The story of how belief is supposed to work is that for each bit of evidence, you consider its likelihood under all the various hypotheses, then multiplying these likelihoods, you find your final result, and it tells you exactly how confident you should be.

You should add, shouldn’t you? Not multiply? Because they’re mutually exclusive and exhaustive probabilities? If you multiply, your probability would change depending on how finely you broke down the hypotheses.

You should add, shouldn’t you? Not multiply? Because they’re mutually exclusive and exhaustive probabilities? If you multiply, your probability would change depending on how finely you broke down the hypotheses.

I think he means multiply once for each piece of evidence, not each hypothesis.