So, of course, the infinities for which probabilities are ill-defined are just those nasty infinities I was talking about where the expected utility is incalculable.
What we actually want to produce is a probability measure on the set of individual experiences that are copied, or whatever thing has moral value, not on single instantiations of those experiences. We can do so with a limiting sequence of probability measures of the whole thing, but probably not a single measure.
This will probably lead to a situation where SIA turns into SSA.
What bothers me about this line of argument is that, according to UDT, there’s nothing fundamental about probabilities. So why should undefined probabilities be more convincing than undefined expected utilities?
We still need something very much like a probability measure to compute our expected utility function.
Kolomogorov should be what you want. A Kolomogorov probability measure is just a measure where the measure of the whole space is 1. Is there something non-self-evident or non-robust about that? It’s just real analysis.
I think the whole integral can probably contained within real—analytic conceptions. For example, you can use an alternate definition of measurable sets.
I disagree with your interpretation of UDT. UDT says that, when making choices, you should evaluate all consequences of your choices, not just those that are causally connected to whatever object is instantiating your algorithm. However, while probabilities of different experiences are part of our optimization criteria, they do not need to play a role in the theory of optimization in general. I think we should determine more concretely whether these probabilities exist, but their absence from UDT is not very strong evidence against them.
The difference between SIA and SSA is essentially an overall factor for each universe describing its total reality-fluid. Under certain infinite models, there could be real-valued ratios.
The thing that worries me second-most about standard measure theory is infinitesimals. A Kolomogorov measure simply cannot handle a case with a finite measure of agents with finite utility and an infinitesimal measure of agents with an infinite utility.
The thing that worries me most about standard measure theory is my own uncertainty. Until I have time to read more deeply about it, I cannot be sure whether a surprise even bigger than infinitesimals is waiting for me.
So, of course, the infinities for which probabilities are ill-defined are just those nasty infinities I was talking about where the expected utility is incalculable.
What we actually want to produce is a probability measure on the set of individual experiences that are copied, or whatever thing has moral value, not on single instantiations of those experiences. We can do so with a limiting sequence of probability measures of the whole thing, but probably not a single measure.
This will probably lead to a situation where SIA turns into SSA.
What bothers me about this line of argument is that, according to UDT, there’s nothing fundamental about probabilities. So why should undefined probabilities be more convincing than undefined expected utilities?
We still need something very much like a probability measure to compute our expected utility function.
Kolomogorov should be what you want. A Kolomogorov probability measure is just a measure where the measure of the whole space is 1. Is there something non-self-evident or non-robust about that? It’s just real analysis.
I think the whole integral can probably contained within real—analytic conceptions. For example, you can use an alternate definition of measurable sets.
I disagree with your interpretation of UDT. UDT says that, when making choices, you should evaluate all consequences of your choices, not just those that are causally connected to whatever object is instantiating your algorithm. However, while probabilities of different experiences are part of our optimization criteria, they do not need to play a role in the theory of optimization in general. I think we should determine more concretely whether these probabilities exist, but their absence from UDT is not very strong evidence against them.
The difference between SIA and SSA is essentially an overall factor for each universe describing its total reality-fluid. Under certain infinite models, there could be real-valued ratios.
The thing that worries me second-most about standard measure theory is infinitesimals. A Kolomogorov measure simply cannot handle a case with a finite measure of agents with finite utility and an infinitesimal measure of agents with an infinite utility.
The thing that worries me most about standard measure theory is my own uncertainty. Until I have time to read more deeply about it, I cannot be sure whether a surprise even bigger than infinitesimals is waiting for me.