes net that shows how your various beliefs (including the auxiliary hypotheses) imply particular observations.
The relative likelihoods they place on the observations allow you to know the relative amount by which those various beliefs are attenuated or amplified by any particular observation. This method gives you the functional equivalent of testing hypotheses in isolation, since some of them will be attenuated the most.
Right, I was speaking in a non-Bayesian context.
If I remember rightly, that’s where poor old Popper came unstuck: having thought of the falsifiability criterion, he couldn’t work out how to rigorously make it flexible. And as no experiment’s exactly 100% uppercase-D Definitive, that led to some philosophers piling on the idea of falsifiability, as JoshuaZ said.
But more recent work in philosophy of science suggests a more sophisticated way to talk about how falsifiability can work in the real world.
The key idea is “severe testing”, where a “severe test” is a test likely to expose a specific error in a model, if such an error is present. Those models that pass more, and more severe, tests can be regarded as more useful than those that don’t. This approach also disarms the “auxiliary hypotheses” objection JoshuaZ paraphrased; one can just submit those hypotheses to severe testing too. (I wouldn’t be surprised to find out that’s roughly equivalent to the Bayes net approach SilasBarta mentioned.)