I’m not convinced that we can have real probability distributions over impossible possible worlds. At the very least, a real probability distribution must sum its exhaustive and exclusive possibilities to 1, but in fact it seems to me that the same type of effort that is needed to show that a set of impossible possibilities sums to 1 also changes the degree to which they have been examined, changing their subjective probabilities. It specifically seems to me that pseudo-probability distribution over impossible possible worlds will generally contain non-correctable biases from framing such as overconfidently narrow probability distributions, or conversely conjunction fallacies and subadditivity.
For a concrete example, after estimating the probability that an albino tiger which has previously performed on the Daily Show is sneaking up behind me as I write this in order to deliver a pizza, the probability that I am left with will be sufficiently low that it will be utterly dominated by skeptical hypotheses about either my calculation (even after checking 10 times I may have misplaced a decimal point. I may even be deluding myself about my knowing how to multiply or about the validity of ‘multiplication’) or my world (which may actually be a short ‘joke sim’ of an agent existing only to make some extremely low estimate of some event’s probability and then be proven wrong). These are specifically the sorts of scenarios in which conjunction fallacies are not actually fallacies, and also where non-additivity is valid, framing effects are valid, etc, as given the skeptical nature of the scenario simply the formation of the frame constitutes evidence. To call this sort of uncertainty, which cannot be mathematically manipulated and processed a “probability distribution” ignores the fact that “Probability distribution” is a mathematical concept with specific properties.
I’m not convinced that we can have real probability distributions over impossible possible worlds. At the very least, a real probability distribution must sum its exhaustive and exclusive possibilities to 1, but in fact it seems to me that the same type of effort that is needed to show that a set of impossible possibilities sums to 1 also changes the degree to which they have been examined, changing their subjective probabilities. It specifically seems to me that pseudo-probability distribution over impossible possible worlds will generally contain non-correctable biases from framing such as overconfidently narrow probability distributions, or conversely conjunction fallacies and subadditivity. For a concrete example, after estimating the probability that an albino tiger which has previously performed on the Daily Show is sneaking up behind me as I write this in order to deliver a pizza, the probability that I am left with will be sufficiently low that it will be utterly dominated by skeptical hypotheses about either my calculation (even after checking 10 times I may have misplaced a decimal point. I may even be deluding myself about my knowing how to multiply or about the validity of ‘multiplication’) or my world (which may actually be a short ‘joke sim’ of an agent existing only to make some extremely low estimate of some event’s probability and then be proven wrong). These are specifically the sorts of scenarios in which conjunction fallacies are not actually fallacies, and also where non-additivity is valid, framing effects are valid, etc, as given the skeptical nature of the scenario simply the formation of the frame constitutes evidence. To call this sort of uncertainty, which cannot be mathematically manipulated and processed a “probability distribution” ignores the fact that “Probability distribution” is a mathematical concept with specific properties.