That only works if you have a countable set of mutually exclusive hypotheses, and exactly one of them is true. Not all worlds are like that. For example, if the “world” is a single real number picked uniformly from [0,1], then it’s hard to say what the hypotheses should be.
If hypotheses aren’t restricted to being mutually exclusive, the approach doesn’t work. For example, if you randomly generate sentences about the integers in some formal theory, then short sentences aren’t more likely to be true than long ones. That leads to a problem if you want to apply Occam’s razor to choosing physical theories, which aren’t mutually exclusive.
Another reason to prefer the simplest theories that fit observations well is that they make life easier for engineers. Kevin Kelly’s Occam efficiency theorem is related, but the idea is really simpler than that.
That only works if you have a countable set of mutually exclusive hypotheses, and exactly one of them is true. Not all worlds are like that. For example, if the “world” is a single real number picked uniformly from [0,1], then it’s hard to say what the hypotheses should be.
If hypotheses aren’t restricted to being mutually exclusive, the approach doesn’t work. For example, if you randomly generate sentences about the integers in some formal theory, then short sentences aren’t more likely to be true than long ones. That leads to a problem if you want to apply Occam’s razor to choosing physical theories, which aren’t mutually exclusive.
Another reason to prefer the simplest theories that fit observations well is that they make life easier for engineers. Kevin Kelly’s Occam efficiency theorem is related, but the idea is really simpler than that.