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.
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.