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Lumifer comments on A basis for pattern-matching in logical uncertainty - Less Wrong
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Consider a parallel case:
We tell our robot these facts: "3 is 'odd'. 5 is 'odd'. 7 is 'odd'. 11 is 'odd'." ... "Well, robot, what do you think is the probability that 10 is 'odd', given what we've told you?"
The simplest hypothesis is that "odd" is just a synonym for "a natural number".
Yup, that is the simplest hypothesis. Interestingly, the next simplest by many lights are actually the exclusion of a single simple number. Then we get to alternating numbers, and soon after that we get enough space to explode the number of possibilities beyond a modern computer's ability to keep track of the implications, necessitating us to call logical uncertainty methods inside our logical uncertainty methods (yo dawg, I heard you like recursion...).