Cyan: “Minimum description length” works for English and probably most other languages as well, including abstract logical languages. Increase the number of properties enough, and it will definitely work for any language.
Caledonian: the Razor isn’t intended to prove anything, it is intended to give an ordering of the probability of various accounts. Suppose we have 100 properties, numbered from one to a hundred. X has property #1 through #100. Y has property #1. Which is more likely: Y has properties #1 through #100 as well, or Y has property #1, all prime numbered properties except #17, and property #85. I think it is easy enough to see which of these is simpler and more likely to be true.
Peter Turney: the argument for the Razor is that on average, more complicated claims must be assigned a lower prior probability than simpler claims. If you assign prior probabilities at all, this is necessary on average, no matter how you define simplicity. The reason is that according to any definition of simplicity that corresponds even vaguely with the way we use the word, you can’t get indefinitely simpler, but you can get indefinitely more complicated. So if all your probabilities are equal, or if more probable claims, on average, are more probable than simpler claims, your prior probabilities will not add to 1, but to infinity.
X has property #1 through #100. Y has property #1. Which is more likely: …
As I understand it, this is an example of the fallacy of the excluded middle.
After all, I could make up my own comparison case:
Which is more likely: Y has properties #1 through #100 as well, or Y just has property #1 ?
and come to the opposite conclusion that you have drawn.
The point being that you have to compare the case “Y has properties 1 through 100” with all other potential possible values of Y. and there’s no reason that you happen to necessarily have in your hands a Y that is actually also an X.
Cyan: “Minimum description length” works for English and probably most other languages as well, including abstract logical languages. Increase the number of properties enough, and it will definitely work for any language.
Caledonian: the Razor isn’t intended to prove anything, it is intended to give an ordering of the probability of various accounts. Suppose we have 100 properties, numbered from one to a hundred. X has property #1 through #100. Y has property #1. Which is more likely: Y has properties #1 through #100 as well, or Y has property #1, all prime numbered properties except #17, and property #85. I think it is easy enough to see which of these is simpler and more likely to be true.
Peter Turney: the argument for the Razor is that on average, more complicated claims must be assigned a lower prior probability than simpler claims. If you assign prior probabilities at all, this is necessary on average, no matter how you define simplicity. The reason is that according to any definition of simplicity that corresponds even vaguely with the way we use the word, you can’t get indefinitely simpler, but you can get indefinitely more complicated. So if all your probabilities are equal, or if more probable claims, on average, are more probable than simpler claims, your prior probabilities will not add to 1, but to infinity.
As I understand it, this is an example of the fallacy of the excluded middle.
After all, I could make up my own comparison case: Which is more likely: Y has properties #1 through #100 as well, or Y just has property #1 ? and come to the opposite conclusion that you have drawn.
The point being that you have to compare the case “Y has properties 1 through 100” with all other potential possible values of Y. and there’s no reason that you happen to necessarily have in your hands a Y that is actually also an X.