I’m confused. What is the countable set of hypotheses you are considering? My claim is merely that if you have hypotheses H1, H2, …, then p(Hi) > 1/n for at most n-1 values of i. This can be thought of as a weak form of Occam’s razor.
In what sense is “every statement being true” a choice of a countable set of hypotheses?
I think maybe the issue is that we are using hypothesis in a different sense. In my case a hypothesis is a complete model of the world, so it is not possible for multiple hypotheses to be true. You can marginalize out / observe a bunch of variables to talk about a subset of the world, but your hypotheses should still be mutually exclusive.
I’m confused. What is the countable set of hypotheses you are considering? My claim is merely that if you have hypotheses H1, H2, …, then p(Hi) > 1/n for at most n-1 values of i. This can be thought of as a weak form of Occam’s razor.
In what sense is “every statement being true” a choice of a countable set of hypotheses?
I think maybe the issue is that we are using hypothesis in a different sense. In my case a hypothesis is a complete model of the world, so it is not possible for multiple hypotheses to be true. You can marginalize out / observe a bunch of variables to talk about a subset of the world, but your hypotheses should still be mutually exclusive.