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Dan_Moore comments on A Proof of Occam's Razor - Less Wrong
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Comments (121)
I think the treatment of complexity is OK in this argument. However, I don't think it proves Occam's Razor. Other than possible exception within set theory, the complexity of an explanation of any phenomenon is always finite. (Counterexample if you disagree?) There is no finite integer which is 'almost' infinite.
So, given xn - the average probability among explanations of complexity n - it's quite possible for a (finite) positive number of integers m > n for which xm > xn.
Yes, I agree with the possibility you mention. I don't think that means it doesn't prove Occam's Razor because I don't think the Razor means that every simpler hypothesis is more probable than every more complex hypothesis. Other things might affect your priors besides how complex the hypothesis is.
<quote>I don't think the Razor means that every simpler hypothesis is more probable than every more complex hypothesis.</quote>
I don't think you've stated the theorem you are trying to prove precisely. I think that would help.
As the complexity of your hypotheses tends to infinity, their probability tends to zero. Still, that doesn't mean that each and every increase of complexity decreases the probability.
I upvoted the article, because I like this definition (i.e., it corresponds well to how I think of Occam's Razor), and I think you've proven it. However, I agree with Oscar Cunningham that the statement at the top of your article is different, and you didn't prove it. In particular, I don't like the phrase 'on average'.
I edited the article.
State that this is what you're trying to prove at the top of your main post. People are downvoting you because you haven't proved what they see as Occam's razor.
I edited the article.