Followup To: Logic as Probability
If we design a robot that acts as if it's uncertain about mathematical statements, that violates some desiderata for probability. But realistic robots cannot prove all theorems; they have to be uncertain about hard math problems.
In the name of practicality, we want a foundation for decision-making that captures what it means to make a good decision, even with limited resources. "Good" means that even though our real-world robot can't make decisions well enough to satisfy Savage's theorem, we want to approximate that ideal, not throw it out. Although I don't have the one best answer to give you, in this post we'll take some steps forward.
Part of the sequence Logical Uncertainty
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i mean that I'm not very sure where that correspondence comes up in Jaynes, but Jaynes is being less explicit than other derivations, which I am more confident about.
Is there any more straightforward way to see the problem? I argued with you about this for a while and I think you convinced me, but it is still a little foggy. If there is a consistency problem, surely this means that we must be vulnerable to Dutch books doesn't it? I.e. they would not seem to be Dutch books to us, with our limited resources, but a superior intelligence would know that they were and would use them to con us out of utility. Do you know of some argument like this?