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Vadim Kosoy added The_idea_of_assigning_probabilities__.tex
about 8 years ago
Commit id: 1a13f0aa2a614420690a0d5c0ab76e1042f1b135
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The idea of assigning probabilities to purely mathematical questions was studied by several authors \cite{gaifman}\cite{hutter}\cite{demski}\cite{christiano}\cite{garrabrant}, mainly in the setting of formal logic. That is, their approach was looking for functions from the set of sentences in some formal logical language to $[0,1]$. However, although there is a strong intuitive case for assigning probabilities to sentences like "7614829 is prime" it is much less clear there is a meaningful assignment of probabilities to sentences like $\varphi_1 := \text{"there are no odd perfect numbers"}$ or (even worse) $\varphi_2 := \text{"there is no cardinality } \kappa \text{ s.t. } \aleph_0 < \kappa < 2^{\aleph_0} \text{."}$. The problem is that a wager on $\varphi_1$ can only become resolved in one direction while a wager on $\varphi_2$ cannot be resolved at all.
