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**Logical Induction **is the attempt to reason formally when you have uncertainty about logical truths. Modern probability theory makes the assumption that one is logically omniscient, not having ~~uncertain~~uncertainty about whether a given number is prime or whether a certain theorem is true. This seems like a hole in our basic understanding of reasoning. In recent years Scott Garrabrant and other researchers have developed the first formal account of how to reason under logical uncertain (the writeup can be found here).

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Applied to Asymptotic Logical Uncertainty: Concrete Failure of the Solomonoff Approach by Abram Demski 4y ago

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Logical Inductionis~~the attempt to reason formally when you have~~a formal theory of reasoning under logical uncertainty~~about logical truths. Modern probability theory makes the assumption that one is logically omniscient, not having uncertainty about whether a given number is prime or whether a certain theorem is true. This seems like a hole in our basic understanding of reasoning. In recent years~~, developed by Scott Garrabrant and other~~researchers have developed the first formal account of how~~researchers. Rationality is defined through a prediction-market analogy. High-quality beliefs are those which are computationally difficult to~~reason under logical uncertain (the~~win bets against. The writeup can be found here~~)~~.