Is it known what is the highest complexity, beyond which the Chaitin's Incompleteness applies? If it is relatively large, it is possible that all hypotheses interesting for humans have complexity lower than that...
In particular I wish to extract from that paper the following very simple (albeit non-constructive) proof of Chaitin's Incompleteness:
Given a (reasonable, sound) formal theory F, we know that F cannot prove all true sentences of the form "Program P never halts" (the reason is that if it could, we could solve the halting problem by searching over all possible proofs in F for the proof of P either halting with a particular run, or never halting, being sure our search will finish in finite time). Consider the shortest program P such that P never hal...
Today's post, The Dilemma: Science or Bayes? was originally published on 13 May 2008. A summary (taken from the LW wiki):
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