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RichardKennaway comments on Solomonoff Cartesianism - Less Wrong
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I find it difficult to know what this is saying, but here are some true statements to set beside it.
The set of sentences of Peano arithmetic is recursive, the set of proofs of theorems is recursive, the set of theorems (provable sentences) is recursively enumerable, and the set of sentences that are not theorems is not recursively enumerable.
A utm (universal Turing machine) is not the thing you are talking about under that name. It is a Turing machine that can emulate any Turing machine by being given a specification of it.