You read the paper! Thanks for pointing out that we know somehow that only a finite number of particles will ever be found.
To explain the “oneicle” problem: It seems like how a scenario is coded into a game matters. For example, if you viewed the timed particles game as having two possible worlds “The device will always emit a particle every 10 seconds.” and “The device will sometimes emit a particle every 10 seconds.”, then the first world cannot pretend to be the second world, but the second world can camouflage itself as the first world for a time, and so (Kelly’s version of) Occam’s razor says the first is simpler—we get the intuitively correct answer.
The alternative coding is somewhat analogous to the color “grue” (which is green up until some date, and blue thereafter). You recode the problem to talk about “oneicles”, a concept that refers to non-particles up to time 1, and particles thereafter. If you allow this sort of recoding, then you would also allow “twoticles”, and the infinite hierarchy of symmetric re-codings causes a problem. I tend to think this is a technical problem that is unlikely to expand into the philosophy part of the theory, but I’m kindof an idiot, and I may be missing something—certainly we would like to avoid coding-dependence.
That’s a problem (the first problem Kelly mentioned in that paper), but do you really require a theory to have no problems remaining in order for it to be counted as insightful? No one else addresses the question “Where does the prior come from?”.
do you really require a theory to have no problems remaining in order for it to be counted as insightful?
It would be one thing if Kelly said that the theory currently can’t predict that another particle will come in 10 seconds, but he hopes to eventually extend it so that it can make predictions like that. But instead he says that Ockham is mute on the question, and that’s the right answer.
No one else addresses the question “Where does the prior come from?”.
Neither does Kelly. I don’t see how we can go from his idea of Ockham to a Bayesian prior, or how to use it directly in decision making. Kelly’s position above suggests that he doesn’t consider this to be the problem that he’s trying to solve. (And I don’t see what is so interesting about the problem that he is trying to solve.)
Okay, I think we’ve reached a point of reflective disagreement.
I agree with you that Kelly was wrong to be enamored of his formalization’s output on the timed particles example; it’s either a regrettable flaw that must be lived with, or a regrettable flaw that we should try to fix, and I don’t understand enough of the topological math to tell which.
However, the unjustified Occam prior in the standard Bayesian account of science is also a regrettable flaw—and Kelly has demonstrated that it’s probably fixable. I find that very intriguing, and am willing to put some time into understanding Kelly’s approach—even if it dissolves something that I previously cherished (such as MDL-based Occam priors).
Reasonable people can reasonably disagree regarding which research avenues are likely to be valuable.
I am very late to the discussion. I have not read Kelley’s papers in detail, so pardon me if my question betrays a fundamental misunderstanding of what you wrote: How can “(Kelly’s version of) Occam’s razor says the first [world] is simpler” and give us “the intuitively correct answer” if an infinite number of particles will be emitted in the first world, even though Kelley has already specified that the device will only emit a finite number of particles?
You read the paper! Thanks for pointing out that we know somehow that only a finite number of particles will ever be found.
To explain the “oneicle” problem: It seems like how a scenario is coded into a game matters. For example, if you viewed the timed particles game as having two possible worlds “The device will always emit a particle every 10 seconds.” and “The device will sometimes emit a particle every 10 seconds.”, then the first world cannot pretend to be the second world, but the second world can camouflage itself as the first world for a time, and so (Kelly’s version of) Occam’s razor says the first is simpler—we get the intuitively correct answer.
The alternative coding is somewhat analogous to the color “grue” (which is green up until some date, and blue thereafter). You recode the problem to talk about “oneicles”, a concept that refers to non-particles up to time 1, and particles thereafter. If you allow this sort of recoding, then you would also allow “twoticles”, and the infinite hierarchy of symmetric re-codings causes a problem. I tend to think this is a technical problem that is unlikely to expand into the philosophy part of the theory, but I’m kindof an idiot, and I may be missing something—certainly we would like to avoid coding-dependence.
That’s a problem (the first problem Kelly mentioned in that paper), but do you really require a theory to have no problems remaining in order for it to be counted as insightful? No one else addresses the question “Where does the prior come from?”.
It would be one thing if Kelly said that the theory currently can’t predict that another particle will come in 10 seconds, but he hopes to eventually extend it so that it can make predictions like that. But instead he says that Ockham is mute on the question, and that’s the right answer.
Neither does Kelly. I don’t see how we can go from his idea of Ockham to a Bayesian prior, or how to use it directly in decision making. Kelly’s position above suggests that he doesn’t consider this to be the problem that he’s trying to solve. (And I don’t see what is so interesting about the problem that he is trying to solve.)
Okay, I think we’ve reached a point of reflective disagreement.
I agree with you that Kelly was wrong to be enamored of his formalization’s output on the timed particles example; it’s either a regrettable flaw that must be lived with, or a regrettable flaw that we should try to fix, and I don’t understand enough of the topological math to tell which.
However, the unjustified Occam prior in the standard Bayesian account of science is also a regrettable flaw—and Kelly has demonstrated that it’s probably fixable. I find that very intriguing, and am willing to put some time into understanding Kelly’s approach—even if it dissolves something that I previously cherished (such as MDL-based Occam priors).
Reasonable people can reasonably disagree regarding which research avenues are likely to be valuable.
I am very late to the discussion. I have not read Kelley’s papers in detail, so pardon me if my question betrays a fundamental misunderstanding of what you wrote: How can “(Kelly’s version of) Occam’s razor says the first [world] is simpler” and give us “the intuitively correct answer” if an infinite number of particles will be emitted in the first world, even though Kelley has already specified that the device will only emit a finite number of particles?
The statements, though contradictory, refer to two different thought experiments.
The two comments, though contradictory, refer to two different thought experiments.
I see. Thanks for the explanation.