Define the “simplicity” of a hypothesis as 1/”complexity”. If you can construct a probability distribution based on the “simplicity” of a hypothesis, then, by the same argument as above, you can prove that you should prefer the hypothesis with less “simplicity”.
There are a finite number of hypotheses less complicated than any given hypothesis, and an infinite number of hypotheses more complicated than any given hypothesis. If there were only a finite number of hypotheses more complicated than any given hypothesis, the theorem would fail.
Define the “simplicity” of a hypothesis as 1/”complexity”. If you can construct a probability distribution based on the “simplicity” of a hypothesis, then, by the same argument as above, you can prove that you should prefer the hypothesis with less “simplicity”.
There are a finite number of hypotheses less complicated than any given hypothesis, and an infinite number of hypotheses more complicated than any given hypothesis. If there were only a finite number of hypotheses more complicated than any given hypothesis, the theorem would fail.