Does it makes sense to call it true or false? Not really; when I try to call it a proposition the response should be “type error; that’s a string that doesn’t parse into a proposition.”
Ah, but what probability do we assign to the statement “‘a xor’ results in a type error because it’s a string that doesn’t parse into a proposition”? 1-epsilon, and we’re done. Remember, the probabilistic model of utility came from somewhere, and has an associated level of evidence and support. It’s not impossible to convince me that it’s wrong.<a>
But does this make me vulnerable to Pascal’s mugging? However low I make epsilon, surely infinity is larger. It does not, because of the difference between inside-model probabilities and outside-model probabilities.
Suppose I am presented with a dilemma. Various different strategies all propose different actions; the alphabetical strategy claims I should pick the first option, the utility-maximizing strategy claims I should pick the option with highest EV, the satisficing strategy claims I should pick any option that’s ‘good enough’, and so on. But the epsilon chance that the utility is in fact infinite is not within the utility-maximizing strategy; it refers to a case where the utility-maximizing strategy’s assumptions are broken, and thus needs to be handled by a different strategy—presumably one that doesn’t immediately choke on infinities!
I understand your argument about breaking the assumptions of the strategy. What does inside model probabilities and outside model probabilities mean? I don’t want to blindly guessing.
Consider the logical proposition “A xor”.
Does it makes sense to call it true or false? Not really; when I try to call it a proposition the response should be “type error; that’s a string that doesn’t parse into a proposition.”
Ah, but what probability do we assign to the statement “‘a xor’ results in a type error because it’s a string that doesn’t parse into a proposition”? 1-epsilon, and we’re done. Remember, the probabilistic model of utility came from somewhere, and has an associated level of evidence and support. It’s not impossible to convince me that it’s wrong.<a>
But does this make me vulnerable to Pascal’s mugging? However low I make epsilon, surely infinity is larger. It does not, because of the difference between inside-model probabilities and outside-model probabilities.
Suppose I am presented with a dilemma. Various different strategies all propose different actions; the alphabetical strategy claims I should pick the first option, the utility-maximizing strategy claims I should pick the option with highest EV, the satisficing strategy claims I should pick any option that’s ‘good enough’, and so on. But the epsilon chance that the utility is in fact infinite is not within the utility-maximizing strategy; it refers to a case where the utility-maximizing strategy’s assumptions are broken, and thus needs to be handled by a different strategy—presumably one that doesn’t immediately choke on infinities!
I understand your argument about breaking the assumptions of the strategy. What does inside model probabilities and outside model probabilities mean? I don’t want to blindly guessing.
See here.