Among all hypotheses consistent with the observations, the simplest is the most likely.
I think this statement of Occam’s razor is slightly misleading. The principle says that you should prefer the simplest hypothesis, but doesn’t say why. As seen in the SEP entry on simplicity, there have been several different proposed justifications.
Also, if I understand Solomonoff induction correctly, the reason for preferring simpler hypotheses is not that such theories are a priori more likely to be true, but rather that using Solomonoff’s universal prior means that there will be a finite bound on the number of prediction errors you make over an infinite string.
Assuming that simpler hypotheses are more likely to be true looks like wishful thinking. But the fact that the number of prediction errors will be bounded seems like a good justification of Occam’s razor.
I think this statement of Occam’s razor is slightly misleading. The principle says that you should prefer the simplest hypothesis, but doesn’t say why. As seen in the SEP entry on simplicity, there have been several different proposed justifications.
Also, if I understand Solomonoff induction correctly, the reason for preferring simpler hypotheses is not that such theories are a priori more likely to be true, but rather that using Solomonoff’s universal prior means that there will be a finite bound on the number of prediction errors you make over an infinite string.
Assuming that simpler hypotheses are more likely to be true looks like wishful thinking. But the fact that the number of prediction errors will be bounded seems like a good justification of Occam’s razor.