Neither the potential infinity of theories, nor the possibility of error favour Popper over Bayes.
“The reason it doesn’t is there’s always infinitely many things supported by any evidence, in this sense. Infinitely many things which make wildly different predictions about the future, but identical predictions about whatever our evidence covers. If Y is 10 white swans, and X is “all swans are white” then X is supported, by your statement. But also supported are infinitely many different theories claiming that all swans are black, and that you hallucinated. You saw exactly what you would see if any of those theories were true, so they get as much support as anything else. There is nothing (in the concept of support) to differentiate between “all swans are white” and those other theories.”
And that doesn’t matter unless they (a) all have equal prior,and (b) will continue to be supported equally
by any future evidence. (a) Is never the case, but doesn’t help that much since, without a solution to (b), the relative
rankings of various theories will never change from their priors, making evidence irrelevant. (b) is also
never the case. The claims that 100% of swans are white, 90% are white, 80%, and so on will not all be
equaly supported by a long series of observations of white swans. A Popperian could argue that the the theories that
are becoming relatively less supported are becoming partially refuted. But relative refutation of T
is relative support for not-T, just because of the meaning of relative. The Popperian can only
rescue the situation by showing that there is absolute refutation, but no absolute support.
“If you do add something else to differentiate, I will say the support concept is useless. The new thing does all the work. And further, the support concept is frequently abused. I have had people tell me that “all swans are black, but tomorrow you will hallucinated 10 white swans” is supported less by seeing 10 white swans tomorrow than “all swans are white” is, even though they made identical predictions (and asserted them with 100% probability, and would both have been definitely refuted by anything else).”
They have different priors. The halucination theory is a skeptical hypothesis, and it is well known that skeptical
hypotheses can’t be refuted empirically. But we can still give them low priors. Or regard them as bad explanations—for instance, reject them because they are unfalsifiable or too easy to vary.
Neither the potential infinity of theories, nor the possibility of error favour Popper over Bayes.
“The reason it doesn’t is there’s always infinitely many things supported by any evidence, in this sense. Infinitely many things which make wildly different predictions about the future, but identical predictions about whatever our evidence covers. If Y is 10 white swans, and X is “all swans are white” then X is supported, by your statement. But also supported are infinitely many different theories claiming that all swans are black, and that you hallucinated. You saw exactly what you would see if any of those theories were true, so they get as much support as anything else. There is nothing (in the concept of support) to differentiate between “all swans are white” and those other theories.”
And that doesn’t matter unless they (a) all have equal prior,and (b) will continue to be supported equally by any future evidence. (a) Is never the case, but doesn’t help that much since, without a solution to (b), the relative rankings of various theories will never change from their priors, making evidence irrelevant. (b) is also never the case. The claims that 100% of swans are white, 90% are white, 80%, and so on will not all be equaly supported by a long series of observations of white swans. A Popperian could argue that the the theories that are becoming relatively less supported are becoming partially refuted. But relative refutation of T is relative support for not-T, just because of the meaning of relative. The Popperian can only rescue the situation by showing that there is absolute refutation, but no absolute support.
“If you do add something else to differentiate, I will say the support concept is useless. The new thing does all the work. And further, the support concept is frequently abused. I have had people tell me that “all swans are black, but tomorrow you will hallucinated 10 white swans” is supported less by seeing 10 white swans tomorrow than “all swans are white” is, even though they made identical predictions (and asserted them with 100% probability, and would both have been definitely refuted by anything else).”
They have different priors. The halucination theory is a skeptical hypothesis, and it is well known that skeptical hypotheses can’t be refuted empirically. But we can still give them low priors. Or regard them as bad explanations—for instance, reject them because they are unfalsifiable or too easy to vary.