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fool comments on A summary of Savage's foundations for probability and utility. - Less Wrong
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Agreed, the structural component is not normative. But to me, it is the structural part that seems benign.
If we assume the agent lives forever, and there's always some uncertainty, then surely the world is thus and so. If the agent doesn't live forever, then we're into bounded rationality questions, and even transitivity is up in the air.
P6 entails that there are (uncountably) infinitely many events. It is at least compatible with modern physics that the world is fundamentally discrete both spatially and temporally. The visible universe is bounded. So it may be that there are only finitely many possible configurations of the universe. It's a big number sure, but if it's finite, then Savage's theorem is irrelevant. It doesn't tell us anything about what to believe in our world. This is perhaps a silly point, and there's probably a nearby theorem that works for "appropriately large finite worlds", but still. I don't think you can just uncritically say "surely the world is thus and so".
If this is supposed to say something normative about how I should structure my beliefs, then the structural premises should be true of the world I have beliefs about.
But it was a conditional statement. If the universe is discrete and finite, then obviously there are no immortal agents either.
Basically I don't see that aspect of P6 as more problematic than the unbounded resource assumption. And when we question that assumption, we'll be questioning a lot more than P6.